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#' ## Functions for frequency, phase, impulse and step response
#' Let's first define functions to plot filter
#' properties.
from pylab import *
import scipy.signal as signal
#Plot frequency and phase response
def mfreqz(b,a=1):
w,h = signal.freqz(b,a)
h_dB = 20 * log10 (abs(h))
subplot(211)
plot(w/max(w),h_dB)
ylim(-150, 5)
ylabel('Magnitude (db)')
xlabel(r'Normalized Frequency (x$\pi$rad/sample)')
title(r'Frequency response')
subplot(212)
h_Phase = unwrap(arctan2(imag(h),real(h)))
plot(w/max(w),h_Phase)
ylabel('Phase (radians)')
xlabel(r'Normalized Frequency (x$\pi$rad/sample)')
title(r'Phase response')
subplots_adjust(hspace=0.5)
#Plot step and impulse response
def impz(b,a=1):
l = len(b)
impulse = repeat(0.,l); impulse[0] =1.
x = arange(0,l)
response = signal.lfilter(b,a,impulse)
subplot(211)
stem(x, response)
ylabel('Amplitude')
xlabel(r'n (samples)')
title(r'Impulse response')
subplot(212)
step = cumsum(response)
stem(x, step)
ylabel('Amplitude')
xlabel(r'n (samples)')
title(r'Step response')
subplots_adjust(hspace=0.5)
#' ## Lowpass FIR filter
#' Designing a lowpass FIR filter is very simple to do with SciPy, all you
#' need to do is to define the window length, cut off frequency and the
#' window.
#' The Hamming window is defined as:
#' $w(n) = \alpha - \beta\cos\frac{2\pi n}{N-1}$, where $\alpha=0.54$ and $\beta=0.46$
#' The next code chunk is executed in term mode, see the [Python script](FIR_design.py) for syntax.
#' Notice also that Pweave can now catch multiple figures/code chunk.
#+ term=True
print("I'm publishing a term chunk")
#' Let's define a highpass FIR filter, if you compare to original blog
#' post you'll notice that it has become easier since 2009. You don't
#' need to do ' spectral inversion "manually" anymore!
a = 12
b = 10
print(a+b)
#' $$
#' \sum_{i=1}^n x_i
#' $$
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