fm_emph.py

#
# Copyright 2005,2007,2012 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 3, 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., 51 Franklin Street,
# Boston, MA 02110-1301, USA.
#

from gnuradio import gr, filter
import math

#
#           1
# H(s) = -------
#         1 + s
#
# tau is the RC time constant.
# critical frequency: w_p = 1/tau
#
# We prewarp and use the bilinear z-transform to get our IIR coefficients.
# See "Digital Signal Processing: A Practical Approach" by Ifeachor and Jervis
#


class fm_deemph(gr.hier_block2):
    """
    FM Deemphasis IIR filter.
    """

    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

        w_p = 1/tau
        w_pp = math.tan(w_p / (fs * 2))  # prewarped analog freq

        a1 = (w_pp - 1)/(w_pp + 1)
        b0 = w_pp/(1 + w_pp)
        b1 = b0

        btaps = [b0, b1]
        ataps = [1, a1]

        if 0:
            print "btaps =", btaps
            print "ataps =", ataps
            global plot1
            plot1 = gru.gnuplot_freqz(gru.freqz(btaps, ataps), fs, True)

        deemph = filter.iir_filter_ffd(btaps, ataps)
        self.connect(self, deemph, self)

#
#         1 + s*t1
# H(s) = ----------
#         1 + s*t2
#
# I think this is the right transfer function.
#
#
# This fine ASCII rendition is based on Figure 5-15
# in "Digital and Analog Communication Systems", Leon W. Couch II
#
#
#               R1
#         +-----||------+
#         |             |
#  o------+             +-----+--------o
#         |      C1     |     |
#         +----/\/\/\/--+     \
#                             /
#                             \ R2
#                             /
#                             \
#                             |
#  o--------------------------+--------o
#
# f1 = 1/(2*pi*t1) = 1/(2*pi*R1*C)
#
#         1          R1 + R2
# f2 = ------- = ------------
#      2*pi*t2    2*pi*R1*R2*C
#
# t1 is 75us in US, 50us in EUR
# f2 should be higher than our audio bandwidth.
#
#
# The Bode plot looks like this:
#
#
#                    /----------------
#                   /
#                  /  <-- slope = 20dB/decade
#                 /
#   -------------/
#               f1    f2
#
# We prewarp and use the bilinear z-transform to get our IIR coefficients.
# See "Digital Signal Processing: A Practical Approach" by Ifeachor and Jervis
#


class fm_preemph(gr.hier_block2):
    """
    FM Preemphasis IIR filter.
    """
    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

        # FIXME make this compute the right answer

        btaps = [1]
        ataps = [1]

        if 0:
            print "btaps =", btaps
            print "ataps =", ataps
            global plot2
            plot2 = gru.gnuplot_freqz(gru.freqz(btaps, ataps), fs, True)

        preemph = filter.iir_filter_ffd(btaps, ataps)
        self.connect(self, preemph, self)