diff options
| author | Marc Lichtman <mlichtman@perspectalabs.com> | 2018-10-22 17:20:00 -0400 |
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| committer | Marc Lichtman <mlichtman@perspectalabs.com> | 2018-10-22 17:20:00 -0400 |
| commit | 474303b00b436e1359e83b1adec55c326d337925 (patch) | |
| tree | a4aa06ad8c4d028801a4d816d4a626b901b65408 /gr-analog/python | |
| parent | 6c7206817e68e6dda26f1249709d9b2c5f7d9f8e (diff) | |
docs- moved documentation inside docstring
Diffstat (limited to 'gr-analog/python')
| -rw-r--r-- | gr-analog/python/analog/fm_emph.py | 375 |
1 files changed, 184 insertions, 191 deletions
diff --git a/gr-analog/python/analog/fm_emph.py b/gr-analog/python/analog/fm_emph.py index 02bdd576ee..106457c07f 100644 --- a/gr-analog/python/analog/fm_emph.py +++ b/gr-analog/python/analog/fm_emph.py @@ -27,91 +27,87 @@ from gnuradio import gr, filter import math import cmath -# -# An analog deemphasis filter: -# -# R -# o------/\/\/\/---+----o -# | -# = C -# | -# --- -# -# Has this transfer function: -# -# 1 1 -# ---- --- -# RC tau -# H(s) = ---------- = ---------- -# 1 1 -# s + ---- s + --- -# RC tau -# -# And has its -3 dB response, due to the pole, at -# -# |H(j w_c)|^2 = 1/2 => s = j w_c = j (1/(RC)) -# -# Historically, this corner frequency of analog audio deemphasis filters -# been specified by the RC time constant used, called tau. -# So w_c = 1/tau. -# -# FWIW, for standard tau values, some standard analog components would be: -# tau = 75 us = (50K)(1.5 nF) = (50 ohms)(1.5 uF) -# tau = 50 us = (50K)(1.0 nF) = (50 ohms)(1.0 uF) -# -# In specifying tau for this digital deemphasis filter, tau specifies -# the *digital* corner frequency, w_c, desired. -# -# The digital deemphasis filter design below, uses the -# "bilinear transformation" method of designing digital filters: -# -# 1. Convert digital specifications into the analog domain, by prewarping -# digital frequency specifications into analog frequencies. -# -# w_a = (2/T)tan(wT/2) -# -# 2. Use an analog filter design technique to design the filter. -# -# 3. Use the bilinear transformation to convert the analog filter design to a -# digital filter design. -# -# H(z) = H(s)| -# s = (2/T)(1-z^-1)/(1+z^-1) -# -# -# w_ca 1 1 - (-1) z^-1 -# H(z) = ---- * ----------- * ----------------------- -# 2 fs -w_ca -w_ca -# 1 - ----- 1 + ----- -# 2 fs 2 fs -# 1 - ----------- z^-1 -# -w_ca -# 1 - ----- -# 2 fs -# -# We use this design technique, because it is an easy way to obtain a filter -# design with the -6 dB/octave roll-off required of the deemphasis filter. -# -# Jackson, Leland B., _Digital_Filters_and_Signal_Processing_Second_Edition_, -# Kluwer Academic Publishers, 1989, pp 201-212 -# -# Orfanidis, Sophocles J., _Introduction_to_Signal_Processing_, Prentice Hall, -# 1996, pp 573-583 -# - class fm_deemph(gr.hier_block2): """ - FM Deemphasis IIR filter. + FM Deemphasis IIR filter + + Args: + fs: sampling frequency in Hz (float) + tau: Time constant in seconds (75us in US, 50us in EUR) (float) + + An analog deemphasis filter: + + R + o------/\/\/\/---+----o + | + = C + | + --- + + Has this transfer function: + + 1 1 + ---- --- + RC tau + H(s) = ---------- = ---------- + 1 1 + s + ---- s + --- + RC tau + + And has its -3 dB response, due to the pole, at + + |H(j w_c)|^2 = 1/2 => s = j w_c = j (1/(RC)) + + Historically, this corner frequency of analog audio deemphasis filters + been specified by the RC time constant used, called tau. + So w_c = 1/tau. + + FWIW, for standard tau values, some standard analog components would be: + tau = 75 us = (50K)(1.5 nF) = (50 ohms)(1.5 uF) + tau = 50 us = (50K)(1.0 nF) = (50 ohms)(1.0 uF) + + In specifying tau for this digital deemphasis filter, tau specifies + the *digital* corner frequency, w_c, desired. + + The digital deemphasis filter design below, uses the + "bilinear transformation" method of designing digital filters: + + 1. Convert digital specifications into the analog domain, by prewarping + digital frequency specifications into analog frequencies. + + w_a = (2/T)tan(wT/2) + + 2. Use an analog filter design technique to design the filter. + + 3. Use the bilinear transformation to convert the analog filter design to a + digital filter design. + + H(z) = H(s)| + s = (2/T)(1-z^-1)/(1+z^-1) + + + w_ca 1 1 - (-1) z^-1 + H(z) = ---- * ----------- * ----------------------- + 2 fs -w_ca -w_ca + 1 - ----- 1 + ----- + 2 fs 2 fs + 1 - ----------- z^-1 + -w_ca + 1 - ----- + 2 fs + + We use this design technique, because it is an easy way to obtain a filter + design with the -6 dB/octave roll-off required of the deemphasis filter. + + Jackson, Leland B., _Digital_Filters_and_Signal_Processing_Second_Edition_, + Kluwer Academic Publishers, 1989, pp 201-212 + + Orfanidis, Sophocles J., _Introduction_to_Signal_Processing_, Prentice Hall, + 1996, pp 573-583 """ def __init__(self, fs, tau=75e-6): - """ - - Args: - fs: sampling frequency in Hz (float) - tau: Time constant in seconds (75us in US, 50us in EUR) (float) - """ gr.hier_block2.__init__(self, "fm_deemph", gr.io_signature(1, 1, gr.sizeof_float), # Input signature gr.io_signature(1, 1, gr.sizeof_float)) # Output signature @@ -144,125 +140,122 @@ class fm_deemph(gr.hier_block2): deemph = filter.iir_filter_ffd(btaps, ataps, False) self.connect(self, deemph, self) -# -# An analog preemphasis filter, that flattens out again at the high end: -# -# C -# +-----||------+ -# | | -# o------+ +-----+--------o -# | R1 | | -# +----/\/\/\/--+ \ - # / -# \ R2 -# / -# \ - # | -# o--------------------------+--------o -# -# (This fine ASCII rendition is based on Figure 5-15 -# in "Digital and Analog Communication Systems", Leon W. Couch II) -# -# Has this transfer function: -# -# 1 -# s + --- -# R1C -# H(s) = ------------------ -# 1 R1 -# s + --- (1 + --) -# R1C R2 -# -# -# It has a corner due to the numerator, where the rise starts, at -# -# |Hn(j w_cl)|^2 = 2*|Hn(0)|^2 => s = j w_cl = j (1/(R1C)) -# -# It has a corner due to the denominator, where it levels off again, at -# -# |Hn(j w_ch)|^2 = 1/2*|Hd(0)|^2 => s = j w_ch = j (1/(R1C) * (1 + R1/R2)) -# -# Historically, the corner frequency of analog audio preemphasis filters -# been specified by the R1C time constant used, called tau. -# -# So -# w_cl = 1/tau = 1/R1C; f_cl = 1/(2*pi*tau) = 1/(2*pi*R1*C) -# w_ch = 1/tau2 = (1+R1/R2)/R1C; f_ch = 1/(2*pi*tau2) = (1+R1/R2)/(2*pi*R1*C) -# -# and note f_ch = f_cl * (1 + R1/R2). -# -# For broadcast FM audio, tau is 75us in the United States and 50us in Europe. -# f_ch should be higher than our digital audio bandwidth. -# -# The Bode plot looks like this: -# -# -# /---------------- -# / -# / <-- slope = 20dB/decade -# / -# -------------/ -# f_cl f_ch -# -# In specifying tau for this digital preemphasis filter, tau specifies -# the *digital* corner frequency, w_cl, desired. -# -# The digital preemphasis filter design below, uses the -# "bilinear transformation" method of designing digital filters: -# -# 1. Convert digital specifications into the analog domain, by prewarping -# digital frequency specifications into analog frequencies. -# -# w_a = (2/T)tan(wT/2) -# -# 2. Use an analog filter design technique to design the filter. -# -# 3. Use the bilinear transformation to convert the analog filter design to a -# digital filter design. -# -# H(z) = H(s)| -# s = (2/T)(1-z^-1)/(1+z^-1) -# -# -# -w_cla -# 1 + ------ -# 2 fs -# 1 - ------------ z^-1 -# -w_cla -w_cla -# 1 - ------ 1 - ------ -# 2 fs 2 fs -# H(z) = ------------ * ----------------------- -# -w_cha -w_cha -# 1 - ------ 1 + ------ -# 2 fs 2 fs -# 1 - ------------ z^-1 -# -w_cha -# 1 - ------ -# 2 fs -# -# We use this design technique, because it is an easy way to obtain a filter -# design with the 6 dB/octave rise required of the premphasis filter. -# -# Jackson, Leland B., _Digital_Filters_and_Signal_Processing_Second_Edition_, -# Kluwer Academic Publishers, 1989, pp 201-212 -# -# Orfanidis, Sophocles J., _Introduction_to_Signal_Processing_, Prentice Hall, -# 1996, pp 573-583 -# class fm_preemph(gr.hier_block2): """ FM Preemphasis IIR filter. + + Args: + fs: sampling frequency in Hz (float) + tau: Time constant in seconds (75us in US, 50us in EUR) (float) + fh: High frequency at which to flatten out (< 0 means default of 0.925*fs/2.0) (float) + + An analog preemphasis filter, that flattens out again at the high end: + + C + +-----||------+ + | | + o------+ +-----+--------o + | R1 | | + +----/\/\/\/--+ \ + / + \ R2 + / + \ + | + o--------------------------+--------o + + (This fine ASCII rendition is based on Figure 5-15 + in "Digital and Analog Communication Systems", Leon W. Couch II) + + Has this transfer function: + + 1 + s + --- + R1C + H(s) = ------------------ + 1 R1 + s + --- (1 + --) + R1C R2 + + + It has a corner due to the numerator, where the rise starts, at + + |Hn(j w_cl)|^2 = 2*|Hn(0)|^2 => s = j w_cl = j (1/(R1C)) + + It has a corner due to the denominator, where it levels off again, at + + |Hn(j w_ch)|^2 = 1/2*|Hd(0)|^2 => s = j w_ch = j (1/(R1C) * (1 + R1/R2)) + + Historically, the corner frequency of analog audio preemphasis filters + been specified by the R1C time constant used, called tau. + + So + w_cl = 1/tau = 1/R1C; f_cl = 1/(2*pi*tau) = 1/(2*pi*R1*C) + w_ch = 1/tau2 = (1+R1/R2)/R1C; f_ch = 1/(2*pi*tau2) = (1+R1/R2)/(2*pi*R1*C) + + and note f_ch = f_cl * (1 + R1/R2). + + For broadcast FM audio, tau is 75us in the United States and 50us in Europe. + f_ch should be higher than our digital audio bandwidth. + + The Bode plot looks like this: + + + /---------------- + / + / <-- slope = 20dB/decade + / + -------------/ + f_cl f_ch + + In specifying tau for this digital preemphasis filter, tau specifies + the *digital* corner frequency, w_cl, desired. + + The digital preemphasis filter design below, uses the + "bilinear transformation" method of designing digital filters: + + 1. Convert digital specifications into the analog domain, by prewarping + digital frequency specifications into analog frequencies. + + w_a = (2/T)tan(wT/2) + + 2. Use an analog filter design technique to design the filter. + + 3. Use the bilinear transformation to convert the analog filter design to a + digital filter design. + + H(z) = H(s)| + s = (2/T)(1-z^-1)/(1+z^-1) + + + -w_cla + 1 + ------ + 2 fs + 1 - ------------ z^-1 + -w_cla -w_cla + 1 - ------ 1 - ------ + 2 fs 2 fs + H(z) = ------------ * ----------------------- + -w_cha -w_cha + 1 - ------ 1 + ------ + 2 fs 2 fs + 1 - ------------ z^-1 + -w_cha + 1 - ------ + 2 fs + + We use this design technique, because it is an easy way to obtain a filter + design with the 6 dB/octave rise required of the premphasis filter. + + Jackson, Leland B., _Digital_Filters_and_Signal_Processing_Second_Edition_, + Kluwer Academic Publishers, 1989, pp 201-212 + + Orfanidis, Sophocles J., _Introduction_to_Signal_Processing_, Prentice Hall, + 1996, pp 573-583 """ def __init__(self, fs, tau=75e-6, fh=-1.0): - """ - - Args: - fs: sampling frequency in Hz (float) - tau: Time constant in seconds (75us in US, 50us in EUR) (float) - fh: High frequency at which to flatten out (< 0 means default of 0.925*fs/2.0) (float) - """ gr.hier_block2.__init__(self, "fm_preemph", gr.io_signature(1, 1, gr.sizeof_float), # Input signature gr.io_signature(1, 1, gr.sizeof_float)) # Output signature |