Echo cancellation by deforming sound waves through inverse convolution R. Ay 1 ward DeywrfmzMf o/ D/g 0001, Gauteng, South Africa

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1 Echo cancellation by deforming sound waves through inverse convolution R. Ay 1 ward DeywrfmzMf o/ D/g 0001, Gauteng, South Africa Abstract This study concerns the mathematical modelling of speech related acoustical hearing discomforts in medium to large environments (e.g. auditoriums and concert halls). Discomforts arise from both phase distortion (echo) and perceived frequency transformations (Comb filters) Borwickfl], Ando[3]. These distortions are caused by the physical constraints imposed on sound transmission within large environments. Deconvolution was applied to the measured signals to recover the original sound from the environmentally distorted sound, thus separating it from the transformation system function (Room impulse response). Several samples were used for different positions within the hall. The different methods investigated for the deconvolution process were cross-correlation, cepstmm and adaptive filter techniques, Oppcnlicim[2]. Upon separation the inverse of the system transfer function was determined and used in the latter part of the study to pre-deform the original sound. Only a part of the system response was used. The first ins constructively contribute to the intelligibility of speech and masked towards the end of the impulse response by the background noise at 40 dba, Borwickfl]. The critical part between and 2 sec was then used as the basis of the filter algorithm design. Because of the length of this part of the impulse response as well as the real time processing constraints a FIR filler could not be implemented, Ando[3, Tohyama[4]. Instead thefilterwas designed in the frequency domain. During transmission the environment now acting on the pre-deformcd (filtered) sound renders better quality speech that is easier to understand, effectively removing part of the deformation. Finally the psychoacouslics of the total system were evaluated by a panel of listeners in the auditorium (concert hall) and the system was found to be effective for some targeted areas within the particular hall. The impact of these results for addressing acoustical problems will be discussed. 1 Introduction Looking at the traditional methods of improving the acoustic properties of a room one finds a wide variety of solutions. Some designs are simple while others are rather elaborate but most often these solutions are all expensive,

2 122 Computational Acoustics and Its Environmental Applications Ando[3]. The need for this special treatment of listening rooms, lecture halls or auditoria, lies with the ease of understanding a speaker at such a venue. The first phenomenon is frequency related. Early reflections act as comb filters. The impulse response for the early reflections is given by Ando[3] as With g < I the reflections decrease exponentially. Taking the Fourier transform of equation (1) gives (0 (2) obtained by using the geometric series properties. The effect of (2) can be seen in Fig. 1. Fig.1 Comb Filter Frequency Response The second phenomenon is that of masking. Strong echoes effectively mask the direct sound. Consonants are especially prone to be masked by echoed vowels. Optimum signal to noise ratio for speech intelligibility is 25dB, which is also true for the ratio between the direct sound and the echoes or reverberation, Borwick[l].

3 Computational Acoustics and Its Environmental Applications 123 Taking the above into consideration the objective of the study was to find an inverse model for part of the impulse and pre-deform the signal before transmission. 2 Room impulse response The room impulse response was measured with a Sennheiser microphone on a standard analog to digital converter card for a PC and afterwards imported into MATLAB. The data was measured at 22 khz with 16 bit resolution. The impulse was generated with an electric spark generator from Grozier Technical Systems. The room response x,[n] of a local class room was obtained by taking the average over M=1024 measured responses, Berwick [1]. This gives signal to noise ratio improvement of 30dB (3) as each doubling in the number of measured responses used, give rise to 6 db improvement of signal and only 3 db 'improvement' of the noise. -improvement - 10* logm (3) Similarly the excitation pulse Xj[n] was measured in an anechoic room and averaged over 1024 sample signals and extended to the same length as Xr[n]. The measured responses were extended to double their original length and filled with zeros to ensure that the discrete signals are causal, Oppenheim [2], Using the properties of the cepstrum the measured room response x,[n] was deconvoluted with the aid of the measured impulse x,[n] (4) (5) (6) (7). (5) (6) = log[ A\ (w)] - log[a\ (7) x,[nj Xj[nj DFT[.] TT / \ LOG[ DFT[ ] 'V / LOG[.] log H,(co) ] ~ EXP[.] xv^v 1DFT[.] Cx[n] Fig. 2 Block diagram for cepstrum-deconvolution.

4 124 Computational Acoustics and Its Environmental Applications Using an M-file based on (Fig 2) to implement equations (5), (6) and (7) the new impulse response x%[n] was obtained. Any artifacts caused by the excitation pulse are now effectively removed from the measured room response. The newly obtained room impulse response (Fig 3) was used in the design of the inverse filter. Fig. 3 Room Impulse Response 2 3 Samples (1=1/22050) x10 3 Inverse response and modelling Enclosed spaces are beneficial to speech intelligibility. The reverberation of small rooms contribute to the total energy reaching the ears as the ears and brain integrate sounds for the P* msec. There after distinct echoes can be heard. In large rooms the early echoes and parts reverberation work destructively on the direct sound waves, Borwick[l]. As mentioned in the introduction some of the reflections are much larger than parts of the direct sound waves. The non sounding consonants are masked and speech intelligibility suffers. The critical section is therefore defined as the period after 25 msec until the response is masked at 40 dba by the background noise (Fig 3). The preferred response is obtained by cutting away the room response %a[n] after 25msec and padding the signal with zeros. The preferred response (Fig 4) is used in the design of the inverse filter to remove the effects of the critical section (Fig 3).

5 Computational Acoustics and Its Environmental Applications Fig. 4 Desired Room Impulse Response CL E Samples (1=1/22050) x10 The inverse response z[n] is obtained using the procedure outlined in Fig. 2. Using equation (8) the result can be verified. with (8) Z(co) is the inverse frequency response of the modified room frequency response XRmod(co) and is used as the required inverse filter. The inverse filter obtained is not directly usable. The zeros of the room response become the poles of the inverse response during the above mentioned process, Oppenheim[2] & Tohyama[4]. As some of the zeros fall outside the unit circle the converted poles are also outside the unit circle and cause the inverse response to be unstable and non causal. To be usable the time response has to be shifted samples. This was done by changing the slope of the phase by multiplying the phase with 2%(21028), Phillips [5] and equation (9). >G(co)e (9) This results in a time response with t = 0 in the middle of the samples instead of at the first sample. This response is a non causal time response. The new time response z[n] can be seen in Fig. 5

6 126 Computational Acoustics and Its Environmental Applications Fig. 5 Inverse Filter Impulse Response o.: Samples (1=1/22050) Implementation and results Implementing z[n] as a convolution filter is a bit unpractical as it consists of samples. This amounts to large size memory for any digital signal processor (DSP) system. As floating point arithmetic is needed for the calculations almost 1 Mbytes of ram is needed, 2 x samples x (80 bits / 8), to implement a circular buffer convolution filter. Sampling at 22 khz the filter will have a 4 second delay before the first results appear. As a real time solution this system can not be implemented. As a non causal system it is further not of practical value. Turning to the frequency domain for answers the memory and real time constraints are once more impairing the practical implementation of the filter. It was decided in the end to implement it as an off-line system. Samples of speech were recorded and manipulated off-line. The spoken words used were shorter than 2 sec. This limitation is due to the causality constraint. The speech samples Sa(co) were filtered in the frequency domain using equation (10). (10)

7 Computational Acoustics and Its Environmental Applications 127 SAmod(co) was transformed back to the time domain using the inverse discrete Fourier transform. These 'filtered' sound samples were then played back in the room where the original samples of the room impulse response were measured. The results were not as effective as originally envisaged. The reason for this is the unstable poles of the inverse filter outside the unit circle. Working with the minimum phase alone does not provide an adequate answer either. 5 Conclusion It has been shown that the echoes can be eliminated alhough the effect is localised to a single position at this time. More robust systems would involve exponetial windowing and elimination of the poles outside the unit circle. Although only limited answers could be found, the author is confident that the results obtained are both encouraging and useful. Traditional methods are still better but future work might bring about less expensive and practical solutions. Current research is directed at the further investigation of the all-pass and minimum phase responses of the inverse filter as well as windowing techniques. Another part of the study is concerned with the modelling of the inverse response by finding a simplified pole-zero descriptions for the inverse response. References 1. Borwick, J. (ed). Loudspeaker and Headphone Handbook, Butterworth, London, Boston, Singapore, Sydney, Toronto and Wellington, Oppenheim, A.V. & Schafer R W Discrete-time Signal Processing, Prentise-Hall, Engelwood Cliffs, New Jersey, Ando, Y. Concert Hall Acoustics, Springer-Verlag, Berlin, Heidelberg New York and Tokyo, Tohyama, M, Suzuki, H. & Ando, Y. The Nature and Technology of Acoustic Space, Academic Press, London, San Diego, NewYork, Boston, Sydney, Tokyo and Toronto, Phillips, C.L. & Parr J.M. Signals, Systems and Transforms, Prentice Hall, Englewood Cliffs, New Jersey, 1995.