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 ...
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 ...
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 ...
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 ...
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 ...
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(\...
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"). ...
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 ...
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 ...
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 ...
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 \$...