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4 votes

Why does the frequency sampling method for FIR filter design operate in this manner?

This answer shows one way of understanding why and how frequency sampling works. Let's assume you're given a desired complex frequency response $H(\omega)$ on the interval $\omega\in[0,\pi]$, where $\...
Matt L.'s user avatar
  • 90.3k
4 votes

Why does the frequency sampling method for FIR filter design operate in this manner?

This is how I would define the frequency-sampling method. Assuming linear phase (to start with). Draw out your desired frequency response magnitude, with as much detail as you need to to define the ...
robert bristow-johnson's user avatar
3 votes
Accepted

Mathematically, why is there a tradeoff between main lobe width and sidelobe level when we apply a window?

There are two main mathematical principles to keep in mind when dealing with this tradeoff: the uncertainty principle (specifically the Gabor limit) and the Gibbs phenomenon. The uncertainty principle ...
Baddioes's user avatar
  • 1,030
3 votes

Why is reconstruction of window function from its DFT difficult/noisy when the sidelobes of DFT are higher?

I think you are maybe misunderstanding how the "beamforming DFT" is actually computed. The beamforming equation you reference is \begin{equation} X[\theta] = \sum_{n=0}^{N-1}x[n]e^{j\frac{2\...
Baddioes's user avatar
  • 1,030
3 votes
Accepted

IFFT return complex values in Matlab

Just repeating what the comments say: The residual imaginary part of the impulse response is simply numerical noise. Matlab uses double precision floating point which has finite precicions As simple ...
Hilmar's user avatar
  • 45.3k
3 votes

Getting the magnitude and phase of a single specific frequency from an audio signal

You can simply use the DTFT $$ X(\omega) = \sum_{n= -\infty}^{+\infty}x[n]e^{-j\omega n} $$ for any frequency you want. The summation limits can be a bit tricky. In practice you can't sum from $ -\...
Hilmar's user avatar
  • 45.3k
3 votes
Accepted

Why does the frequency sampling method for FIR filter design operate in this manner?

Explanation: The impulse response and frequency response of a filter are Fourier Transform pairs. The time domain response of a filter is its impulse response: you put an impulse at the input of the ...
Dan Boschen's user avatar
  • 51.9k
2 votes

Generate a Time Series from Power Spectral Density Python

Sorry, this is a rather tortured implementation of something that's pretty straight forward. It's hard to point out what exactly is wrong in your code since most of it seems nonsensical to me and ...
Hilmar's user avatar
  • 45.3k
2 votes

Why does the frequency sampling method for FIR filter design operate in this manner?

Interesting to see the links and history from Dan and Robert and reference to Matt's thesis and derivation for FDLS, which I hadn't viewed previously. This is similar to approaches we've used since ...
vml's user avatar
  • 51
2 votes

Why does the frequency sampling method for FIR filter design operate in this manner?

Thanks to all for your help! Here's what I understand, please correct me if I'm wrong When performing a time sampling using $T$ as the sampling step, it produces a frequency periodicization with $1/T=...
minghierid's user avatar
1 vote

IFFT return complex values in Matlab

Here is a dumb MATLAB program I wrote nearly 3 decades ago (and modified a little since with the 'var' thing for exist() and ...
robert bristow-johnson's user avatar

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