# Questions tagged [fourier]

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2answers
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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 ...
3answers
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 ...
3answers
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 ...
1answer
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 ...
1answer
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 ...
1answer
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 ...
0answers
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 ...
1answer
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, ...
0answers
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 ...
2answers
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 ...
1answer
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 ...
3answers
4k views

### Fast Fourier transform- non-integer number of cycles in the FFT aperture

There are a few excellent discussion threads and answers on this site (eletronics.se) on the theory of Fourier transforms. I tried implementing the same in a simulation tool (MS Excel :)). I have a ...
1answer
747 views

### Mathematics / Signal theory behind billiard ball 'wave pendulum' effect

This YouTube video shows a very interesting effect. What is the underlying science? I have recently started studying Fourier theory and DSP, and and trying to understand what is going on in terms of ...