From 2ede969ec5f3f6d361814403b7375db5f15ec14d Mon Sep 17 00:00:00 2001
From: Josh Morman <jmorman@gnuradio.org>
Date: Wed, 24 Nov 2021 12:01:00 -0500
Subject: analog: pep8 formatting
Signed-off-by: Josh Morman <jmorman@gnuradio.org>
---
gr-analog/python/analog/fm_emph.py | 124 +++++++++++++++++++------------------
1 file changed, 63 insertions(+), 61 deletions(-)
(limited to 'gr-analog/python/analog/fm_emph.py')
diff --git a/gr-analog/python/analog/fm_emph.py b/gr-analog/python/analog/fm_emph.py
index 9c1107bb14..a581bdf2ac 100644
--- a/gr-analog/python/analog/fm_emph.py
+++ b/gr-analog/python/analog/fm_emph.py
@@ -16,22 +16,22 @@ import cmath
class fm_deemph(gr.hier_block2):
r"""
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
@@ -39,39 +39,39 @@ class fm_deemph(gr.hier_block2):
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
@@ -81,20 +81,21 @@ class fm_deemph(gr.hier_block2):
-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):
gr.hier_block2.__init__(self, "fm_deemph",
- gr.io_signature(1, 1, gr.sizeof_float), # Input signature
+ # Input signature
+ gr.io_signature(1, 1, gr.sizeof_float),
gr.io_signature(1, 1, gr.sizeof_float)) # Output signature
# Digital corner frequency
@@ -111,8 +112,8 @@ class fm_deemph(gr.hier_block2):
p1 = (1.0 + k) / (1.0 - k)
b0 = -k / (1.0 - k)
- btaps = [ b0 * 1.0, b0 * -z1 ]
- ataps = [ 1.0, -p1 ]
+ btaps = [b0 * 1.0, b0 * -z1]
+ ataps = [1.0, -p1]
# Since H(s = 0) = 1.0, then H(z = 1) = 1.0 and has 0 dB gain at DC
@@ -120,18 +121,17 @@ class fm_deemph(gr.hier_block2):
self.connect(self, deemph, self)
-
class fm_preemph(gr.hier_block2):
r"""
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)
-
+ 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
+-----||------+
| |
@@ -144,12 +144,12 @@ class fm_preemph(gr.hier_block2):
\
|
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
@@ -157,58 +157,58 @@ class fm_preemph(gr.hier_block2):
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
@@ -224,19 +224,21 @@ class fm_preemph(gr.hier_block2):
-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):
gr.hier_block2.__init__(self, "fm_preemph",
- gr.io_signature(1, 1, gr.sizeof_float), # Input signature
+ # Input signature
+ gr.io_signature(1, 1, gr.sizeof_float),
gr.io_signature(1, 1, gr.sizeof_float)) # Output signature
# Set fh to something sensible, if needed.
@@ -244,7 +246,7 @@ class fm_preemph(gr.hier_block2):
# at z = -1.0 or z = 1.0 respectively. That makes the filter unstable
# and useless.
if fh <= 0.0 or fh >= fs / 2.0:
- fh = 0.925 * fs/2.0
+ fh = 0.925 * fs / 2.0
# Digital corner frequencies
w_cl = 1.0 / tau
@@ -268,11 +270,11 @@ class fm_preemph(gr.hier_block2):
# That isn't what users are going to expect, so adjust with a
# gain, g, so that H(z = 1) = 1.0 for 0 dB gain at DC.
w_0dB = 2.0 * math.pi * 0.0
- g = abs(1.0 - p1 * cmath.rect(1.0, -w_0dB)) \
+ g = abs(1.0 - p1 * cmath.rect(1.0, -w_0dB)) \
/ (b0 * abs(1.0 - z1 * cmath.rect(1.0, -w_0dB)))
- btaps = [ g * b0 * 1.0, g * b0 * -z1 ]
- ataps = [ 1.0, -p1 ]
+ btaps = [g * b0 * 1.0, g * b0 * -z1]
+ ataps = [1.0, -p1]
preemph = filter.iir_filter_ffd(btaps, ataps, False)
self.connect(self, preemph, self)
--
cgit v1.2.3