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452 lines
15 KiB
C
452 lines
15 KiB
C
/* fix_fft.c - Fixed-point Fast Fourier Transform */
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/*
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fix_fft() perform FFT or inverse FFT
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window() applies a Hanning window to the (time) input
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fix_loud() calculates the loudness of the signal, for
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each freq point. Result is an integer array,
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units are dB (values will be negative).
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iscale() scale an integer value by (numer/denom).
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fix_mpy() perform fixed-point multiplication.
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Sinewave[1024] sinewave normalized to 32767 (= 1.0).
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Loudampl[100] Amplitudes for lopudnesses from 0 to -99 dB.
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Low_pass Low-pass filter, cutoff at sample_freq / 4.
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All data are fixed-point short integers, in which
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-32768 to +32768 represent -1.0 to +1.0. Integer arithmetic
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is used for speed, instead of the more natural floating-point.
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For the forward FFT (time -> freq), fixed scaling is
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performed to prevent arithmetic overflow, and to map a 0dB
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sine/cosine wave (i.e. amplitude = 32767) to two -6dB freq
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coefficients; the one in the lower half is reported as 0dB
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by fix_loud(). The return value is always 0.
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For the inverse FFT (freq -> time), fixed scaling cannot be
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done, as two 0dB coefficients would sum to a peak amplitude of
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64K, overflowing the 32k range of the fixed-point integers.
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Thus, the fix_fft() routine performs variable scaling, and
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returns a value which is the number of bits LEFT by which
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the output must be shifted to get the actual amplitude
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(i.e. if fix_fft() returns 3, each value of fr[] and fi[]
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must be multiplied by 8 (2**3) for proper scaling.
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Clearly, this cannot be done within the fixed-point short
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integers. In practice, if the result is to be used as a
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filter, the scale_shift can usually be ignored, as the
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result will be approximately correctly normalized as is.
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TURBO C, any memory model; uses inline assembly for speed
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and for carefully-scaled arithmetic.
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Written by: Tom Roberts 11/8/89
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Made portable: Malcolm Slaney 12/15/94 malcolm@interval.com
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Timing on a Macintosh PowerBook 180.... (using Symantec C6.0)
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fix_fft (1024 points) 8 ticks
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fft (1024 points - Using SANE) 112 Ticks
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fft (1024 points - Using FPU) 11
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*/
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#define fixed short
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/* FIX_MPY() - fixed-point multiplication macro.
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This macro is a statement, not an expression (uses asm).
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BEWARE: make sure _DX is not clobbered by evaluating (A) or DEST.
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args are all of type fixed.
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Scaling ensures that 32767*32767 = 32767. */
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#define FIX_MPY(DEST,A,B) DEST = ((long)(A) * (long)(B))>>15
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#define N_WAVE 1024 /* dimension of Sinewave[] */
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#define LOG2_N_WAVE 10 /* log2(N_WAVE) */
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#define N_LOUD 100 /* dimension of Loudampl[] */
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extern fixed gst_spectrum_Sinewave[N_WAVE]; /* placed at end of this file for clarity */
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extern fixed gst_spectrum_Loudampl[N_LOUD];
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static int gst_spectrum_db_from_ampl(fixed re, fixed im);
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static fixed gst_spectrum_fix_mpy(fixed a, fixed b);
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/*
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fix_fft() - perform fast Fourier transform.
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if n>0 FFT is done, if n<0 inverse FFT is done
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fr[n],fi[n] are real,imaginary arrays, INPUT AND RESULT.
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size of data = 2**m
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set inverse to 0=dft, 1=idft
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*/
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int gst_spectrum_fix_fft(fixed fr[], fixed fi[], int m, int inverse) {
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int mr, nn, i, j, l, k, istep, n, scale, shift;
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fixed qr, qi, tr, ti, wr, wi, t;
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n = 1 << m;
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if (n > N_WAVE)
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return -1;
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mr = 0;
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nn = n - 1;
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scale = 0;
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/* decimation in time - re-order data */
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for (m = 1; m <= nn; ++m)
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{
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l = n;
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do
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{
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l >>= 1;
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}
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while (mr + l > nn);
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mr = (mr & (l - 1)) + l;
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if (mr <= m)
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continue;
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tr = fr[m];
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fr[m] = fr[mr];
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fr[mr] = tr;
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ti = fi[m];
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fi[m] = fi[mr];
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fi[mr] = ti;
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}
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l = 1;
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k = LOG2_N_WAVE - 1;
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while (l < n)
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{
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if (inverse)
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{
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/* variable scaling, depending upon data */
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shift = 0;
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for (i = 0; i < n; ++i)
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{
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j = fr[i];
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if (j < 0)
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j = -j;
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m = fi[i];
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if (m < 0)
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m = -m;
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if (j > 16383 || m > 16383)
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{
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shift = 1;
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break;
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}
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}
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if (shift)
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++scale;
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}
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else
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{
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/* fixed scaling, for proper normalization -
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there will be log2(n) passes, so this
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results in an overall factor of 1/n,
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distributed to maximize arithmetic accuracy. */
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shift = 1;
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}
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/* it may not be obvious, but the shift will be performed
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on each data point exactly once, during this pass. */
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istep = l << 1;
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for (m = 0; m < l; ++m)
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{
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j = m << k;
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/* 0 <= j < N_WAVE/2 */
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wr = gst_spectrum_Sinewave[j + N_WAVE / 4];
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wi = -gst_spectrum_Sinewave[j];
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if (inverse)
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wi = -wi;
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if (shift)
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{
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wr >>= 1;
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wi >>= 1;
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}
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for (i = m; i < n; i += istep)
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{
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j = i + l;
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tr = gst_spectrum_fix_mpy(wr, fr[j]) -
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gst_spectrum_fix_mpy(wi, fi[j]);
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ti = gst_spectrum_fix_mpy(wr, fi[j]) +
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gst_spectrum_fix_mpy(wi, fr[j]);
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qr = fr[i];
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qi = fi[i];
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if (shift)
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{
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qr >>= 1;
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qi >>= 1;
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}
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fr[j] = qr - tr;
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fi[j] = qi - ti;
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fr[i] = qr + tr;
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fi[i] = qi + ti;
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}
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}
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--k;
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l = istep;
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}
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return scale;
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}
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/* window() - apply a Hanning window */
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void gst_spectrum_window(fixed fr[], int n) {
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int i, j, k;
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j = N_WAVE / n;
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n >>= 1;
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for (i = 0, k = N_WAVE / 4; i < n; ++i, k += j)
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FIX_MPY(fr[i], fr[i], 16384 - (gst_spectrum_Sinewave[k] >> 1));
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n <<= 1;
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for (k -= j; i < n; ++i, k -= j)
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FIX_MPY(fr[i], fr[i], 16384 - (gst_spectrum_Sinewave[k] >> 1));
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}
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/* fix_loud() - compute loudness of freq-vis components.
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n should be ntot/2, where ntot was passed to fix_fft();
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6 dB is added to account for the omitted alias components.
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scale_shift should be the result of fix_fft(), if the time-series
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was obtained from an inverse FFT, 0 otherwise.
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loud[] is the loudness, in dB wrt 32767; will be +10 to -N_LOUD.
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*/
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void gst_spectrum_fix_loud(fixed loud[], fixed fr[], fixed fi[], int n, int scale_shift) {
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int i, max;
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max = 0;
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if (scale_shift > 0)
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max = 10;
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scale_shift = (scale_shift + 1) * 6;
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for (i = 0; i < n; ++i)
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{
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loud[i] = gst_spectrum_db_from_ampl(fr[i], fi[i]) + scale_shift;
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if (loud[i] > max)
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loud[i] = max;
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}
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}
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/* db_from_ampl() - find loudness (in dB) from
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the complex amplitude.
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*/
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int gst_spectrum_db_from_ampl(fixed re, fixed im) {
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static long loud2[N_LOUD] =
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{0};
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long v;
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int i;
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if (loud2[0] == 0)
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{
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loud2[0] = (long) gst_spectrum_Loudampl[0] * (long) gst_spectrum_Loudampl[0];
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for (i = 1; i < N_LOUD; ++i)
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{
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v = (long) gst_spectrum_Loudampl[i] * (long) gst_spectrum_Loudampl[i];
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loud2[i] = v;
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loud2[i - 1] = (loud2[i - 1] + v) / 2;
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}
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}
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v = (long) re *(long) re + (long) im *(long) im;
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for (i = 0; i < N_LOUD; ++i)
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if (loud2[i] <= v)
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break;
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return (-i);
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}
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/*
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fix_mpy() - fixed-point multiplication
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*/
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fixed gst_spectrum_fix_mpy(fixed a, fixed b) {
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FIX_MPY(a, a, b);
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return a;
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}
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/*
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iscale() - scale an integer value by (numer/denom)
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*/
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int gst_spectrum_iscale(int value, int numer, int denom) {
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return (long) value *(long) numer / (long) denom;
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}
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/*
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fix_dot() - dot product of two fixed arrays
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*/
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fixed gst_spectrum_fix_dot(fixed * hpa, fixed * pb, int n) {
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fixed *pa;
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long sum;
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register fixed a, b;
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unsigned int seg, off;
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/* seg = FP_SEG(hpa);
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off = FP_OFF(hpa);
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seg += off>>4;
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off &= 0x000F;
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pa = MK_FP(seg,off);
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*/
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sum = 0L;
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while (n--)
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{
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a = *pa++;
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b = *pb++;
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FIX_MPY(a, a, b);
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sum += a;
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}
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if (sum > 0x7FFF)
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sum = 0x7FFF;
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else if (sum < -0x7FFF)
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sum = -0x7FFF;
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return (fixed) sum;
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}
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#if N_WAVE != 1024
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ERROR:N_WAVE != 1024
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#endif
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fixed gst_spectrum_Sinewave[1024] = {
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0, 201, 402, 603, 804, 1005, 1206, 1406,
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1607, 1808, 2009, 2209, 2410, 2610, 2811, 3011,
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3211, 3411, 3611, 3811, 4011, 4210, 4409, 4608,
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4807, 5006, 5205, 5403, 5601, 5799, 5997, 6195,
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6392, 6589, 6786, 6982, 7179, 7375, 7571, 7766,
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7961, 8156, 8351, 8545, 8739, 8932, 9126, 9319,
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9511, 9703, 9895, 10087, 10278, 10469, 10659, 10849,
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11038, 11227, 11416, 11604, 11792, 11980, 12166, 12353,
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12539, 12724, 12909, 13094, 13278, 13462, 13645, 13827,
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14009, 14191, 14372, 14552, 14732, 14911, 15090, 15268,
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15446, 15623, 15799, 15975, 16150, 16325, 16499, 16672,
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16845, 17017, 17189, 17360, 17530, 17699, 17868, 18036,
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18204, 18371, 18537, 18702, 18867, 19031, 19194, 19357,
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19519, 19680, 19840, 20000, 20159, 20317, 20474, 20631,
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20787, 20942, 21096, 21249, 21402, 21554, 21705, 21855,
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22004, 22153, 22301, 22448, 22594, 22739, 22883, 23027,
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23169, 23311, 23452, 23592, 23731, 23869, 24006, 24143,
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24278, 24413, 24546, 24679, 24811, 24942, 25072, 25201,
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25329, 25456, 25582, 25707, 25831, 25954, 26077, 26198,
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26318, 26437, 26556, 26673, 26789, 26905, 27019, 27132,
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27244, 27355, 27466, 27575, 27683, 27790, 27896, 28001,
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28105, 28208, 28309, 28410, 28510, 28608, 28706, 28802,
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28897, 28992, 29085, 29177, 29268, 29358, 29446, 29534,
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29621, 29706, 29790, 29873, 29955, 30036, 30116, 30195,
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30272, 30349, 30424, 30498, 30571, 30643, 30713, 30783,
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30851, 30918, 30984, 31049,
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31113, 31175, 31236, 31297,
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31356, 31413, 31470, 31525, 31580, 31633, 31684, 31735,
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31785, 31833, 31880, 31926, 31970, 32014, 32056, 32097,
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32137, 32176, 32213, 32249, 32284, 32318, 32350, 32382,
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32412, 32441, 32468, 32495, 32520, 32544, 32567, 32588,
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32609, 32628, 32646, 32662, 32678, 32692, 32705, 32717,
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32727, 32736, 32744, 32751, 32757, 32761, 32764, 32766,
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32767, 32766, 32764, 32761, 32757, 32751, 32744, 32736,
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32727, 32717, 32705, 32692, 32678, 32662, 32646, 32628,
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32609, 32588, 32567, 32544, 32520, 32495, 32468, 32441,
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32412, 32382, 32350, 32318, 32284, 32249, 32213, 32176,
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32137, 32097, 32056, 32014, 31970, 31926, 31880, 31833,
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31785, 31735, 31684, 31633, 31580, 31525, 31470, 31413,
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31356, 31297, 31236, 31175, 31113, 31049, 30984, 30918,
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30851, 30783, 30713, 30643, 30571, 30498, 30424, 30349,
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30272, 30195, 30116, 30036, 29955, 29873, 29790, 29706,
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29621, 29534, 29446, 29358, 29268, 29177, 29085, 28992,
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28897, 28802, 28706, 28608, 28510, 28410, 28309, 28208,
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28105, 28001, 27896, 27790, 27683, 27575, 27466, 27355,
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27244, 27132, 27019, 26905, 26789, 26673, 26556, 26437,
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26318, 26198, 26077, 25954, 25831, 25707, 25582, 25456,
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25329, 25201, 25072, 24942, 24811, 24679, 24546, 24413,
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24278, 24143, 24006, 23869, 23731, 23592, 23452, 23311,
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23169, 23027, 22883, 22739, 22594, 22448, 22301, 22153,
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22004, 21855, 21705, 21554, 21402, 21249, 21096, 20942,
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20787, 20631, 20474, 20317, 20159, 20000, 19840, 19680,
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19519, 19357, 19194, 19031, 18867, 18702, 18537, 18371,
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18204, 18036, 17868, 17699, 17530, 17360, 17189, 17017,
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16845, 16672, 16499, 16325, 16150, 15975, 15799, 15623,
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15446, 15268, 15090, 14911, 14732, 14552, 14372, 14191,
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14009, 13827, 13645, 13462, 13278, 13094, 12909, 12724,
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12539, 12353, 12166, 11980, 11792, 11604, 11416, 11227,
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11038, 10849, 10659, 10469, 10278, 10087, 9895, 9703,
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9511, 9319, 9126, 8932, 8739, 8545, 8351, 8156,
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7961, 7766, 7571, 7375, 7179, 6982, 6786, 6589,
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6392, 6195, 5997, 5799, 5601, 5403, 5205, 5006,
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4807, 4608, 4409, 4210, 4011, 3811, 3611, 3411,
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3211, 3011, 2811, 2610, 2410, 2209, 2009, 1808,
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1607, 1406, 1206, 1005, 804, 603, 402, 201,
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0, -201, -402, -603, -804, -1005, -1206, -1406,
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-1607, -1808, -2009, -2209, -2410, -2610, -2811, -3011,
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-3211, -3411, -3611, -3811, -4011, -4210, -4409, -4608,
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-4807, -5006, -5205, -5403, -5601, -5799, -5997, -6195,
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-6392, -6589, -6786, -6982, -7179, -7375, -7571, -7766,
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-7961, -8156, -8351, -8545, -8739, -8932, -9126, -9319,
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-9511, -9703, -9895, -10087, -10278, -10469, -10659, -10849,
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-11038, -11227, -11416, -11604, -11792, -11980, -12166, -12353,
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-12539, -12724, -12909, -13094, -13278, -13462, -13645, -13827,
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-14009, -14191, -14372, -14552, -14732, -14911, -15090, -15268,
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-15446, -15623, -15799, -15975, -16150, -16325, -16499, -16672,
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-16845, -17017, -17189, -17360, -17530, -17699, -17868, -18036,
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-18204, -18371, -18537, -18702, -18867, -19031, -19194, -19357,
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-19519, -19680, -19840, -20000, -20159, -20317, -20474, -20631,
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-20787, -20942, -21096, -21249, -21402, -21554, -21705, -21855,
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-22004, -22153, -22301, -22448, -22594, -22739, -22883, -23027,
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-23169, -23311, -23452, -23592, -23731, -23869, -24006, -24143,
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-24278, -24413, -24546, -24679, -24811, -24942, -25072, -25201,
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-25329, -25456, -25582, -25707, -25831, -25954, -26077, -26198,
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-26318, -26437, -26556, -26673, -26789, -26905, -27019, -27132,
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-27244, -27355, -27466, -27575, -27683, -27790, -27896, -28001,
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-28105, -28208, -28309, -28410, -28510, -28608, -28706, -28802,
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-28897, -28992, -29085, -29177, -29268, -29358, -29446, -29534,
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-29621, -29706, -29790, -29873, -29955, -30036, -30116, -30195,
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-30272, -30349, -30424, -30498, -30571, -30643, -30713, -30783,
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-30851, -30918, -30984, -31049, -31113, -31175, -31236, -31297,
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-31356, -31413, -31470, -31525, -31580, -31633, -31684, -31735,
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-31785, -31833, -31880, -31926, -31970, -32014, -32056, -32097,
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-32137, -32176, -32213, -32249, -32284, -32318, -32350, -32382,
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-32412, -32441, -32468, -32495, -32520, -32544, -32567, -32588,
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-32609, -32628, -32646, -32662, -32678, -32692, -32705, -32717,
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-32727, -32736, -32744, -32751, -32757, -32761, -32764, -32766,
|
|
-32767, -32766, -32764, -32761, -32757, -32751, -32744, -32736,
|
|
-32727, -32717, -32705, -32692, -32678, -32662, -32646, -32628,
|
|
-32609, -32588, -32567, -32544, -32520, -32495, -32468, -32441,
|
|
-32412, -32382, -32350, -32318, -32284, -32249, -32213, -32176,
|
|
-32137, -32097, -32056, -32014, -31970, -31926, -31880, -31833,
|
|
-31785, -31735, -31684, -31633, -31580, -31525, -31470, -31413,
|
|
-31356, -31297, -31236, -31175, -31113, -31049, -30984, -30918,
|
|
-30851, -30783, -30713, -30643, -30571, -30498, -30424, -30349,
|
|
-30272, -30195, -30116, -30036, -29955, -29873, -29790, -29706,
|
|
-29621, -29534, -29446, -29358, -29268, -29177, -29085, -28992,
|
|
-28897, -28802, -28706, -28608, -28510, -28410, -28309, -28208,
|
|
-28105, -28001, -27896, -27790, -27683, -27575, -27466, -27355,
|
|
-27244, -27132, -27019, -26905, -26789, -26673, -26556, -26437,
|
|
-26318, -26198, -26077, -25954, -25831, -25707, -25582, -25456,
|
|
-25329, -25201, -25072, -24942, -24811, -24679, -24546, -24413,
|
|
-24278, -24143, -24006, -23869, -23731, -23592, -23452, -23311,
|
|
-23169, -23027, -22883, -22739, -22594, -22448, -22301, -22153,
|
|
-22004, -21855, -21705, -21554, -21402, -21249, -21096, -20942,
|
|
-20787, -20631, -20474, -20317, -20159, -20000, -19840, -19680,
|
|
-19519, -19357, -19194, -19031, -18867, -18702, -18537, -18371,
|
|
-18204, -18036, -17868, -17699, -17530, -17360, -17189, -17017,
|
|
-16845, -16672, -16499, -16325, -16150, -15975, -15799, -15623,
|
|
-15446, -15268, -15090, -14911, -14732, -14552, -14372, -14191,
|
|
-14009, -13827, -13645, -13462, -13278, -13094, -12909, -12724,
|
|
-12539, -12353, -12166, -11980, -11792, -11604, -11416, -11227,
|
|
-11038, -10849, -10659, -10469, -10278, -10087, -9895, -9703,
|
|
-9511, -9319, -9126, -8932, -8739, -8545, -8351, -8156,
|
|
-7961, -7766, -7571, -7375, -7179, -6982, -6786, -6589,
|
|
-6392, -6195, -5997, -5799, -5601, -5403, -5205, -5006,
|
|
-4807, -4608, -4409, -4210, -4011, -3811, -3611, -3411,
|
|
-3211, -3011, -2811, -2610, -2410, -2209, -2009, -1808,
|
|
-1607, -1406, -1206, -1005, -804, -603, -402, -201,
|
|
};
|
|
|
|
#if N_LOUD != 100
|
|
ERROR:N_LOUD != 100
|
|
#endif
|
|
fixed gst_spectrum_Loudampl[100] = {
|
|
32767, 29203, 26027, 23197, 20674, 18426, 16422, 14636,
|
|
13044, 11626, 10361, 9234, 8230, 7335, 6537, 5826,
|
|
5193, 4628, 4125, 3676, 3276, 2920, 2602, 2319,
|
|
2067, 1842, 1642, 1463, 1304, 1162, 1036, 923,
|
|
823, 733, 653, 582, 519, 462, 412, 367,
|
|
327, 292, 260, 231, 206, 184, 164, 146,
|
|
130, 116, 103, 92, 82, 73, 65, 58,
|
|
51, 46, 41, 36, 32, 29, 26, 23,
|
|
20, 18, 16, 14, 13, 11, 10, 9,
|
|
8, 7, 6, 5, 5, 4, 4, 3,
|
|
3, 2, 2, 2, 2, 1, 1, 1,
|
|
1, 1, 1, 0, 0, 0, 0, 0,
|
|
0, 0, 0, 0,
|
|
};
|