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FIR Filter

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    FIR Filter Design with Python

    In this paragraph we see how to design a FIR filter using SciPy, NumPy and MatplotLib.

    You can install SciPy, NumPy and MatplotLib as normal Python libraries, otherwise you can simply install the Enthought Python distribution.

    The Enthought Python distribution is packaging for you a Python interpreter and all the above libraries in a single convenient installer: http://enthought.com/products/epd_free.php

    Python FIR Filter Design

    from numpy import sin, arange, pi
from scipy.signal import lfilter, firwin
from pylab import figure, plot, grid, show

#------------------------------------------------
# Create a signal for demonstration.
#------------------------------------------------
# 320 samples of (1000Hz + 15000 Hz) at 48 kHz
sample_rate = 48000.
nsamples = 320

F_1KHz = 1000.
A_1KHz = 1.0

F_15KHz = 15000.
A_15KHz = 0.5

t = arange(nsamples) / sample_rate
signal = A_1KHz * sin(2*pi*F_1KHz*t) + A_15KHz*sin(2*pi*F_15KHz*t)

#------------------------------------------------
# Create a FIR filter and apply it to signal.
#------------------------------------------------
# The Nyquist rate of the signal.
nyq_rate = sample_rate / 2.

# The cutoff frequency of the filter: 6KHz
cutoff_hz = 6000.0

# Length of the filter (number of coefficients, i.e. the filter order + 1)
numtaps = 29

# Use firwin to create a lowpass FIR filter
fir_coeff = firwin(numtaps, cutoff_hz/nyq_rate)

# Use lfilter to filter the signal with the FIR filter
filtered_signal = lfilter(fir_coeff, 1.0, signal)

#------------------------------------------------
# Plot the original and filtered signals.
#------------------------------------------------

# The first N-1 samples are "corrupted" by the initial conditions
warmup = numtaps - 1

# The phase delay of the filtered signal
delay = (warmup / 2) / sample_rate

figure(1)
# Plot the original signal
plot(t, signal)

# Plot the filtered signal, shifted to compensate for the phase delay
plot(t-delay, filtered_signal, 'r-')

# Plot just the "good" part of the filtered signal.  The first N-1
# samples are "corrupted" by the initial conditions.
plot(t[warmup:]-delay, filtered_signal[warmup:], 'g', linewidth=4)

grid(True)

show()

#------------------------------------------------
# Print values
#------------------------------------------------
def print_values(label, values):
    var = "float32_t %s[%d]" % (label, len(values))
    print "%-30s = {%s}" % (var, ', '.join(["%+.10f" % x for x in values]))

print_values('signal', signal)
print_values('fir_coeff', fir_coeff)
print_values('filtered_signal', filtered_signal)

    coefficients

    float32_t fir_coeff[29]        = {-0.0018225230, -0.0015879294, +0.0000000000, +0.0036977508, +0.0080754303, +0.0085302217, -0.0000000000, -0.0173976984, -0.0341458607, -0.0333591565, +0.0000000000, +0.0676308395, +0.1522061835, +0.2229246956, +0.2504960933, +0.2229246956, +0.1522061835, +0.0676308395, +0.0000000000, -0.0333591565, -0.0341458607, -0.0173976984, -0.0000000000, +0.0085302217, +0.0080754303, +0.0036977508, +0.0000000000, -0.0015879294, -0.0018225230}

    /media/uploads/emilmont/dsp_fir.png

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