MOKHOV ILYA IGOREVICH (RU)
VASILIEVA ALEKSANDRA SERGEEVNA (RU)
KUSHNIKOV OLEG VADIMOVICH (RU)
MOKHOV ILYA IGOREVICH (RU)
VASILIEVA ALEKSANDRA SERGEEVNA (RU)
| CLAIMS 1. A method for compressing data D(nT) (65) representing a time dependent signal A(t) (45), wherein the time dependent signal A(t) (45) comprises a plurality of time dependent partial signals Aj(t) (with i=l ,2,...,NoS) (46-50), the method comprising: - a step (210) of receiving a plurality of spectra Sj(f) (with i=l,2,...,NoS) (106- 110), wherein each spectrum Sj(f) (with i=l ,2,...,NoS) (106-1 10) uniquely corresponds to one of the time dependent partial signals Aj(t) (with i=l ,2,...,NoS) (46-50), wherein each spectrum Si(f) (with i=l ,2,...,NoS) (106-1 10) comprises a plurality of frequencies fj (with j=l,2,...,ΝοΡ) (1 1 1-1 16) and a plurality of amplitudes ajj (with j=l,2,...,ΝοΡ; with i=l ,2,...,NoS) (121-126) of the plurality of frequencies fj (with j=l,2,...,NoP) (1 1 1-1 16), - for each spectrum Si(f) (with i=l,2,...,NoS) (106-1 10), a step (220) of normalising the plurality of amplitudes ajj (with j=l ,2,...,NoP; with i=l ,2,...,NoS) (121-126) for obtaining a plurality of normalised amplitudes bjj (with j=l,2,...,NoP; with i=l ,2,...,NoS) (141-146), - for each frequency fj (with j= 1 ,2,..., NoP) (1 1 1-1 16), a step (250) of processing the normalised amplitudes (with j= 1 ,2,..., NoP; with i=l,2,...,NoS) (141 -146) of the frequency fj (with j= 1,2,..., NoP) (1 1 1-1 16) based on a distribution of the normalised amplitudes bjj (with j=l,2,...,NoP; with i=l,2,...,NoS) (141-146) of the frequency fj (with j== 1 ,2,..., NoP) (141 -146) with respect to the threshold value (Tv) for determining one or more respective model parameters (MPj) (with j=l,2,...,NoP) for representing the distribution of the normalised amplitudes bjj (with j=l ,2,...,NoP; with i=l,2,...,NoS) (141-146), and - a step (250) of generating a compressed data set (CDS) comprising at least the one or more model parameters (MPj) (with j=l,2,...,NoP) and the frequency fj (with j=l ,2,..., NoP) (111-1 16). 2. The method according to claim 1 , wherein for each partial signal A,(t) (with i=l ,2,...,NoS) (46-50), a time stamp tj (with i=l ,2,...,NoS) (56-60) is generated, wherein the time stamp tj (with i=l,2,...,NoS) (56-60) represents a time instant at which the partial signal Aj(t) (with i=l ,2,...,NoS) (46-50) was acquired. 3. The method according to claim 2, wherein, for each frequency fj (with j=l,2,...,NoP) (111-116), in case every normalised amplitude bj,, (with j= 1,2,..., NoP; with i=l,2,...,NoS) (141-146) of the frequency fj (with j=l,2,...,NoP) (111-116) is less than the threshold value (Tv), - the respective model parameter (MPj) (with j=l,2,...,NoP) determined by the step (250) of processing comprises an average value (AV) of the normalised amplitudes b (with j=l,2,...,NoP; with i=l,2,...,NoS) (141-146) of the frequency fj (with j= 1,2,..., NoP) (111-116), and - the compressed data set (CDS) further comprises the time stamp tj. 4. The method according to claim 2 or 3, wherein, for each frequency fj (with j=l,2,...,NoP) (111-116), in case a difference A-b^-b™'" between extreme values (bjf.bjf) of the normalised amplitudes bjj (with j= 1,2,..., NoP; with i=l,2,...,NoS) 141-146 of the frequency fj (with j= 1,2,..., NoP) (111-116) is less than the threshold value (Tv), - the respective parameter (MPj) (with j= 1,2,..., NoP) determined by the step (250) of processing comprises an average value (AV) of the normalised amplitudes bjj (with j=l,2,...,NoP; with i=l,2,...,NoS) (141-146) of the frequency fj (with j=l,2,...,NoP)(lll-116), and - the compressed data set (CDS) further comprises the time stamp i\. 5. The method according to any of the claims 1 to 4, wherein, for each frequency fj (with j = 1 ,2, ... ,ΝοΡ) ( 111 - 116), in case - at least one of the normalised amplitudes by (with j=l,2,...,NoP; with i=l,2,...,NoS) (141-146) of the frequency fj (with j=l,2,...,NoP) (111-116) is not less than the threshold value (Tv) and - a difference Δ= b^f - bg" between extreme values (bjf.bjf) of the normalised amplitudes bj,j (with j=l,2,...,NoP; with i=l,2,...,NoS) (141-146) of the frequency fj (with j= 1,2,..., NoP) (111-116) is not less than the threshold value (Tv), the step (250) of processing performs an approximation algorithm for modelling the distribution of the normalised amplitudes bj,j (with j=l,2,...,NoP; with i=l,2,...,NoS) (141-146), wherein the one or more model parameters (MPj) (with j= 1,2,..., NoP) are resulting model parameters of the approximation algorithm. 6. The method according to claim 5, wherein, for those frequencies fk, for which in the step (250) of processing the approximation algorithm for modelling the distribution of the normalised amplitudes has been performed, the compressed data set (CDS) further comprises the respective time stamps tk (with i=l,2,...,NoS). 7. The method according to claim 5 or 6, wherein the approximation algorithm is a polynomial fit. 8. The method according to claim 5 or 6, wherein the approximation algorithm is a step function. 9. The method according to claim 5 or 6, wherein the approximation algorithm is an iterative end point fit algorithm. 10. The method according to any of the claims 1 to 9, wherein the compressed data set (CDS) further comprises for each spectrum Si(f) (with i=l,2,...,NoS) (106- 1 10), a sum SFj (with i=l ,2,...,NoS) (131-135) of the plurality of amplitudes aj,j (with j=l ,2,...,NoP; with i=l ,2,...,NoS) (121-126). 1 1. The method according to any of the claims 1 to 10, wherein in the step (250) of processing, the threshold value (Tv) is proportional to: - a reciprocal of a cardinal number (NoP) of the plurality of frequencies fj (with j=l,2,...,NoP) (1 1 1-1 16) and - to a tolerance factor (Tf). 12. The method according to any of the claims 1 to 1 1, further comprising: - after the step (250) of processing, a step (270) of constructing a reconstructed data D'(nT) by processing the compressed data set (CDS), - a step (260) of determining a correlation coefficient (CC) by correlating the data D(nT) (65) and the reconstructed data D'(nT), and, responsive to the correlation coefficient (CC), a step of repeating the step (240) of processing and the step (250) of generating a compressed data set (CDS), wherein in the step () of processing, the threshold value (Tv) is proportional to - a reciprocal of a cardinal number (NoP) of the plurality of frequencies fj (with j=l ,2,...,NoP) (1 1 1-1 16) and - a tolerance factor (Tf). 13. A signal processing device (40), configured to compress data D(nT) (65) according to any of the methods 1 to 1 1 , the signal processing device (40) comprising: - a spectral data receiver module (130) for receiving the plurality of spectra Sj(f) (with i=l ,2,...,NoS) (106-1 10), - an amplitude normaliser module (140) for normalising the plurality of amplitudes a^ (with j=l,2,...,NoP; with i=l,2,...,NoS) (121 -126) for each of the plurality of frequencies f] (with j= 1,2,..., NoP) (1 1 1-1 16) of each of the plurality of spectra Sj(f) (with i=l ,2,...,NoS) (106-1 10) for obtaining the plurality of normalised amplitudes b (withj=l ,2,...,NoP; with i=l ,2,...,NoS) (141-146), - a comparator module (150) for comparing each of the plurality of normalised amplitudes bj (with j=l ,2,...,NoP; with i=l ,2,...,NoS) (141-146) with the threshold value (Tv), - a parameter module (160) for processing the normalised amplitudes b^ (with j=l ,2,...,NoP; with i=l,2,...,NoS) (141-146) of the frequency fj (with j= 1,2,..., NoP) (1 1 1-1 16) based on the distribution of the normalised amplitudes b (with j= 1,2,..., NoP; with i=l,2„..,NoS) (141-146) of each frequency fj (with j= 1,2,..., NoP) (141-146) with respect to the threshold value (Tv) for determining the one or more respective parameters (MPj) (with j= 1,2,..., NoP) for representing the distribution of the normalised amplitudes bjj (with j= 1,2,..., oP; with i=l ,2,...,NoS) (141 -146), and - a memory unit (100) for storing the compressed data set (CDS). 14. The signal processing device (40) according to claim 13, further comprising: - a correlation module (170) for determining the correlation coefficient (CC) between the data D(nT) (65) and the reconstructed data D'(nT). 15. The signal processing device (40) according to claim 13, or claim 14 further comprising: - a spectrum module (105) for receiving each of the time dependent partial signals Aj(t) (with i=l,2,...,NoS) (46-50) for computing the respective spectrum Sj(f) (with i=l,2,...,NoS) (106-1 10). |
REPRESENTING A TIME DEPENDENT SIGNAL
The present invention relates to a method and a signal processing device for compressing data representing a time dependent signal.
Data compression plays a pivotal role in managing a colossal amount of data. For instance, many modern day engineering, scientific, and statistical activities mandate the collection of massive amounts of electronic data for processing and maintaining information. For example, the electronic data can be a representation of a time varying signal. The management of the data is an extremely demanding task, wherein the management can also comprise storage and transmission of the data. Efficient data management is achievable by intelligent data compression techniques whereupon the storage space required for storing the information present in the data and/or the transmission bandwidth required for transmitting the data are greatly reduced.
Currently, when colossal amounts of data are collected, for example in case of a continuous stream of data representing a time varying signal collected during a continuous monitoring exercise performed on a machine, i.e. monitoring vibrations of the machine during its operation, the computation and the storage of the Fourier transform, i.e. spectrum data of the time varying signal, especially in its entirety, necessitates a huge amount of storage space.
The normal methods of compressing the spectrum data involve either using universal lossless compression tools (ZIP) or using memory optimised encoding. However, compression ratios (ratio of the storage space/resources required to store the compressed data to the storage space/resources required to store the actual data) for the aforementioned methods are remarkably low and are inefficient methods of data compression. Herewith, the storage space and data transmission bandwidth are not substantially reduced.
The object of the present invention is to provide an efficient method and a signal processing device for compressing data representing a time dependent signal.
The above object is achieved by a method for compressing data according to claim 1 and a signal processing device according to claim 13.
The underlying object of the invention is to compress data D(nT) representing a time dependent signal A(t). The time dependent signal A(t) comprises a plurality of time dependent partial signals Aj(t). The method of compressing commences with a step, wherein a plurality of spectra Sj(f) is received. Each spectrum Si(f) uniquely corresponds to one of the time dependent partial signals Aj(t) and each spectrum Sj(f) comprises a plurality of frequencies fj and a plurality of amplitudes ay of the plurality of frequencies fj. The amplitudes ay are uniquely assigned to f j and are measures of contributions of fj in Aj(t). In a subsequent step, for each spectrum Sj(f) the plurality of amplitudes ajj are normalised for obtaining a plurality of normalised amplitudes b . In a following step, for each frequency fj, the normalised amplitudes b j j are processed based on a distribution of the normalised amplitudes b with respect to a threshold value (T v ), and one or more respective model parameters (MP,) are determined for representing the distribution of the normalised amplitudes b j j. In a subsequent step, a compressed data set (CDS) is generated. CDS comprises at least the one or more model parameters and the frequency fj. Therefore, the CDS is possible to compress huge amounts of data.
According to an embodiment of the present invention, for each partial signal
Aj(t), a time stamp tj is generated. The time stamp t, represents a time instant at which the partial signal A,(t) was acquired. The time stamps t, are beneficial for identifying the sequence of occurrence of Aj(t), for spectrum wise indexing of the plurality of amplitudes a and the plurality of normalised amplitudes by, and for processing the plurality of normalised amplitudes by for obtaining the CDS.
According to another embodiment of the present invention, for each frequency f j , if every normalised amplitude by is lesser than the threshold value (T v ), then the MP j determined from the step of processing will comprise an average value (AV) of the normalised amplitudes by for f j . Additionally, CDS further comprises the first time stamp tj. Though the contribution of f j in D(nT) is less than a desired value (i.e. the threshold value), i.e. f j is not a significant frequency. However, the contribution of fj can be modelled and maintained by preserving the mean value of fj in D(nT) for a obtaining a faithful representation of D(nT) by the CDS.
According to yet another embodiment of the present invention, for each frequency f j , if every normalised amplitude by is greater than the threshold value (T v ), and if a difference A=b¾ ax - bg n between extreme values ( bj \ bg n ) of the normalised amplitudes by is less than the threshold value (T v ), then the MPj determined from the step of processing will comprise an average value (AV) of the normalised amplitudes bj,j for fj. Additionally, CDS further comprises the first time stamp ti. The contribution of fj in D(nT) is more than a desired value (i.e. the threshold value), thereby making fj a significant frequency. The contribution of f j can be modelled and maintained by preserving the mean value of f j in D(nT) for a obtaining a faithful representation of D(nT) by the CDS.
According to yet another embodiment of the present invention, for each frequency fj, if at least one of the normalised amplitudes bj,j is not less than the threshold value (T v ) and if the difference between the extreme values Δ= b™* - b™" of the normalised amplitudes b j j is not less than the threshold value (T v ), then in the step of processing an approximation algorithm is performed for modelling the distribution of the normalised amplitudes b j ,j of fj. Thus, the MPj determined from the step of processing will comprise one or more model parameters of the approximation algorithm. By this, the approximation algorithm simplifies the modelling complicated distributions. According to a variation of the aforementioned embodiment, CDS also comprises the respective time stamps t k .
According to a variation of the aforementioned embodiment, the approximation algorithm is a polynomial fit, which is a simple method of modelling a distribution.
According to another variation of the aforementioned embodiment, the approximation algorithm is a step function, which increases the speed of modelling a non-linear distribution.
According to a preferred variation of the aforementioned embodiment, the approximation algorithm is an iterative end point fit algorithm, for example a Ramer- Douglas-Peucker algorithm. Thus, a fewer set of points are obtained for defining a distribution containing a large set of points. Thus, very high compression ratios and accuracy of compression are achieved.
According to yet another embodiment of the present invention, CDS comprises for each spectrum Sj(f), a sum SFj of the plurality of amplitudes ajj. This is advantageous because it helps in the reconstruction of aj , because the processing is performed on the normalised amplitudes.
According to yet another embodiment of the present invention, the threshold value is proportional to a reciprocal of a cardinal number (NoP) of the plurality of frequencies fj and also to a tolerance factor (T f ). This renders the threshold variable, and helps in influencing the distribution of the normalised amplitudes b .
According to yet another embodiment of the present invention, the method further comprises a step subsequent to the step of processing, wherein a reconstructed data D'(nT) is constructed by processing CDS. In a subsequent step, a correlation coefficient (CC) is determined between the data D(nT) and the reconstructed data D'(nT). The threshold is varied responsive to the CC, and the aforementioned steps are repeated till a satisfactory CC is obtained. By this, the accuracy of CDS is improved.
A signal processing device configured to compress data D(nT) according to anz of the aforementioned embodiments is hereby disclosed. The signal processing device comprises a spectral data receiver module, an amplitude normaliser module, a comparator module, a parameter module and a memory unit. The spectral data receiver module receives the plurality of spectra Sj(f). The amplitude normaliser module normalises the plurality of amplitudes ay for each of the plurality of frequencies f j of each of the plurality of spectra Sj(f). Thus, a plurality of normalised amplitudes by is obtained. The comparator module compares each of the plurality of normalised amplitudes by with the threshold value (T v ). The parameter module processes the normalised amplitudes by of the frequency fj based on the distribution of the normalised amplitudes by with respect to the threshold value (T v ). Thus, the one or more respective parameters (MPj) for representing the distribution of the normalised amplitudes by are determined. The memory unit stores the compressed data set (CDS).
According to an embodiment of the present invention, the signal processing device further comprises a correlation module. The correlation module determines the correlation coefficient (CC) between the data D(nT) and the reconstructed data D'(nT). By this, the accuracy of CDS for representing the data D(nT) is improved.
According to an embodiment of the present invention, the signal processing device further comprises a spectrum module. The spectrum module receives each of the time dependent partial signals Aj(f) and computes the respective spectrum Sj(f). The spectrum module can be integrated with the aforementioned modules in cascade. By this, the versatility of the signal processing device is improved, as the spectra Sj(f) is readily computed and is available for compressing the data D(nT).
The aforementioned and other embodiments of the invention related to a method and a signal processing device for compressing data representing a time dependent signal will now be addressed with reference to the accompanying drawings of the present invention. The illustrated drawings and the embodiments are intended to illustrate, but not to limit the invention. The accompanying drawings contain the following figures, in which like numbers refer to like parts, throughout the description and drawings.
The figures illustrate in a schematic manner further examples of the embodiments of the invention, in which:
FIG 1 depicts a condition monitoring system comprising a data acquisition module and a signal processing device compressing data representing a time dependent signal,
FIG 2 depicts various modules of the signal processing device referred to in FIG 1 , wherein exploded views of a plurality of spectra, an amplitude array, and a normalised amplitude array schematically illustrate operations of a spectrum module, a spectral data receiver module, an amplitude normaliser module respectively,
FIG 3 depicts an exemplary amplitude array, and an exemplary normalised amplitude array referred to in FIG 2, and
FIG 4 depicts an exemplary manner of constructing a compressed data set for reconstructing data for compressing the data representing the time dependent signal referred to in FIG 1 , and
FIG 5 depicts a flowchart of the method for compressing data representing compressing data representing the time dependent signal.
A condition monitoring system 10 coupled to a motor 20 for monitoring health of the motor 20 is depicted in FIG 1.
The condition monitoring system 10 comprises a data acquisition module 30
(hereinafter referred to as "the DAQ 30") and a signal processing device 40 in accordance with an embodiment of the invention. The DAQ 30 acquires a time dependent signal A(t) 45, which is a continuous signal (characterised by an independent time variable "t") that pertains to vibrations of the motor 20. The DAQ 30 provides data D(nT) 65 to the signal processing device 40. D(nT) 65 is a discrete-time (characterised by an independent variable "nT") representation of A(t) 45, which is subsequently processed for compressing D(nT) 65 for achieving the object of the present invention.
The DAQ 30 comprises a sensor 31 , a signal conditioner 32, and an analog to digital converter ADC 33 (ADC). The sensor 31 acquires A(t) 45 and provides the same to the signal conditioner 32. The signal conditioner 32 conditions A(t) 45 and provides A'(t) to the ADC 33. The ADC 33 digitises A'(t), thereby creating D(nT) 65, which is provided to the signal processing device 40, which effectively represents A(t).
A(t) 45 may be continuously acquired by the DAQ 30 and may be construed as comprising a plurality of time dependent partial signals Aj(t) (with i= 1 ,2,..., NoS) 46- 50. Aj(t) 46-50 can be construed as A(t) 45 acquired during a plurality of individual time intervals Atj (with i=l ,2,...,NoS) 51-55, respectively, or as time domain windowed A(t) 45, wherein window intervals correspond to Atj 51-55. Alternatively, the DAQ 30 may acquire A(t) 45 during At, 51-55 by means of time domain windowing, therewith A(t) 45 may be construed as a sequential collection of Aj(t) 46-50.
Durations of At, 51-55 may be definable by a user or can be fixed or variable depending on the type of A(t) 45, signal processing requirements, features of the DAQ 30 and/or the signal processing device 40, et cetera. The durations can be microseconds, milliseconds, or in seconds. At, 51 -55 are generally contiguous. However, At, 51-55 may be overlapping or separated by certain spans of time, et cetera.
Herein, the term "partial signals" is defined as a portion of A(t) 45 acquired by the DAQ during respective Atj 51 -55.
Herein "NoS" is a dimensionless entity and refers to a cardinal number of Aj(t) 46-50 acquired during Atj 51-55, which in entirety constitute to form A(t) 45. I.e. NoS represents the number of partial signals Aj(t).
A plurality of time stamps tj (with i= 1 ,2,..., NoS) 56-60 are determined from A(t), wherein each time stamp tj 56-60 represents a time of start of the respective partial signal A,(t) 46-50 acquired during the time interval Atj 51-55. For instance, time stamp ti 56 denotes the time of start of the partial signal A^t) 46.
The data D(nT) 65 is a discrete-time representation of A(t) 45. Thus, Aj(t) 46-50 results in a plurality of discrete-time partial signals Dj(nT) (with i=T,2,...,NoS; n=T,2,...,NoP) 66-70 respectively, wherein Dj(nT) 66-70 corresponds to D(nT) 65 present in Atj 51-55. Dj(nT) 66-70 may also be obtained by discrete-time domain windowing of A(t) 45. Therefore, D(nT) 65 comprises discrete-time representations of the plurality of partial signals Aj(t) 51-55, i.e. Dj(nT) 66-70. Furthermore, D(nT) 65 may also be a digital representation of the discrete-time equivalent of A(t).
Herein, "NoP" is a dimensionless entity and refers to a cardinal number of samples contained in each discrete-time partial signal Dj(nT) 66-70. "NoP" is also equal to a cardinal number of frequencies determinable from an NoP-point Discrete Fourier Transform (DFT) performed on Dj(nT) 66-70. The significance of the term "NoP" will be elucidated in the subsequent sections.
"NoP" for Dj(nT) 66-70 may be varied by varying a sampling rate of the ADC 33, i.e. by under sampling or over sampling. The "NoP" may also be modified by zero- padding, or in another alternative aspect, the duration of Atj 51 -55 may be varied to effect a change of "NoP". A variation of "NoP" accordingly varies the cardinal number of frequencies determinable from an NoP-point DFT.
Herein, the time stamps t, 56-60 also represent the time of start for Dj(nT) 66-70 respectively. Therefore, the time stamps t, 56-60 contain information regarding the time of acquisition of the D,(nT) 66-70, i.e. the start time of Atj 51 -55, and are beneficial for compression of D(nT) 65 as well as for reconstruction of D(nT) 65. In an alternate aspect, tj 56-60 can be any instances of time of the respective At, 51 -55, from which the information regarding the time of acquisition of the Aj(nT) 66-70 is computable. In other words, the time stamps tj 56-60 represent a time instant at which the respective partial signal Aj(t) and Dj(nT), respectively, have been acquired.
The signal processing device 40 comprising a processor 90 and a memory unit 100 for compressing D(nT) 65 is depicted in FIG 2. Exemplary NoP = 6 and NoS = 5 is depicted in FIG 2.
The processor 90 comprises a spectrum module 105, a spectral data receiver module 130, an amplitude normaliser module 140, a comparator module 150, a parameter module 160, and a correlation module 170. The aforementioned modules 105, 130, 140, 150, 160, 170 are configured to compress data D(nT).
The spectrum module 105 receives Dj(nT) 66-70 and computes a plurality of spectra S,(f) (with i= 1 ,2,..., NoS) 106-1 10.
The module 105 computes Sj(f) 106-1 10 may be a plurality of NoP-point
(Discrete Fourier Transforms) DFTs. Si(f) 106-1 10 comprises a plurality of frequencies fj (with j= 1 ,2,..., NoP) 1 1 1 -1 16 and a plurality of amplitudes a j, , (with j= 1 ,2,..., NoP; with i=l ,2,...,NoS) 121-126 of the frequencies f j 1 1 1 -1 16. Herein, the computed amplitudes ajj 121-126 are uniquely assigned to f j 1 1 1-1 16 and are measures of contributions of fj 1 1 1 -1 16 in Aj(t) 46-50. This assignment of amplitudes a j j 121-126 and frequencies f j 1 1 1-1 16 is in compliance with the well-known definition of a spectrum of a time dependent signal, i.e. the amplitudes are a measure of the contribution of the assigned frequency to the underlying time dependent signal.
A schematic operation of the module 105 is depicted as an exploded view "105". Herein, for each of Sj(f) 106-1 10, the horizontal axis "f ' represents "frequency" (f j 1 1 1- 1 16), and the vertical axis "A" represents "amplitude", that is the amplitudes (ajj 121- 126) of f j 11 1 - 116 of the underlying time dependent signal .
An exemplary manner for realizing the operation of the module 105 is elucidated herein. For example, Dj(nT) 66-70 are received by the signal processing device 40 and the same are buffered as blocks of data of a particular length in the memory unit 100. Each block of data corresponds to each of Dj(nT) 66-70 acquired during each of Atj 51 - 55. Each block of data is time stamped with a respective t, 56-60 for identifying the start time of the Dj(nT) 66-70. The blocks corresponding to Dj(nT) 66-70 are then retrieved and processed for computing Sj(f) 106-1 10.
Herein, a j, j 121-126 and f j 1 1 1-1 16 of Sj(f) 106-1 10 may be displayed as a two dimensional amplitude array 128 arranged in rows and columns, for example with NoP rows (representing the NoP f j 1 1 1-1 16) and NoS columns (representing the NoS Dj(nT) 66-70).
Each of the S,(f) 106-1 10 is computed from a respective Dj(nT) 66-70. Therefore, "NoS" also stands for "Number of Spectra".
The spectral data receiver module 130 receives the spectra Sj(f) 106-1 10 from the spectrum module 105. The module 130 then arranges a vector of ajj 121-126 and a vector of f j 1 1 1-1 16 present in Sj(f) 106-110. Thus, a vector aj,, 121 -126 is assigned to a respective time stamp tj 56-60.
In the amplitude array 128, each column "i" of the NoS columns is designated with a respective time stamp t, 56-60, which corresponds to the respective Dj(nT) 66- 70. Similarly, each row "j" of the NoP rows is designated with a respective frequency fj 1 1 1-1 16. For example, the first column is designated with time stamp ti 56 and contains all the amplitudes a 121-126 of the frequencies fj 1 1 1-1 16 computed from S](f) 106. Similarly, the first row is designated with fj 1 1 1 and contains the amplitudes ap 121-126 of fi 111 computed from NoS number of spectra Sj(f) 106-1 10.
An exploded view "130" illustrates an example of the amplitude array 128 for five spectra Sj(f) 106-1 10 (NoS=5) and six frequencies fj 111-116 (NoP=6). For example, the column values aij 121 to a 6 j 126 represent the values of the six frequencies fi 111 to f 6 116 determined from Si(f) 106 computed for Di(nT) 66 bearing the time stamp tj 56. The row values a 3 ,i 123 to a 3)5 123 represent the values of the third frequency '¾ 13" determined from Si(f) 106 to S 5 (f) 110 computed respectively for D](nT) 66 to D 5 (nT) 70 bearing the respective time stamps t\ 56 to t 5 60.
Furthermore, for each of Sj(f) 106-110 the module 130 computes an algebraic sum SFj (with i=l to NoS) 135 of the amplitudes a j j 121-126 of the frequencies f j 1 1 1 - 1 16.
For example,
J , J , et cetera.
Thus, SFj 135 is also a vector of length "NoS". Furthermore, each of SFj 135 can uniquely correspond to each of the NoS time stamps tj 56-60. For example, SFi corresponds to ti, SF 3 corresponds to t 3 , et cetera.
The amplitude normaliser module 140 receives the amplitude array 128 from the spectral data receiver module 130. For each of Sj(f) 106-1 10, the amplitudes ajj 121- 126 are normalised by the module 140. Thus, a plurality of normalised amplitudes bjj (with j=l,2,..., NoP; with i=l,2,...,NoS) 141-146 is obtained. Each of by 141-146 is computed in accordance with the following formula:
I.e.
For example,
, et cetera.
Herein, bj,j 141-146 is also arranged into a normalised amplitude array 148 with respect to Sj(f) 106-1 10 bearing the time stamps t, 56-60, respectively. The normalised amplitude array 148 again comprises NoP rows and NoS columns. A schematic operation of the module 140 is depicted as an exploded view "140".
In the aforementioned context, the term "normalisation" is defined as, for each Sj(f) 106-1 10, a process of dividing the individual amplitudes a j, , 121-126 of fj 1 1 1-1 16 by the algebraic sum of amplitudes 121-126. Therefore, by normalisation, relational contributions or percentage contributions of each of f j 1 1 1-1 16 present in each of Aj(t) 46-50 can be measured. Thus, the contribution of a certain frequency f j 1 1 1-116 is assessable and measurable for determining how that particular frequency f j 1 1 1-1 16 may be represented for the compression of D(nT) 65, which will be explained subsequently.
The NoP rows and NoS columns of the amplitude array 128 and the normalised amplitude array 148 merely illustrate and represent the manner in which the received a j j 121-126 of f j 1 1 1-1 16 of each of Si(f) 106-1 10 and the corresponding b j j 141-146 may be arranged for processing the information in a facile manner. These NoP rows and NoS columns may be transposed and the information therein can be represented and processed accordingly without loss of generality.
The aforementioned example (NoP=6 and NoS=5) is merely illustrative, and is not to be construed to be limiting the invention. The NoP and the NoS can be any two positive integers and the magnitudes of NoP and NoS may be immense. For example, for a 256-point FFT computed for 300 spectra, "NoP" is 256, and "NoS" is 300.
Herein, the cardinal number of f j 1 1 1-1 16, i.e. NoP, determinable from Sj(f) 106- 1 10 is equal to the cardinal number of samples, i.e. again NoP, present in each of Dj(nT) 66-70. For example, the cardinal number is "16" for a 16-point DFT, "32" for a 32-point DFT, and so on. However, for computing Sj(f) 106-1 10 from Dj(nT) 66-70 in an efficient manner, i.e. for customizing the number of frequencies fj 1 1 1 -1 16 determinable from each of Sj(f) 106-1 10, Dj(nT) 66-70 may be up-sampled, down- sampled, zero-padded, et cetera, as aforementioned without loss of generality of Dj(nT)
66-70.
Herein, each Sj(f) 106-1 10 comprises the same vector of frequencies f j 1 1 1-1 16, i.e. different Sj(f) 106-110 may only differ in the vector of amplitudes 121-126 computed for different Dj(nT) 66-70. Herein, each frequency f j 1 1 1-1 16 comprises the same vector of time stamps tj 56-60.
The comparator module 150 receives the normalised amplitude array 148. For each spectrum Sj(f) 106-1 10, the module 150 compares the normalised amplitudes b j j 141-146 with a threshold value T v .
T v is proportional to a reciprocal of "NoP", i.e. the cardinal number of frequencies (NoP) of f j 111-116. Herein, a relation between T v and NoP may be indicated as the followin :
By comparing each normalized amplitude b j j 141-146 of each spectrum Sj(f) 106- 1 10 with the threshold value T v , the comparator module 150 generates a distribution of normalized amplitudes b j; j 141-146 of frequency f j with respect to T v .
Thereafter, by processing the normalised amplitude array 148 containing bj,j 141- 146, and the distribution of of bj,, 141-146 with respect to T v in the parameter module 160, it is possible to model the distribution of bj,j 141-146 over Sj(f) 106-1 10.
The parameter module 160 receives the normalised amplitude array 148 containing b j, j 141-146, and the distribution of b j j 141-146 for each frequency fj 1 1 1- 1 16 with respect to T v .
For each frequency f j 111-116, the normalised amplitude bj ; i 141-146 and the distribution of b jj 141-146 with respect to T v , respectively, are processed to obtain one or more model parameters (MP j ) (with j=l to NoP). The model parameters MPj are suitable for modelling the distribution of the normalised amplitudes bjj 141-146. For instance, b, j to bi ,6 141 are processed for obtaining MPi for modelling fi 1 1 1 and b 4j) to b 4j6 144 are processed for obtaining MP 4 for modelling f 4 1 14, et cetera.
For each of fj 1 1 1-1 16, the MP j depends on a trend of distribution of the b j j 141- 146 of fj 1 1 1-1 16 with respect to T v . MP j is computed by modelling the frequencies f j 1 11-116 based on the different trends of the distribution of the respective b 141-146.
For this, three different cases are distinguished:
Case 1) In case the trend of the distribution of the respective b jj 141-146 of a particular frequency fj 1 1 1-1 16 is such that each of b j ,i 141 -146 is less than T v , MP j for representing the normalised amplitudes b j j of that particular frequency f j 1 1 1-1 16 is an average value (AV) of the normalized amplitudes b j 141-146 of the particular frequency f j 111-116 of the spectra Sj(f). The average value (AV) for that particular frequency f j 1 1 1-1 16 is computed by processing the normalised amplitudes by of that particular frequency f j 1 1 1 -1 16 over Sj(f) 106-1 10 as indicated below:
For example, if for f] 1 1 1, if all of b lsl to bi,5 141 are less than T v , then AV for fi 1 1 1 is computed as indicated below:
Case 2) In case the trend of the distribution of the normalised amplitudes bj 141- 146 of frequency f j 1 1 1-1 16 is such that a difference Δ= b "-" * - b™ η between extreme values (i.e. the difference Δ between the maximum value b - 1 * and the minimum value b™" 1 of b jj ) of the normalised amplitudes b j j of that particular frequency fj 1 1 1-1 16 is less than T v , then MP j for representing the normalised amplitudes bjj 141-146 of that particular frequency f j 1 1 1 -1 16 is once again the average value (AV) of the normalised amplitudes b jj 141-146 of the particular frequency fj 1 1 1-1 16 as computed above.
For example, if for f 5 1 15, if b 5j4 is the maximum value b™* and b 5 , 5 is the minimum value b™ 11 , and if the difference Δ between b 5 , 4 and b 5 , 5 is less than T v , then AV for f 1 15 is computed as indicated below:
Case 3) In the remaining cases, if the trend of the distribution of b j j 141-146 of the particular frequency f j 111-116 is different from the trends of the aforementioned 5 distributions in cases 1) and 2), the distribution of the normalised amplitudes b j j 141 - 146 is modelled and represented by an approximation algorithm. Herein, the MP j of that particular frequency fj 1 1 1-1 16 are the resulting model parameters of the approximation algorithm. The approximation algorithm may be one of the following: a linear fit, wherein the resulting MP j defining a linear equation for modelling b jj
10 141 - 146 comprises a slope value, and an axis intercept value;
a quadratic fit, wherein the resulting MP j defining a quadratic equation for modelling b j 141-146 are one or more coefficients representing a variable of the quadratic equation;
a cubic fit, wherein the resulting MPj defining a cubic equation for modelling b j j
I S 141-146 are one or more coefficients representing a variable of the cubic equation;
an n th order polynomial fit, wherein the resulting MP j defining an n th order polynomial equation for modelling b j j 141-146 are one or more coefficients representing a variable of the n th order polynomial equation;
a step function, wherein the resulting MPj defining the step function for 0 modelling b j 141-146 is a cumulative function defined as a sum of elementary step functions; or
an iterative end point fit algorithm, wherein the resulting MP j defining the iterative end point fit algorithm for modelling bjj 141-146 may be obtained from a Ramer-Douglas-Peucker algorithm, et cetera.
5 Thus, depending on the respective distributions of normalized amplitudes bjj 141-
146 for the different frequencies f j 1 1 1-116, model parameters MP j are computed, finally resulting in data which are suitable to be used as a basis for generating a compressed data set CDS for representing the original data D(nT) 65.
The CDS representing the data D(nT) 65 comprises the following:
30 the vector of frequencies f j 1 1 1-1 16, the vector of time stamps t, 56-60,
the algebraic sum SFj 135 of the amplitudes 121-126 of every spectrum Sj(f), which is beneficial for scaling the MPj for each of f j 1 1 1-1 16, because MP j was created using only b j j 141-146, and
the model parameters MPj for representing the trends of distribution of the normalised amplitudes b j j 141-148 of every frequency f j 1 1 1-1 16.
Moreover, for those frequencies fj 1 1 1-1 16 for which the respective model parameter MPj is chosen to be the average value (AV) of the normalised amplitudes b j, j 141-146 (i.e. cases 1) and 2) as described above), additionally the first time stamp ti 56 is assigned to AV.
In general, for all other cases (i.e. cases than cases 1) and 2)) and for all frequencies, respectively, CDS has to contain information whether MP j is an average value (cases 1) and 2)) or has been modeled by an approximation algorithm (case 3)). If MP j for a particular frequency f j 1 1 1-1 16 is based on an approximation algorithm, then the CDS further comprises the following:
information about the type of approximation algorithm (for example, the step function, the iterative end point fit algorithm, et cetera) used for approximating the normalised amplitudes bjj 141-148 of the particular frequency fj 1 11-116, and
the MP j of the approximation algorithm for that particular frequency f j 1 1 1 -1 16 will also contain pairs of one or more amplitude values and respective one or more timestamps t, 56-60 of that particular frequency fj 1 1 1-1 16. Herein, the amplitude values can be one or more normalised amplitudes bj,, 141-146 itself or average of a certain number of normalised amplitudes b 141-146 of that particular frequency fj 1 1 1-1 16.
By processing the CDS, it is possible to substantially reconstruct the data D(nT).
In order to assess the quality of compression before finally storing CDS, a data signal D'(nT) is reconstructed from the compressed data set CDS and compared with the original signal D(nT). For the assessment, the correlation module 170 receives the compressed data set CDS and processes the same for constructing data signal D'(nT) for for the corresponding Atj 51 -55.
The reconstruction of D'(nT) by processing CDS is explained in an exemplary manner with reference to FIG 4. The correlation module 170 determines a correlation co-efficient CC by correlating D'(nT) and D(nT). CC is a dimensionless entity and is merely a qualitative index for representing a similarity between D'(nT) and D(nT).
Based on the determined CC, it may be decided to repeat the compression with other preconditions. For example, if the correlation co-efficient indicates that the similarity of D'(nT) and D(nT) is not sufficient, the threshold value T v would have to be varied. This can result in a varied trend of the distribution of the normalized amplitudes bjj 141-146 of the frequency fj 1 1 1-1 16 and, thus, in new model parameters MPj' for that frequency.
The threshold value T v may be varied to obtain a varied threshold value T v ' by multiplying T v with a tolerance factor T f . Herein, a relation between T v \ NoP and T f may be indicated as the following:
T f may be varied in order to vary T v . In fact, this results in a change of the distribution of bj,j 141-146 with respect to T v . Thereby, this results in changing the MP j for every f j 1 1 1-1 16. For example, if the CC between D'(nT) and D(nT) is between "0" and "0.8", it may be assumed that the quality of the reconstructed signal D'(nT) is poor, and the quality can be improved by lowering the T v , i.e. by reducing T f , thereby selecting different MPj.
Similarly, if CC is "0.8" or more, it can be assumed that the MP j for reconstructing D'(nT) are sufficient. Then the current CDS is considered as the final CDS and it is stored in memory.
T v , T'v and T f are dimensionless entities. T f merely serves to increase or decrease T v . If T f is chosen between "0" and "1", then T v is decreased. Alternatively, if T f is greater than "1", then T v is increased. However, preferably T f should be unequal to "1".
After the variation of the threshold value, the newly defined threshold value T' v is sent to the comparator module 150. There, the threshold value T v which is used for comparison with the normalised amplitudes b j ,, 141-146 is set to be the new threshold value T'v, i.e. T V =T' V .
Thereafter, the same steps as described above for determining the distribution of normalized amplitudes by 141-146 of each spectrum Sj(f) 106-1 10 with respect to the threshold value T v are conducted. I.e. the comparator module 150 again generates a distribution of by 141-146 with respect to T v , wherein T v corresponds to the varied threshold value T' v .
After the determination of the distribution, it is again possible to model the distribution of bjj 141-146 over S j(f) 106- 1 10.
The parameter module 160 receives information regarding the comparison between each of by 141-146 with T v , i.e. information about the aforementioned distribution.
Again, for each frequency fj 1 1 1-1 16, the normalised amplitude by 141-146 and the distribution of by 141-146 with respect to T v , respectively, are processed to obtain one or more model parameters MP j , as described above. MP j is again computed by modelling the frequencies f j 1 1 1-1 16 based on the different trends of the distribution of the respective by 141-146, again considering the aforementioned three different cases 1), 2) and 3).
After calculation of model parameters MP j for each frequency f j 111-116, a new compressed data set CDS is generated, which comprises:
the vector of frequencies f j 1 1 1-1 16,
the vector of time stamps tj 56-60,
the algebraic sum SFj 135 of the amplitudes ay 121-126 of every spectrum Sj(f), which is beneficial for scaling the MPj for each of fj 1 1 1-1 16, because MPj was created using only by 141-146, and
the model parameters MP j for representing the trends of distribution of the normalised amplitudes by 141-148 of every frequency f j 1 1 1-1 16.
Moreover, for those frequencies f j 111-116 for which the respective model parameter MP j is chosen to be the average value (AV) of the normalised amplitudes by 141 -146 (i.e. cases 1) and 2) as described above), additionally the first time stamp ti 56 is assigned to AV.
In general, for all other cases (i.e. cases than cases 1) and 2)) and for all frequencies, respectively, CDS has to contain information whether MPj is an average value (cases 1) and 2)) or has been modeled by an approximation algorithm (case 3)). If MP j for a particular frequency f j 111-1 16 is based on an approximation algorithm, then the CDS further comprises the following:
information about the type of approximation algorithm (for example, the step function, the iterative end point fit algorithm, et cetera) used for approximating the normalised amplitudes bjj 141-148 of the particular frequency fj 1 1 1-1 16, and
the MPj of the approximation algorithm for that particular frequency fj 1 1 1-1 16 will also contain pairs of one or more amplitude values and respective one or more timestamps tj 56-60 of that particular frequency fj 1 1 1 -1 16. Herein, the amplitude values can be one or more normalised amplitudes b j j 141-146 itself or average of a certain number of normalised amplitudes bj,j 141-146 of that particular frequency f j 1 1 1 -1 16.
The frequencies for which the model parameters have been computed using the approximation algorithms are f k and the corresponding time stamps stored in the model parameters of f k are t k .
To assure a sufficient compression quality, as described above, a data signal D'(nT) is again reconstructed from the compressed data set CDS and compared with the original signal D(nT). The correlation module 170 determines the new correlation co-efficient CC by correlating D'(nT) and D(nT).
Based on the determined CC, it may be decided to repeat the compression again with other preconditions. In this case, the aforementioned procedure starting with the variation of the threshold value T v with another tolerance factor T f would be repeated, resulting in a new distribution and new model parameters MP j etc.
Finally, when the CC indicates a sufficient similarity between D'(nT) and D(nT), the respective compressed data set CDS is stored. Since instead of all amplitudes only average values and/or model parameters MP j are stored, an effective compression rate can be achieved.
The spectrum module 105 and the spectral data receiver module 130 may be consolidated to form a single module capable of executing the functions of both the modules 105, 130.
The comparator module 150, the parameter module 160 and the correlation module 180 may be consolidated to form a single module capable of executing the functions of the modules 150, 160, 170.
The memory unit 100 is capable of storing the Dj(nT) 66-70 received from the DAQ 30, interim data obtained during different stages of processing Dj(nT) 66-70, by the aforementioned modules 105, 130, 140, 150, 160, 170, a j j 121-126 and f] 1 1 1-1 16 computed from Sj(f) 106-1 10, et cetera.
The one or more of the aforementioned modules 105, 130, 140, 150, 160, 170 are operably coupled to the processor 90 and are realizable as independent modules or as partly consolidated modules or a wholly consolidated module, wherein the processor 90 is configured accordingly for performing respective functions of the one or more aforementioned modules 105, 130, 140, 150, 160, 170. Additionally, the one or more modules 105, 130, 140, 150, 160, 170, may be interconnected and may be locatable inside or outside the processor 90.
The processor 90 may be a general purpose processor, a microcontroller, a Digital Signal Processor, a Field Programmable Gate Array (FPGA), a Partial Dynamic Reconfigurable FPGA, an Application Specific Integrated Circuit, and a combination thereof.
The sufficient modules for achieving the object of the invention are the module
130, the module 140, the module 150 and the module 160. However, signal processing device of FIG 2 is provided with supplementary modules, i.e. the memory unit 100, the module 105, and the module 170.
An example of the amplitude array 128 and the normalised amplitude array 148, wherein NoP=4 and NoS=10, comprising exemplary values of ajj 121-126 and bj 141- 146 respectively are illustrated in FIG 3. Since NoP is equal to "4", the corresponding T v is "0.25". The columns of the amplitude array 128 and the normalised amplitude array 148 bear the respective time stamps tj 56-60.
Herein, for fj, the amplitude array 128 comprises exemplary amplitude values of [5, 6, 6, 7, 5, 6, 1, 2, 5, 3], for f 2 , the amplitude array 128 comprises exemplary amplitude values of [54, 56, 52, 54, 52, 58, 59, 55, 53, 51], for f 3 , the amplitude array 128 comprises exemplary amplitude values of [10, 20, 30, 10, 20, 30, 0, 20, 30, 30], and for f 4 , the amplitude array 128 comprises exemplary amplitude values of [20, 5, 25, 30, 23, 5, 24, 6, 23, 5] obtained from exemplary ten spectra Si(f) to Sio(f). Correspondingly, SFi is 89, SF 2 is 87, SF 3 is 1 13, SF 4 is 101, SF 5 is 100, SF 6 is 99, SF 7 is 84, SF 8 is 83, SF 9 is 1 1 1, and SF 10 is 89. The each column of the amplitude array 128 is assigned to a respective time stamp tj to tio, generated from the respective Di(nT) to D,o(nT).
Herein, for fi, the normalised amplitude array 148 comprises exemplary normalised amplitude values of [0.06, 0.07, 0.05, 0.07, 0.05, 0.06, 0.01 , 0.02, 0.05, 0.03], for f 2 , the normalised amplitude array 148 comprises exemplary normalised amplitude values of [0.61 , 0.64, 0.46, 0.53, 0.52, 0.59, 0.70, 0.66, 0.48, 0.57], for f 3 , the normalised amplitude array 148 comprises exemplary normalised amplitude values of [0.1 1 , 0.23, 0.27, 0.10, 0.20, 0.30, 0.00, 0.24, 0.27, 0.34], and for f 4 , the normalised amplitude array 148 comprises exemplary normalised amplitude values of [0.22, 0.06, 0.22, 0.30, 0.23, 0.05, 0.29, 0.07, 0.21 , 0.06].
For f] , it may be observed from here that each of the normalised amplitude values of [0.06, 0.07, 0.05, 0.07, 0.05, 0.06, 0.01 , 0.02, 0.05, 0.03] is below T v . Therefore, MP, corresponding to f, is the average value (AV) of [0.06, 0.07, 0.05, 0.07, 0.05, 0.06, 0.01 , 0.02, 0.05, 0.03], which is "0.047" and the first time stamp ti.
For f 2 , it may be observed from here that each of the normalised amplitude values of [0.61, 0.64, 0.46, 0.53, 0.52, 0.59, 0.70, 0.66, 0.48, 0.57] is above T v , as well as the difference between the extreme values ("0.70" and "0.46") is "0.24", which is below T v . Therefore, MP 2 corresponding to f 2 is the average value (AV) of [0.61, 0.64, 0.46, 0.53, 0.52, 0.59, 0.70, 0.66, 0.48, 0.57], which is "0.576" and first time stamp t, .
For f 3 , it may be observed from here that some of the normalised amplitude values of [0.1 1, 0.23, 0.27, 0.10, 0.20, 0.30, 0.00, 0.24, 0.27, 0.34] are above T v , whereas others are below T v . Also, the difference between the extreme values ("0.30" and "0.00") is "0.30", which is above T v . Therefore, MP 3 corresponding to f 3 are obtained from Ramer-Douglas-Peucker algorithm, wherein the MP 3 constitutes [(0.1 1, t,), (0.3, t 6 ), (0, t 7 ), (0.24, t 8 ), (0.34, t 10 )].
For f 4 , it may be observed from here that some of the normalised amplitude values of [0.22, 0.06, 0.22, 0.30, 0.23, 0.05, 0.29, 0.07, 0.21, 0.06] are above T v , whereas others are below T v . Also, the difference between the extreme values ("0.30" and "0.05") is "0.25", which is equal to T v . Therefore, MP 3 corresponding to f 4 are obtained from Ramer-Douglas-Peucker algorithm, wherein the MP 3 constitutes [(0.22, t,), (0.06, t 2 ), (0.3, t 4 ), (0.05, t 6 ), (0.29, t 7 ), (0.07, tg), (0.21 , fc), (0.06, t 10 )].
Therefore the CDS comprises the following:
the vector of frequencies fi to fio, the vector of time stamps ti to t] 0 ,
the algebraic sum SF] to SFjo of the amplitudes of every spectrum Si(f) to Sio(f), i.e., [89, 87, 1 13, 101 , 100,99, 84, 83, 1 1 1, 89], and
the model parameters (MP) as indicated below:
MP, : [(0.047, t,)]
MP 2 : [(0.576, t,)]
MP 3 : [(0.11 , t , (0.3, t 6 ), (0, t 7 ), (0.24, tg), (0.34, t 10 )], and
MP 4 : [(0.22, t , (0.06, t 2 ), (0.3, t 4 ), (0.05, t 6 ), (0.29, t 7 ), (0.07, tg), (0.21 , fc), (0.06, tio)].
Herein, f 3 and f 4 constitute f k , and the time stamps ti, t 6 , t 7 , t 8 and tio constitute the t k for MP 3 and the time stamps t], t 2 , t 4 , t 7 , tg, t 9 and tio constitute the t k for MP 4 .
FIG 4 depicts an exemplary reconstructed amplitude array for reconstructing D'(nT) based on the aforementioned CDS. For each frequency ζ the reconstructed amplitude of fj depends on the type of model parameter MP j .
In the aforementioned case 1) and case 2), if a frequency fj is represented by a corresponding MP j that comprises only the average value of the normalised amplitudes of fj and the first time stamp ti, then each reconstructed amplitude a' j of f j for a time stamp tj in the reconstructed amplitude array will be generated by multiplying the average value of the normalised amplitudes of f j with the corresponding SF,. That is, the reconstructed amplitudes a' j j of f j will be as follows: [AV*SFi, AV*SFi,— , AV*SF NoS-1 , AV*SF NoS ].
In the aforementioned case 3), if a frequency fj is represented by MP j obtained from an approximation algorithm, for example, a Ramer-Douglas-Peucker algorithm, then each reconstructed amplitude a' j ,, of f j may be generated by passing the MP j to an inverse approximation algorithm module, in this case an inverse Ramer-Douglas- Peucker algorithm module for obtaining each of reconstructed amplitude a'j of f j for each of the time stamp tj.
As aforementioned, the CDS is processed for reconstructing a reconstructed normalised amplitude array 180 and subsequently the reconstructed amplitude array 190 of f j . By computing the inverse DFT of each of the columns of the reconstructed amplitude array 190 it is possible to construct D'j(nT), i.e., the reconstructed partial signals. By contiguous and sequential placement of D'j(nT) with respect to the time stamps, D'(nT) is constructed.
FIG 5 depicts a summarizing flowchart of the method for compressing D(nT) 65 representing A(t) 45.
In a step 200, signals Dj(nT) 66-70 with tj 56-60 are received and the respective Sj(f) 106-110 are computed.
In a subsequent step 210, for each of the NoS number of Sj(f) 106-1 10, the NoP number of amplitudes 121-126, each of which correspond to each of fj 111-116, are received and arranged as aforementioned. Each of Sj(f) 106-1 10 is time stamped with the respective tj 56-60. Thus, the amplitude array 128 with NoP rows and NoS columns, wherein each column is assigned to a time-stamp tj 56-60, is created. The amplitude array 128 may be created providing outputs of the module 105 to the module 130. Furthermore, for each of Sj(f) 106-1 10, the corresponding SF, 135 is computed as aforementioned.
In a following step 220, each column of the amplitude array 128 is normalised to obtain the normalised amplitude array 148 as disclosed in the preceding sections. The amplitude array 128 may be provided to the module 140 for obtaining b j ,i 141 -146. For each of Sj(f) 106-110, the respective 121-126 are normalised to obtain b j ,, 141-146.
In a subsequent step 230, each of b j ,, 141-146 of each of Sj(f) 106-1 10 is compared with T v , which is proportional to the reciprocal of "NoP", i.e. the cardinal number of frequencies f j 1 1 1-1 16 of each of Sj(f) 106-1 10. The normalised amplitude array 148 may be provided to the module 150 for comparing each of bjj 141-146 of each of Sj(f) 106-1 10 with T v . Herewith, a distribution of bjj 141 -146 with respect to T v may be obtained and exemplified.
In a following step 240, for each of fj 111-116, the distribution of bjj 141-146 of f j 1 1 1-1 16 over Si(f) 106-1 10 is received for computing the respective MPj for the respective frequency f j 1 1 1-116 as described above.
In a step 250, the compressed data set (CDS) as defined above is generated.
In a step 260, D'(nT) is reconstructed from CDS. In a following step 270, D'(nT) is correlated with D(nT) 65 for obtaining the correlation co-efficient CC. Based on the determined CC as elucidated in the preceding sections, T f may be varied in order to vary the threshold value T v . In case CC indicates that the similarity between D'(nT) and D(nT) is not sufficient, a new threshold value T\ is generated by varying the last threshold value T v . Then, the procedure returns to step 230, wherein each of the normalised amplitudes bjj 141-146 of each of spectrum Sj(f) 106-1 10 is compared with the threshold value T V =T' V . In case CC indicates that the similarity between D'(nT) and D(nT) is sufficient, the procedure continues with step 280.
The correlation co-efficient CC is inversely proportional to the tolerance factor
T f .
In step 280, the current compressed data set CDS is stored or, depending on the application, further processed.
Finally, D(nT) 65 is compressed, i.e. storage space for storing the information (amplitude, frequency and time) contained in D(nT) 65 is greatly reduced by merely storing CDS in the memory unit 100. Subsequently, it is possible to use the same either for reference or for transmission also.
In the aforementioned method for compressing D(nT) 65, the step 200 and the steps 260, 270 are optional steps for achieving the object of the invention.
Though the invention has been described with reference to specific embodiments, this description is not meant to be construed in a limiting sense. Various examples of the disclosed embodiments, as well as alternate embodiments of the invention, will become apparent to persons skilled in the art upon reference to the description of the invention. It is therefore contemplated that such modifications can be made without departing from the embodiments of the present invention as defined.
List of reference signs
10 Condition monitoring system
20 Motor
30 Data acquisition module
31 Sensor
32 Signal conditioner
33 Analog to Digital converter
40 Signal processing device
45 Time dependent signal A(t)
46-50 Plurality of time dependent partial signals Aj(t)
51-55 Plurality of time intervals Atj
56-60 Plurality of time instances tj (time stamps) Date D(nT)
-70 Plurality of discrete time partial signals Dj(nT)
Processor
0 Memory unit
5 Spectrum module
6-110 Plurality of spectra S s (f)
1 -1 16 Plurality of frequencies fj
1-126 Plurality of amplitudes a j, i
8 Amplitude array
0 Spectral data receiver module
1-135 Sum of frequencies SFj
0 Amplitude normaliser module
1 - 146 Plurality of normalised amplitudes b j, ,
8 Normalised amplitude array
0 Comparator module
0 Parameter module
0 Correlation module
0 Reconstructed normalised amplitude array
0 Reconstructed amplitude array
0 Step of receiving Dj(nT) and computing Si(f)
Step of creating the amplitude array
Step of creating the normalised amplitude array
0 Step of comparing the normalised amplitude array with the threshold
Step of processing normalised amplitudes bjj for computing model parameters MP j
Step of generating a compressed data set
0 Step of constructing D'(nT)
0 Step of correlating D'(nT) and D(nT)
0 Step of storing the compressed data set
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