python - How to make a low pass filter in scipy.signal?

Question

I have several questions on making a lowpass filter in python/scipy.signal. Would appreciate any answers.

1. I'm trying to understand how scipy.signal.lfilter works. Does it take the filter coefficients and multiply them by the data values, so that for data[500], it'll do

for b in range(0,len(coeff)):
    filtered = filtered + data[500-b]*coeff[b]

What's the difference between doing that and what it's doing?

2. I also don't understand how the number of taps affects when it starts filtering. For different number of taps I see it starting at different values on the data. I assumed it'll start only after it has the necessary coefficients. In my example I have 683 coefficients from scipy.signal.firwin, but the filter starts at 300-400, as you can see in the image Firwin lowpass filter (filter is in blue; sinewave is in red; x goes from 0-1000)

from scipy import signal

a = signal.firwin(683, cutoff = 1/30, window = "hamming")
t = signal.lfilter(a,1,sig)

3. With an fs=1, cutoff = fs/30, I get a lowpass filter with firwin that is delayed a lot as shown by the image above. What can I do to improve the delay?

4. How would changing the sampling rate affect the filter?

5. I've found two methods online to approximate the number of taps:

import math

(2/3) * math.log10(1/(10*ripple*attenuation)) * fs/transition_width
((-10*math.log10(ripple*attenuation) - 13)/(14.6)) * fs/transition_width

Which is a better approximation?

Any clarification would be greatly appreciated.

Answer 1

等待大神解答