It is a common requirement with personal computers (PCs), particularly with video games played on a PC, that realistic sound effects should be provided, giving an impression of the sound source location in three dimensions. Since memory and processing power are limited resources, it is common to store a library of sound effects in monophonic form, and subject sounds selected from the library to a sound processor, which generates binaural or expanded stereo versions of the monophonic signals. The sound processor incorporates placement filters for creating an impression of sound source location, and typically these filters are selected from a number of filters, each of which is designed to create an impression of sound from a specific direction; see for example US-A-5,052,685.

The present invention is specifically concerned with binaural placement filters, which create binaural signals from a monophonic source. The processing of binaural signals to produce highly realistic three-dimensional sound images is well known, see our International Patent Application No. WO 94/22278 (our ref. PQ12529). Binaural technology is based on recordings made using a so-called "artificial head" microphone system, and the recordings are subsequently processed digitally. The use of the artificial head ensures that the natural three-dimensional sound cues, which the brain uses to determine the position of sound sources in three-dimensional space, are incorporated into the stereo recording. Subsequent signal processing of the binaural signals ensures that transaural crosstalk is cancelled (crosstalk occurs when an audio signal intended for one ear of a listener is also received by the other ear) and that the three-dimensional cues are effective on playback of the material through loudspeakers, such that the brain can interpret the cues correctly. Without the processing the recordings sound tonally incorrect and do not reproduce their three-dimensional attributes through loudspeaker auditioning. For the purposes of the present specification, the term "binaural signals" is intended to mean two-channel or stereophonic signals which include a component representing audio diffraction effects created by an artificial head means which modifies the signals received by microphone means. The artificial head means may be a physical object positioned between a pair of spaced apart microphones, and may be as is common a precise model of a human head and torso, with microphones in the ear structures; alternatively it may be something far less precise, for example a block or sheet of wood positioned between a pair of spaced microphones, which nevertheless creates diffraction signals from the source of sound signals. The artificial head means may comprise an

electrical synthesis circuit or system which creates and applies such a diffraction signal component to stereophonic signals, the stereophonic signals being derived from a pair of spaced apart microphones, or from a single microphone wherein the monophonic signal is processed, e.g. by pan-potting, to synthesise stereophonic signals.

It will be appreciated that filters used in processing of binaural signals are key to the success of a three dimensional sound impression.. The filters represent various combinations of two basic functions, firstly the transfer function (S) between a loudspeaker of a pair of loudspeakers and the ear of a listener closer to such loudspeaker, and secondly a function (A) representing the transmission function from such loudspeaker to the far ear of the listener (closer to the other loudspeaker). These functions S and A are termed head related transfer functions (HRTFs), and such functions have been measured and are widely published - see for example HL Han, J.

Audio Eng. Soc., Jan./Feb. 1994, 42, (1/2), pp.15-36. Of course, precise values of the HRTFs may vary if instead of measurements on a real human head, the HRTF is derived from measurements or calculations based on a model; if the model chosen is simply a block of wood between the microphones then the transfer function will be much simpler than that of a realistic dummy head; for the purposes of this specification, "head related transfer function" is intended to cover all such functions as measured on a real head or measured or calculated from a model of a human head, and any combination of two or more such functions.

The more accurately an electronic filter reproduces an HRTF, in general the better the sound impression created. However, a filter would have to be extremely complex to reproduce all the details of an empirically measured HRTF and it is usually necessary to adopt some form of approximation to the measured version.

WO 95/31881 describes a technique for simplifying an HRTF wherein frequency components of known transfer functions are smoothed over bandwidths which are a function of the width of the ear's critical bands.

When simplifying digital filters, a critical area is the low frequency region, say between DC and 100 Hz, or 200 Hz or more, since this region plays an important part in creating the desired sound impression.

Referring to Figure 1 of the drawings, this shows an HRTF created with a finite impulse response ( FIR) filter having 200 tapping points. An FIR filter is of a well known configuration comprising a chain of delay elements, and tapping points between the delay elements. The signals from such tapping points are multiplied by separate coefficient multipliers, and the resultant is summed and provided as an output signal.

The HRTF transfer function shown in Figure 1 is reasonably true to an empirically measured version. However a 200 order filter is a complex filter for implementation on a PC and shorter filters are required.

It is possible to simplify filters by using an infinite impulse response design (IIR).

Such filters involve delay elements coupled in multiple feed forward and feed back loops. However there are problems associated with IIR filters, in particular they can become unstable and are more sensitive to quantisation of the filter coefficients than FIR.

In addition IIR filters frequently create errors in the low frequency region of 0 to 200 Hz.

Referring to Figure 2 which shows a filter function created with an IIR filter, there is a constant error between DC and up to 1000 Hz, wherein the filter provides a constant gain of approaching 1 decibel, whereas, comparing this with Figure 1, there should be zero gain.

As disclosed in Figure 4 of WO 95/31881, a method for converting a high order FIR to a low order FIR is a windowing technique. In this technique, the response of the filter in the time domain to an impulse input signal is measured or calculated, and the filter is simplified by placing a window of time over the time response so that only the response within a shorter time period determined by the window is taken into account.

However filters created using a windowing technique may still suffer from inaccuracies in the low frequency region. Referring to Figure 3, this shows a 25 order FIR filter designed using a Hanning window.

Summary of the Invention It is an object of the invention to provide a FIR filter representing a desired HRTF which is simple in construction but does not create undue errors in frequency response, in particular in the region between dc and 100 Hz.

The present invention provides a filter implementing a desired HRTF, the filter comprising an FIR filter of a desired order, tapping points of the filter being connected to respective coefficient multipliers and thence to a common summing means, wherein the values of the coefficients for the multipliers are calculated as follows:- (1) providing a time-domain impulse response of a predetermined HRTF and simplifying the HRTF by applying a predetermined window function to the response, (2) computing the transfer function of a simplified filter having the windowed transfer function and comparing the transfer function with the predetermined HRTF in a low frequency region of about 100 Hz to determine an error value between the functions for this region, (3) modifying the response of the predetermined HRTF independence upon the error, and repeating steps (1) and (2); and (4) repeating steps (1), (2) and (3) a predetermined number of times until a desired level of accuracy is achieved.

Description of the Preferred Embodiment A preferred embodiment of the invention will now be described with reference to the accompanying drawings, wherein:- Figure 1 is a graph of a predetermined HRTF approximated by a 200 tap FIR filter; Figure 2 is a graph of the transfer function of a 12th order IIR filter approximating the filter of Figure 1; Figure 3 is a graph of the transfer function of a 25th order FIR filter approximating the filter of Figure 1; Figure 4 is a graph of the transfer function of a 25th order FIR filter approximating the filter of Figure 1, but constructed in accordance with the invention; Figure 5 is a detailed view of the graph of Figure 4 in a low frequency region; Figure 6 is a schematic diagram of a preferred embodiment of the invention; and Figure 7 is a graph of the HRTF of a 90 tap FIR filter in the time domain, with a Hanning window function applied, as a step in the carrying out of the invention.

Preferred Embodiment of the Invention This invention is a new way to overcome the inaccuracy in the low frequency region of a shortened filter compared with that of a high order filter. An iterative algorithm is used that compensates for the low frequency inaccuracy until the desired error criteria is achieved. In the following embodiment a high order filter having say 200 tapping points (or more or less) is used and a shortened or low order FIR filter having 25 tapping points is created but a filter with more or less tapping points could be created.

The algorithm to do this is as follows:- 1) Window the high order FIR filter to the produce a filter of the desired lower order 2) Calculate the magnitude at low frequencies of the low order FIR filter and compare this with magnitude at the same frequencies of a high order filter. This is done by taking the Fast Fourier Transform (FFT) of each filter, zero-padded for better accuracy. The FFT length is 4096 points giving a frequency resolution of approximately 11 Hz at 44.1 kHz. The area of interest is between dc and 100 Hz. So a sum of all the magnitude coefficients of the FFT below 100 Hz for the two filters is computed and an error is calculated. This error is a signed function. If the error is negative, the high order, or long, FIR filter's low frequency response is cut by that amount.

3) Repeat steps 1 and 2 until the low frequency error is acceptable. The level of the acceptable error can be set to any desired value. In our filter designs the error was set to 0.001dB.

The algorithm has the added advantage that it always converges and is always stable.

Referring now to Figure 7, this shows the HRTF of Figure 1 in the time domain. A Hanning window function (this is a well known mathematical function and may be found in e.g. "Introduction to Digital Signal Processing" by J G Proakis and D G Manolakis ISBN 0-02-946253-3) is applied to the time domain functions, and gradually converges to 0 at about 25 milliseconds, so that only values of the response below that time are taken into account.

The magnitude at low frequencies of a 25th order FIR filter (Figure 3) is calculated and compared with the magnitude of the high order filter response of Figure 1. This is done by taking the Fast Fourier Transform (FFT) (a description of FFT may be found in "Introduction to Digital Signal Processing" by J G Proakis and D G Manolakis ISBN 0- <BR> <BR> <BR> 02-946253-3) of each filter, zero-padded for better accuracy. The FFT l length is 4096 points giving a frequency resolution of approximately 11 Hz at 44.1 kHz. The area of interest is between dc and 100 Hz. So a sum of all the magnitude coefficients of the FFT below 100 Hz for each of the two filters is computed and an error is calculated. This error is a signed function. If the error is negative, the long FIR filter's low frequency response is cut by that amount.

Figure 6 shows a preferred embodiment of the invention comprising an input 2, a chain of twenty five one sampling interval delay elements 4 having tapping points T1...T25.

The tapping points are coupled through coefficient multipliers 6 where the signals are multiplied by coefficients A1...A25, the resultant signals being summed at 8 to provide an output on line 10.

The values of the coefficients A1...A25 are as follows Al 1.19328710e+00 A2 1.41424313e-02 A3 -2.54093879e-01 A4 -3.64418450e-01 A5 -2.67181561e-02 A6 4.25012212e-01 A7 2.89676415e-01 A8 -3.11707697e-02 A9 -2.46670114e-01 A 10 7.15748790e-02 All 3.74178117e-02 A 12 3.39381336e-02

A 13 -5.58106533e-02 A 14 -1.35675785e-01 A 15 1.00898088e-01 A 16 2.39355289e-02 A 17 -3.32903574e-02 A 18 -4.24033082e-02 A 19 -2.01112893e-02 A20 2.78780209e-02 A21 1.10371166e-02 A22 -9.33746274e-03 A23 -8.56964531e-03 A24 -1.08391439e-03 A 25 5.77991245e-04 Figure 4 shows the frequency response of this filter. The number of iterations needed to design this particular filter was 5. Figure 5 shows the same filter on a .OdB scale over the range of 0.01 to 0.1 kHz.