CODEWITHSUNDEEP
pythonscipysignal-processing
Yu Cheng
Yu Cheng

Reputation: 73

frequency response for a repeating 1-2-1 filter

I'm trying to estimate the effect of applying a simple 1-2-1 filter for multiple times, and determined the residual scales. In specific, I'm trying to reproduce this plot:

from Small et al., 2013

I used the scipy.signal.freqz as below

filt = np.array([0.25,0.5,0.25])
w, h=signal.freqz(filt)

And I thought that for a repeating filter, I just need to multiply h by itself for many times (since it's in frequency domain, and filtering is just convolution.)

However, I cannot get the same plot as they did in the paper. I have three major questions,

  1. I thought the 1-2-1 filter is just the triangle filter, is there other way to check its response in frequency domain?

  2. How to check its frequency response for a repeating 1-2-1 filter in python? Isn't it just h times itself for multiple times?

  3. I have hard time understanding the w(normalized frequency) unit in the freqz output. Could some one explain to me how to convert to wavenumber as in the plot?

Thank you.

Upvotes: 0

Views: 1182

Answers (1)

Yu Cheng
Yu Cheng

Reputation: 73

It turned out that I was not wrong. By plotting the absolute value of the transfer function, and dividing the normalized frequeny by 2pi, I got the exact same plots, and applying mutilpe time of filter is exactly mutiplying the frequency response to itself for multiple times. 

filt = np.array([0.25,0.5,0.25])
w, h=signal.freqz(filt)
plt.plot(w/(2*pi), abs(h**400), label='400 pass')

Comparison between frequency response of repeating 1-2-1 filter

Upvotes: 0

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