Questions tagged [fourier]

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Frequency domain confusion

I'm a bit confused with some details about frequency domain or studying systems with Laplace and Fourier analysis. Let's say we have a system with a transfer function $H(s)$ with no poles and zero's ...
10k views

How do you relate imaginary numbers with phase shift? How to imagine this?

So I found this answer on one of the questions. I wanted to ask how the complex part can be related with the phase shift. I wanted to ask this on the same question but it didn't allow me. Could anyone ...
272 views

Is sinusoids the nature's default signals?

I know the basic working principle of sinusoidal oscillators. But I have a doubt on this matter when I came across Gram-Schmidt orthogonalization procedure. I have read that the source for sinusoid ...
153 views

g(x)=x odd and even expansions

I'm studying book about digital filter by Richard Hamming. And there is exercise to get odd and even expansion of g(x)=x where x is from 0 to $\pi$. I understood even expansion, but can't get into odd ...
2k views

Fourier transform of Autocorrelation function, what am I missing here? (Power spectrum)

Given this problem I know that the autcorrelation and power spectrum are fourier pairs, so when taking taking fourier transform of Rxx, one should end up with Sxx However, when I take the transform ...
3k views

Discrete Fourier Transform bandwidth?

In a problem I'm working on, I have a signal that is sampled 256 times for 3.5 microseconds. After performing a Discrete Fourier Transform on the data, what is the frequency step between the ...
118 views

understanding windowed fourier ridges

I am studying windowed Fourier ridges for my project. I know that it computes the instantaneous frequencies and amplitudes from the spectrogram. But I don't really know how it relates to signal ...
588 views

Normalized cross correlation via FHT - how can I get correlation score?

I'm using the 2D Fast Hartley Transform to do fast correlation of two images in the frequency domain, which is the equivalent of NCC (normalized cross correlation) in the spatial domain. However, ...
278 views

Points of interest in a spectrogram

We have several audio tracks, all of which are different versions of the same track under one type of distortion: the speed of the track is increased by a constant factor K (hence frequences are ...
2k views

Intuition for how a Fourier transform handles signals where the frequency varies with time?

I created a discrete signal sampled at 44.1kHz that is 330Hz for 1 second, 360Hz for 0.5s, and 390Hz for 0.25s. I did an FFT transformation of this, and got the magnitude graph below: I don't ...
336 views

Signal Processing using Fourier Transform

So I'm trying to understand how MRI machines work. I understand all the concepts of it, the parts, what they do, how the machine works, etc. The part I'm having trouble with is the fourier transform ...