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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About Discrete Fourier Transform vs. Discrete Fourier Series

I am new to the field of signal processing. I am wondering what is the difference between DFS(Fourier Series) vs. DFT(Fourier Transform). For common applications, usually we get a segment(length <...
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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 ...
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What is the physical significance of negative frequencies?

This has been one of the holes in my cheddar cheese block of understanding DSP, so what is the physical interpretation of having a negative frequency? If you have a physical tone at some frequency ...
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Does Zero Padding Distort the Spectrum of a Signal?

It's said to "sample the DTFT", revealing what "DFT fails to see". And I fail to see how this sampling isn't distortion. The "spectrum" aims to provide the sinusoidal ...
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Why is the Fourier transform so important?

Everyone discusses the Fourier transform when discussing signal processing. Why is it so important to signal processing and what does it tell us about the signal? Does it only apply to digital signal ...
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Replicate MATLAB's conv2() in Frequency Domain

When conv2d is on same mode, the image needs no padding, because the result is the same size as the image. When ...
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Difference between Discrete Time Fourier Transform and Discrete Fourier Transform

I have read many articles about DTFT and DFT but am not able to discern the difference between the two except for a few visible things like DTFT goes till infinity while DFT is only till $N-1$. Can ...
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Power Spectrum: Definition

I am new to the study of time series. Recently I have asked a question about the covariance of real and imaginary part of a real(in time domain) stochastic time series and I have received an answer ...
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DFT of a sine, closed form solution and insights

I seek to calculate, mathematically, the Discrete Fourier Transform, $$\texttt{DFT}\{x\}[k] = \sum_{n=0}^{N - 1} x[n] e^{-j2\pi k n / N}$$ of any arbitrary real-valued sine: any frequency, duration, ...
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What effect does a delay in the time domain have in the frequency domain?

If I have a signal that is time limited, say a sinusoid that only lasts for $T$ seconds, and I take the FFT of that signal, I see the frequency response. In the example this would be a spike at the ...
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Where is the flaw in this derivation of the DTFT of the unit step sequence $u[n]$?

This question is related to this other question of mine where I ask for derivations of the discrete-time Fourier transform (DTFT) of the unit step sequence $u[n]$. During my search for derivations I ...
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Image Processing and applicability of 2D Fourier Transform

As a newbie in the world of signal processing, I am having a hard time in appreciating image 2-D fourier transforms. I am fully able to appreciate the concept of 1-D Fourier transform. Essentially, ...
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Applying Image Filtering (Circular Convolution) in Frequency Domain

To filter an image we can: Use a 3x3, 5x5, 7x7, etc. filter, that is convolve the image and the filter in the space domain. Use a FFT on both the image and the filter, multiply them together in the ...
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