Re: Filter response curve
Re: Filter response curve
- Subject: Re: Filter response curve
- From: Evan Balster <email@hidden>
- Date: Tue, 17 Jan 2017 11:30:47 -0600
I must disagree. The cleanest way to compute the
transfer function, is to
compute the transfer function, directly — you'll get an exact answer, with minimal computational expense.
If I have a filter defined as:
y[t] = b0*x[t]
+ b1*x[t-1] + b2*x[t-2]
- a1*y[t-1] - a2*y[t-2];
This corresponds to a transfer function:
H(z) = (b0 + b1*z^-1 + b2*z^-2) / (1 + a1*z^-1 + a2*z^-2)
(Note that "a" coefficients become negative.)
If I want to find the response of that filter to a frequency of 1000 hz, where the sample-rate is 10000 hz, I compute this Z-function for the corresponding complex frequency:
z = e^(i*2pi*f/S)
... = e^(i*2pi*1000/10000)
... = cos(2pi*.1) + i*sin(2pi*.1)
Pass that number through the transfer function H(z) above, and you'll get an exact answer for whatever frequency you like.
There's a lot of misinformation floating around about this topic, and I imagine it's because people are put off by complex numbers and Z-domain math. It isn't as spooky as it looks!
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