
Rockbox mail archiveSubject: Re: DSP: low pass filterRe: DSP: low pass filter
From: Jacob <jacob01_at_gmx.net>
Date: Wed, 17 Aug 2005 02:27:53 +0200 Hi, just to add my 5c and just because I spent several hours digging again into digital filter design 2 nights ago, here are the results. I've used floats even in the filter, but changing it to int (32bit) shouldn't be a big issue. You get an approximated 2nd order (12dB/octave) Butterworth lowpass IIR filter with a cutoff frequency (3dB) of 120 Hz by applying the following piece of 'code': { float x, y1 = 0, y2 = 0, y; float alpha_0 = 7.22031e05, beta_1 = 1.97582, beta_2 = 0.976111; while (/* input samples left */) { /* read sample into x */ /* filter */ x = x * alpha_0; y = y1 + x; y1 = y2 + 2 * x  y * beta_1; y2 = x  y * beta_2; /* output is in y */ } } To compute the coefficients: f_a = 44100 f_g = 120 F_g = f_g / f_a norm = cos (pi * F_g) / sin (pi * F_g) /* Coefficients for Butterworth 2. order, continuous world */ a_1 = 1.4142 b_1 = 1.0000 /* discrete coefficients */ alpha_0 = 1 / (1 + a_1 * norm + b_1 * norm * norm) beta_1 = 2 * (1  b_1 * norm * norm) / (1 + a_1 * norm + b_1 * norm * norm) float beta_2 = (1  a_1 * norm + b_1 * norm * norm) / (1 + a_1 * norm + b_1 * norm * norm) If 12dB/octave are not enough, you can cascade several filters but you have to use different coefficients a_1 and b_1 in each of them to get the same cutoff frequency: Given that there are N 2nd order filter (see above), for each stage k (1 <= k <= N) you get the coefficients like this: a_1[k] = 2 * cos (( 2 * k  1) * pi / ( 4 * N )) b_1[k] = 1 E.g. for an 24dB/oct filter (4th order): a_1[1] = 1.84776, b_1[1] = 1 a_1[2] = 0.765367, b_1[2] = 1 alpha_0[1] = 7.19397e05, beta_1[1] = 1.96861, beta_2[1] = 0.968901 alpha_0[2] = 7.2601e05, beta_1[2] = 1.98671, beta_2[2] = 0.987 You might get instabilities with low cutoff frequencies and high N. Even though you are already happy with your solution, I hope someone besides myself will find this at least interesting ;) Jacob On Mon, Aug 15, 2005 at 09:54:00PM +0200, Tomas wrote: > Well... following my calculations and Dave's suggestion I have just used > a 128 samples moving average, and it works great. > > [...] > > [IDC]Dragon wrote: > > >I suggest using an IIR filter instead of FIR. You need way less past > >samples > >for each step. > >[...] _______________________________________________ http://cool.haxx.se/mailman/listinfo/rockbox Received on 20050817 Page template was last modified "Tue Sep 7 00:00:02 2021" The Rockbox Crew  Privacy Policy 