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| author | jcorgan <jcorgan@221aa14e-8319-0410-a670-987f0aec2ac5> | 2006-08-03 04:51:51 +0000 |
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| committer | jcorgan <jcorgan@221aa14e-8319-0410-a670-987f0aec2ac5> | 2006-08-03 04:51:51 +0000 |
| commit | 5d69a524f81f234b3fbc41d49ba18d6f6886baba (patch) | |
| tree | b71312bf7f1e8d10fef0f3ac6f28784065e73e72 /gnuradio-core/src/python/gnuradio/optfir.py | |
Houston, we have a trunk.
git-svn-id: http://gnuradio.org/svn/gnuradio/trunk@3122 221aa14e-8319-0410-a670-987f0aec2ac5
Diffstat (limited to 'gnuradio-core/src/python/gnuradio/optfir.py')
| -rw-r--r-- | gnuradio-core/src/python/gnuradio/optfir.py | 242 |
1 files changed, 242 insertions, 0 deletions
diff --git a/gnuradio-core/src/python/gnuradio/optfir.py b/gnuradio-core/src/python/gnuradio/optfir.py new file mode 100644 index 0000000000..eb3f321bee --- /dev/null +++ b/gnuradio-core/src/python/gnuradio/optfir.py @@ -0,0 +1,242 @@ +# +# Copyright 2004,2005 Free Software Foundation, Inc. +# +# This file is part of GNU Radio +# +# GNU Radio is free software; you can redistribute it and/or modify +# it under the terms of the GNU General Public License as published by +# the Free Software Foundation; either version 2, or (at your option) +# any later version. +# +# GNU Radio is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +# GNU General Public License for more details. +# +# You should have received a copy of the GNU General Public License +# along with GNU Radio; see the file COPYING. If not, write to +# the Free Software Foundation, Inc., 59 Temple Place - Suite 330, +# Boston, MA 02111-1307, USA. +# + +''' +Routines for designing optimal FIR filters. + +For a great intro to how all this stuff works, see section 6.6 of +"Digital Signal Processing: A Practical Approach", Emmanuael C. Ifeachor +and Barrie W. Jervis, Adison-Wesley, 1993. ISBN 0-201-54413-X. +''' + +import math +from gnuradio import gr + +remez = gr.remez + +# ---------------------------------------------------------------- + +def low_pass (gain, Fs, freq1, freq2, passband_ripple_db, stopband_atten_db, + nextra_taps=0): + passband_dev = passband_ripple_to_dev (passband_ripple_db) + stopband_dev = stopband_atten_to_dev (stopband_atten_db) + desired_ampls = (gain, 0) + (n, fo, ao, w) = remezord ([freq1, freq2], desired_ampls, + [passband_dev, stopband_dev], Fs) + taps = gr.remez (n + nextra_taps, fo, ao, w, "bandpass") + return taps + +# FIXME high_passs is broken... +def high_pass (Fs, freq1, freq2, stopband_atten_db, passband_ripple_db, + nextra_taps=0): + """FIXME: broken""" + passband_dev = passband_ripple_to_dev (passband_ripple_db) + stopband_dev = stopband_atten_to_dev (stopband_atten_db) + desired_ampls = (0, 1) + (n, fo, ao, w) = remezord ([freq1, freq2], desired_ampls, + [stopband_dev, passband_dev], Fs) + taps = gr.remez (n + nextra_taps, fo, ao, w, "bandpass") + return taps + +# ---------------------------------------------------------------- + +def stopband_atten_to_dev (atten_db): + """Convert a stopband attenuation in dB to an absolute value""" + return 10**(-atten_db/20) + +def passband_ripple_to_dev (ripple_db): + """Convert passband ripple spec expressed in dB to an absolute value""" + return (10**(ripple_db/20)-1)/(10**(ripple_db/20)+1) + +# ---------------------------------------------------------------- + +def remezord (fcuts, mags, devs, fsamp = 2): + ''' + FIR order estimator (lowpass, highpass, bandpass, mulitiband). + + (n, fo, ao, w) = remezord (f, a, dev) + (n, fo, ao, w) = remezord (f, a, dev, fs) + + (n, fo, ao, w) = remezord (f, a, dev) finds the approximate order, + normalized frequency band edges, frequency band amplitudes, and + weights that meet input specifications f, a, and dev, to use with + the remez command. + + * f is a sequence of frequency band edges (between 0 and Fs/2, where + Fs is the sampling frequency), and a is a sequence specifying the + desired amplitude on the bands defined by f. The length of f is + twice the length of a, minus 2. The desired function is + piecewise constant. + + * dev is a sequence the same size as a that specifies the maximum + allowable deviation or ripples between the frequency response + and the desired amplitude of the output filter, for each band. + + Use remez with the resulting order n, frequency sequence fo, + amplitude response sequence ao, and weights w to design the filter b + which approximately meets the specifications given by remezord + input parameters f, a, and dev: + + b = remez (n, fo, ao, w) + + (n, fo, ao, w) = remezord (f, a, dev, Fs) specifies a sampling frequency Fs. + + Fs defaults to 2 Hz, implying a Nyquist frequency of 1 Hz. You can + therefore specify band edges scaled to a particular applications + sampling frequency. + + In some cases remezord underestimates the order n. If the filter + does not meet the specifications, try a higher order such as n+1 + or n+2. + ''' + # get local copies + fcuts = fcuts[:] + mags = mags[:] + devs = devs[:] + + for i in range (len (fcuts)): + fcuts[i] = float (fcuts[i]) / fsamp + + nf = len (fcuts) + nm = len (mags) + nd = len (devs) + nbands = nm + + if nm != nd: + raise ValueError, "Length of mags and devs must be equal" + + if nf != 2 * (nbands - 1): + raise ValueError, "Length of f must be 2 * len (mags) - 2" + + for i in range (len (mags)): + if mags[i] != 0: # if not stopband, get relative deviation + devs[i] = devs[i] / mags[i] + + # separate the passband and stopband edges + f1 = fcuts[0::2] + f2 = fcuts[1::2] + + n = 0 + min_delta = 2 + for i in range (len (f1)): + if f2[i] - f1[i] < min_delta: + n = i + min_delta = f2[i] - f1[i] + + if nbands == 2: + # lowpass or highpass case (use formula) + l = lporder (f1[n], f2[n], devs[0], devs[1]) + else: + # bandpass or multipass case + # try different lowpasses and take the worst one that + # goes through the BP specs + l = 0 + for i in range (1, nbands-1): + l1 = lporder (f1[i-1], f2[i-1], devs[i], devs[i-1]) + l2 = lporder (f1[i], f2[i], devs[i], devs[i+1]) + l = max (l, l1, l2) + + n = int (math.ceil (l)) - 1 # need order, not length for remez + + # cook up remez compatible result + ff = [0] + fcuts + [1] + for i in range (1, len (ff) - 1): + ff[i] *= 2 + + aa = [] + for a in mags: + aa = aa + [a, a] + + max_dev = max (devs) + wts = [1] * len(devs) + for i in range (len (wts)): + wts[i] = max_dev / devs[i] + + return (n, ff, aa, wts) + +# ---------------------------------------------------------------- + +def lporder (freq1, freq2, delta_p, delta_s): + ''' + FIR lowpass filter length estimator. freq1 and freq2 are + normalized to the sampling frequency. delta_p is the passband + deviation (ripple), delta_s is the stopband deviation (ripple). + + Note, this works for high pass filters too (freq1 > freq2), but + doesnt work well if the transition is near f == 0 or f == fs/2 + + From Herrmann et al (1973), Practical design rules for optimum + finite impulse response filters. Bell System Technical J., 52, 769-99 + ''' + df = abs (freq2 - freq1) + ddp = math.log10 (delta_p) + dds = math.log10 (delta_s) + + a1 = 5.309e-3 + a2 = 7.114e-2 + a3 = -4.761e-1 + a4 = -2.66e-3 + a5 = -5.941e-1 + a6 = -4.278e-1 + + b1 = 11.01217 + b2 = 0.5124401 + + t1 = a1 * ddp * ddp + t2 = a2 * ddp + t3 = a4 * ddp * ddp + t4 = a5 * ddp + + dinf=((t1 + t2 + a3) * dds) + (t3 + t4 + a6) + ff = b1 + b2 * (ddp - dds) + n = dinf / df - ff * df + 1 + return n + + +def bporder (freq1, freq2, delta_p, delta_s): + ''' + FIR bandpass filter length estimator. freq1 and freq2 are + normalized to the sampling frequency. delta_p is the passband + deviation (ripple), delta_s is the stopband deviation (ripple). + + From Mintzer and Liu (1979) + ''' + df = abs (freq2 - freq1) + ddp = math.log10 (delta_p) + dds = math.log10 (delta_s) + + a1 = 0.01201 + a2 = 0.09664 + a3 = -0.51325 + a4 = 0.00203 + a5 = -0.57054 + a6 = -0.44314 + + t1 = a1 * ddp * ddp + t2 = a2 * ddp + t3 = a4 * ddp * ddp + t4 = a5 * ddp + + cinf = dds * (t1 + t2 + a3) + t3 + t4 + a6 + ginf = -14.6 * math.log10 (delta_p / delta_s) - 16.9 + n = cinf / df + ginf * df + 1 + return n + |