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0
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1answer
22 views

Reason for bimodal behavior while low second fourier coefficient

If I have a time series (for eg. for 23 timestamps) and if I plot it and see that it is bimodal, that means it might be having high value of second fourier coefficient (with frequency = 2). But when I ...
0
votes
1answer
24 views

How to check if Fourier components are in phase of out of phase?

I have a time series (of 23 timestamps) of which I take the Fourier transform. Now the fourier transform has 23 imaginary values and each has an amplitude and a phase. When I get the phase angle, it ...
0
votes
1answer
86 views

Computing narrowband spectrograms using MATLAB [closed]

I'm having an assignment of computing narrowband spectrograms using MATLAB. And I totally have no idea about the code. Can someone help me writing the code and explaining what's going on to me. Lots ...
1
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2answers
37 views

Complex numbers in a frequency domain of a 2D image [duplicate]

I am try to grasp the idea of frequency domain for images. I think get the basics, but now I've stuck with a question that I can't find appropriate answer anywhere. How are frequency domain and ...
2
votes
1answer
64 views

Is it possible to open up this particular convolution equation?

I have three vectors, $x[n]$, $w[n]$, and $z[n]$. I need to compute: $y[n] = z[n] * \Big(x[n] \cdot w[n] \Big)$. This is easy to do. However, is there a way I can do this by 'opening' up the ...
0
votes
1answer
33 views

How is the complexity of applying Short term fourier transform over n samples with a moving window of size m amount to O(nmlogm)

I have been trying to understand a publication here where Short time fourier transform is applied over n samples in steps of m samples each (m is the size of the moving window). I understand that the ...
4
votes
2answers
77 views

Convolution of an image with a kernel that is a product of two functions

Suppose that $G(i,j)$ is a Gaussian decay function on the distance between points $i$ and $j$ of an image. In addition, $D(i,j)$ is the difference between the VALUES of the image at those points. ...
2
votes
2answers
115 views

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 ...
3
votes
3answers
160 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 ...
1
vote
1answer
93 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 ...
0
votes
1answer
84 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 ...
1
vote
2answers
640 views

Obtaining the fourier transform of cosine and sine

In this answer, Jim Clay writes, use the fact that "$F\{\cos(x)\} = \frac{\delta(w - 1) + \delta(w + 1)}{2}$" The expression above is not too different from $F\{{\cos(2\pi ...
3
votes
2answers
521 views

For a LTI system, why does the Fourier transform of the impulse response give the frequency response?

I know that for a given system, the Fourier transform of its impulse response gives its frequency response. I want to find where this property comes from, but haven't been able to find if it's a ...
1
vote
3answers
494 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 ...
3
votes
1answer
174 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 ...
0
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0answers
42 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 ...
4
votes
1answer
318 views

Example of Fourier Transform not existing for real-life signals?

I got curious based on this question here, but basically, is there ever a real-life signal that exists where its Fourier transform does not exist? If a signal is not finite energy, then its Fourier ...
3
votes
0answers
122 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 ...
2
votes
1answer
226 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, ...
5
votes
2answers
202 views

What do colored noises look like in the time domain?

I understand that the time domain representation of white noise looks like impulses. How do colored noises like brown, pink etc. look like when we perform an inverse Fourier Transform on them ? What ...
2
votes
2answers
204 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 ...
3
votes
1answer
176 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 ...
2
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4answers
793 views

Fourier Transform minimum sample requirement

Assuming a signal is sampled adequately, what is the minimum size of an FFT window that would allow detecting a specific frequency? Is it necessary to have samples for at least one complete period at ...
12
votes
3answers
733 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 ...
3
votes
1answer
328 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 ...