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# Questions tagged [fourier-transform]

The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.

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### Why are edges in spatial images represented as edges in their Fourier transform image?

Here is a well-known image and its Fourier Transform (magnitude). If I understand correctly the theory behind the FFT, each pixel in the FFT image represents a certain 2D sine wave with frequency ...
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### How do I interpret the result of a Fourier Transform?

For example, I entered the following "equation" into Wolfram|Alpha: FourierTransform[Piecewise[{{sin[t],t > 0 and t < 2*pi}}, 0], t, \[Omega]] So as to ...
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### What is the correct solution for Fourier transform of unit step signal?

The unit step signal defined as $$u[n]= \lbrace 1; n>=0; \\ \qquad0; n<0 \rbrace$$ has three possible solutions for its Fourier domain representation depending on the type of ...
315 views

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### Which Approach Is Better for Decomposing an Image into High Frequency and Low Frequency Components?

Which approach is better or there is mathematical justification for using Bilater filter and Fourier Transform to decompose a image into High Frequency and Low Frequency Component. Both Bilateral ...
467 views

### DFT as convolution question

I have tried to make this question as readable and consistent as possible. The short of it, is that I am trying to ascertain how one gets from the math equation shown, (which I understand), to the ...
92 views

### Create an aliased image in FD

Is there an accurate way to create an aliased image from the Fourier transform of the original image? in other words, i have the Fourier coefficients of an image and i want to make down-sample in ...
2k views

### How to interpret output of matched filter with complex input?

I have implemented a matched filter based on the Fourier Transform approach. In the real numbers domain that means that I use as the coefficients of my filter (B) the inverted time-samples of the ...
182 views

### Properties of Spectral Transformations - Allocation (decomposition into even and odd part)

I am trying to understand the Allocation property of Spectral Transformations. I can't. I know that every function can be separated into an even part and into an odd part. My problem is ...
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### Prove the dirac delta contains all frequencies

I'm looking for a mathematical proof that the dirac delta contains all frequencies. I just read in a text book that the frequency spectrum of a dirac is just a horizontal line of amplitude 1, whereas ...
2k views

### How do I understand Fourier descriptors more visually and intuitively?

I read the book Image Processing, Vision and Machine Vision and find the concept Fourier descriptors hard to understand, although literally its derivation is somewhat reasonable. Can anyone give me a ...
267 views

### Why are the basis functions for DFT so?

When you get a DFT of a signal, you use the basis functions as: $e^{-j2\pi kn/N}$ Why is it so? Why don't we use the conjugate, $e^{j2\pi kn/N}$, or any other function?
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### convergence of Fourier transform of $e^{-t}\sin(2\pi ft)u(t)$

As you see Fourier transform function is being divergent for the first statement but it seems to converge. What is my fault?  \begin{align} \int\limits_{-\infty }^{+\infty }{{{e}^{-t}}\sin(2\pi ...
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### What's the significance of lomb-scargle power?

What is the significance of Lomb-scargle power (y-axis)? I have two data sets. For each plot, above plot is Lomb-scargle periodogram of the lower plot (original data). The first data set has an ...
236 views

### Is there a closed form expression for main-lobe width increase given a window?

We know that when we window a signal, we increase the main-lobe width. Let 'main-lobe-width' here be the null-to-null bandwidth of the main lobe. Let us further more say that the main-lobe width of a ...
49 views

### Implementing rotation in frequency domain and map it back to spatial domain

Please consider the following small example: ...
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### Why doesn't this complex multiplication in the frequency domain produce my expected phase shift?

I know how to change the phase of a complex number by multiplying by $\cos \theta + i \sin \theta$. And I understand that the phase of a sine wave is reflected in its Fourier transform. So, I am ...
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### Simple FFT filtering vs. e.g. butterworth filtering

I am currently working on functional connectivity analysis of EEG, and need to bandpass filter my data into different frequency bands (Delta, Theta, Alpha and Beta). An important thing is that the ...
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### how to match 2 signals that have same information, though shifted and scaled

I have 2 signals S1 and S2 that contain the same information, but S2 is shifted and scaled compared to S1 by an unknown amount (but small; eg shift would be of the order of 1-10 samples). What is the ...
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### One sided frequency spectrum (Matlab vs. Origin)

There are a lot of queries on fft frequency all over the web. I guess the following point not discussed anywhere explicitly. Hope someone can provide an insight here. If we have and even number of ...
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### I have a pressure signal and want to do SPL analysis on it

Signal I have an acoustic signal from a Ffowcs Williams Hawkings CFD analysis and would like to convert it to the frequency domain and see the SPL and OASPL. I know I need to use fft() but I am ...