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10 votes

Given a signal that is not bandlimited, how do you properly take the FFT?

In the real world, there is always some amount of aliasing, because no real signal is actually bandlimited. In many cases, the signal spectrum tends to zero relatively quickly as the frequency ...
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6 votes
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Can anyone explain how dft works as a filter bank?

@Ahmet. The DFT equation you posted does not compute an array of complex numbers. For any single given integer value of frequency-domain index $k$ the equation tells us how to compute the single ...
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4 votes

Given a signal that is not bandlimited, how do you properly take the FFT?

If your signal is not band-limited prior to sampling, then without any further information (such as a copy of the signal sampled at a time offset, which could synthesize a higher sampling rate), ...
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4 votes

Can anyone explain how dft works as a filter bank?

To add to Richard's good answer, I specifically want to show the difference between: Down-conversion and low-pass filtering (heterodyne the signal). Bandpass filtering the signal directly (...
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  • 36.1k
4 votes

FFT with High Time and Frequency Resolution

Time frequency resolution is a long debate in the DSP communities. But modern models has proved that the resolution isn't limited by the DFT because usually we know more about the signal but its ...
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3 votes
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Does Zero padding cause noise in the high frequency region?

Is that correct? No. This zero padding just leads to interpolation with a (cyclic) sinc kernel. It affects all subcarriers the same (as you can see in your own DFT!). So, this has to be a problem ...
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2 votes

FFT of a gaussian signal in Python

There are two issues: The time axis is not long enough to capture a sufficient length of the Gaussian. The FFT is not properly scaled. For the first item mentioned regarding the time axis, the ...
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2 votes
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Average of discrete periodic signal

It appears the OP would like to estimate the mean of the signal efficiently. A moving average will provide the best estimate under condition of white noise; assuming that is the case, the CIC (Cascade-...
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2 votes
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Sparse signal FFT

Partial FFT Sparse FFT Can also subsample the input, which will alias (fold) the high frequencies onto lower, then take FFT at the lower length, and then shift the result back onto higher frequencies ...
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2 votes

Should I be using FFT

According to the scipy.fft doc page, if you don't specify the FFT size it will use FFT size equal to the length of the input. At sampling rate of 256 Hz and input size of 100 samples, each frequency ...
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2 votes
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Phase Spectrum 0 Phase

I was working on the zero-phase Ricker wavelet. Chances you were working on the "linear-phase" wavelet. Assuming a real input, zero-phase requires time symmetry, i.e. $x[-n] = x[n]$. If you ...
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2 votes

Given a signal that is not bandlimited, how do you properly take the FFT?

In real life (as opposed to mathematical fictions) there is always noise (thermal and quantum at the limit), measurement errors, finite durations of operation, finite precision data types and ...
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1 vote

Sampling, filters, windowing, FFT. From theory to help on this coding list

There is a lot of detail in the question and I am not sure of all the requirements and desired results that would affect the processing after the 16 KHz decimated samples are produced. However I can ...
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1 vote
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Adding Fractional STO to an OFDM Signal using Frequency Domain Zero Padding

I believe the distortion is from using the FFT of the complete OFDM symbol including the CP to introduce time delay with a zero-padded FFT. Even before zero-padding is added the FFT result will no ...
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1 vote

Does Zero padding cause noise in the high frequency region?

If you've got it in the frequency domain anyway, why not phase shift it by (delay)(frequency)? It may still do odd things (like, shift whatever's at the end of the sample to the beginning), but you'...
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1 vote

Lowering Spectral Resolution of FFT

As @MBaz says in the comments, just do: ...
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1 vote

Is it possible to implement a block-wise Hilbert transformer using FFT

If the issue is in implementing the Hilbert block by block in either case (using MATLAB's hilbert or own method) then this would properly be done using overlap-add ...
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1 vote
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Butterworth filter cutoff attenuation is not exactly 0.707(-3dB)

Filter needs time to settle down. This settling process altered the beginning of time domain data and created the small difference. I took the second half of time domain filtered data and got a ratio ...
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  • 11
1 vote

Butterworth filter cutoff attenuation is not exactly 0.707(-3dB)

What you see there are margin issues. By not applying a window function to your signal before the FFT, you effectively convolute your spectrum with an $\text{si}$ function, which leads to artifacts ...
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