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% This script generates a sqrt(j k) pre-equalization filter
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% for Wave Field Synthesis
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% Deutsche Telekom Laboratories
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% ===== parameters ========================================================
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% sampling frequency of filter
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% aliasing frequency of system (= upper frequency limit of equalization filter)
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% lower frequency limit of filter (= frequency when subwoofer is active)
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% number of coefficients for filter
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% ===== variables =========================================================
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f = linspace(0,f_s/2,441*10);
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idx_al=max(find(f<f_al));
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idx_sw=max(find(f<f_sw));
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H = ones(1,length(f));
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% -------------------------------------------------------------------------
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% computation of pre-equalization filter
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% -------------------------------------------------------------------------
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H(1:idx_al) = sqrt(2*pi*f(1:idx_al))./sqrt(2*pi*f_al);
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H(1:idx_sw) = H(idx_sw)*ones(1,idx_sw);
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h = firls(Nfilt,2*f/f_s,H);
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% truncate length to power of 2
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% -------------------------------------------------------------------------
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% plot resulting filter characteristics
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% -------------------------------------------------------------------------
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Hfilt=fftshift(fft(h));
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Hfilt=Hfilt(Nfilt/2+1:end);
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f2 = linspace(0,f_s/2,length(Hfilt));
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plot(f,20*log10(abs(H)));
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plot(f2,20*log10(abs(Hfilt)),'ro-');
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xlabel('frequency -> [Hz]');
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ylabel('magnitude response -> [dB]');
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legend('desired response','filter response','Location','SouthEast');
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axis([0 2*f_al -20 2]);
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% -------------------------------------------------------------------------
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% save filter coefficients
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% -------------------------------------------------------------------------
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fname = sprintf('wfs_prefilter_%d_%d_%d.wav',f_sw,f_al,f_s);
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disp(['Wrote pre-equalization filter into file: ' fname]);
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wavwrite(h,f_s,fname);
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data/matlab_scripts/make_wfs_prefilter.m
