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Is it possible to find the FFT of a 1024-point signal by taking 8-input points at a time and calculating the FFT of those 8-points until the end?

There is a divide and conquer approach to computing the FFT detailed in this PDF. Here is an implementation as in section 8.1 ...
rtclark's user avatar
  • 121
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
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
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0 votes

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

You are using a formulation that I am not familiar with, which I can see has several problems, only one of which you've recognised. The problem you've noticed occurs because the standard discrete ...
Stephen's user avatar
  • 336
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
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0 votes

Signal response amplitude depends on the time interval in simulation

Reading your question and comments, and testing your code, my understanding of your problem is that you do not understand why you need to normalise the transformed signal so that the amplitudes in the ...
Stephen's user avatar
  • 336
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
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
0 votes

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

For example I want to come up with an algorithm that is similar to that of the DFT, except given an input frequency (say 440Hz) it will return only the magnitude and phase at THAT specific frequency ...
Marcus Müller's user avatar
0 votes

Constant Q transform where you keep the window size constant (so Q is no longer constant)?

This is equivalent to just doing a single DFT, and then interpolating the spectrum to get fractional bin indices for arbitrary frequencies. You don't get any extra information compared to a standard ...
cloudfeet's user avatar
  • 301
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
0 votes

Does Zero Padding Distort the Spectrum of a Signal?

Let me put no equations, rather try to talk intuitively... DFT is an N-length sequence. This indirectly means that only discrete number of frequencies are available. Or in another way we are telling ...
Subramanian T R's user avatar
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
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
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
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
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

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