823 views

### A DFT “periodic inputs” question

Why do people say that the fast Fourier transform (FFT) “views”, or “interprets”, or “assumes” its input sequence is periodic? I ask this question because the activities of viewing, interpreting, and ...
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817 views

### How Do I Measure the Time Duration of a Finite Length Discrete Sequence?

Assume I have a five-sample time-domain sequence (none of the five samples are zero valued) and the time period between each pair of samples is one second. Measured in seconds, what is the time ...
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2k views

### Sequence expansion by zeros and interpolation - does it insert additional frequencies?

I am struggling with understanding the consequences of oversampling on the frequency spectrum of the signal. If I understand correctly, with an oversampling rate of 8X we insert 7 new values for each ...
5k views

### DFT coefficients meaning?

What "are" they? What's a sensible way to interpret the coefficients (and what isn't)? To pose specifics: DFT coefficients describe the frequencies present in a signal They describe the ...
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4k views

### FFT of a AM modulated signal

I am generating an AM modulated sinusoidal wave. The carrier frequency is set at $1000 \ \rm Hz$; the modulation frequency is set to $40 \ \rm Hz$ and $100 \%$ of the amplitude is modulated. I ...
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3k views

### DFT of pure sinusoidal wave

I'm writing a program in which you can synthesize waves by adding to a sound's Fourier transform, and then inverse the transform to get the modified sound. In order to do this, I need to know what to ...
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2k views

### PyWavelets CWT: normalization? Vs Scipy?

Related. The equation being implemented normalizes by sqrt(1 / scale):  C_{a, b} = \frac{1}{\sqrt{a}} \sum_k s(k)\left( \int_{-\infty}^{k+1} \overline{\psi \left(\...
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203 views

### Resource recommendations to learn audio processing

I'm looking for some good resources to learn audio processing for a machine learning task based on classification of users as either 'COVID-19 positive' or 'COVID-19 negative' based on their cough ...
805 views

### FFT for long waveform

I should take FFT of a very long vector of length 1,636,399,763 (i.e. length order is 10^9) preferably in MATLAB. However, on 128 GB RAM, my code throws ...
452 views

### Why DFT is used for approximating CTFT when you can approximate CTFT-integral itself?

I was using MATLAB for approximating FTs. Why DFT is used if we can approximate the transform-integration using summation.
1 vote
885 views

### How is wavelet center frequency computed?

PyWavelets (1) takes index of max DFT magnitude, (2) adds 1 to it, (3) divides by domain, which is the range of input values to the wavelet ("support"). ...
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343 views

### Real time FFT - Wouldn't zero-padding a signal at the end distorts the output?

I have looked at previous similar questions, but I am still not very clear on this. Most real-time or otherwise fft functions suggest adding zeros at the end of the input to make the sample size an ...
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1 vote
435 views

### Unexpected imaginary part in the fft of a zero-padded cosine

I simulated a cosine waveform $y = \cos(\omega t)$ and I applied the FFT algorithm to it. As expected, I have a frequency peak at $\pm \omega$ only in the real part, and nothing in the imaginary ...
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157 views

### FFT of 2 sine tones using windowing and zero padding. Wrong FFT amplitude

Here is my attempt to perform an FFT on a random signal with 2 tones in which I applied zero padding AFTER windowing. (I did not apply zero padding before windowing because that would suggest that the ...
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1 vote
I'm trying to grasp some intuition about why zero-padding the time domain sequence $x[n]$ interpolates the frequency domain bins of the $DFT\{x[n]\} = X[k]$ and how does this relate to the $DTFT$ of \$...