# 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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### Does spectral leakage include negative frequencies?

When choosing a window function, window duration, and/or transmission frequency (assuming sampling rate satisfies Nyquist), one may want to understand what sort of spectral leakage would occur at a ...
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### Spherical equivalent of Nyquist frequency

Let $\phi$ be a scalar function defined on the surface of a sphere. I have samples of $\phi$ at various locations on the sphere. I want to apply a spherical harmonic transform. I know that $\phi$ is '...
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### Fourier transformed acceleration from Fourier Transform of velocity and position using Omega arithmetic

Let's say the position of an object is given by simple sine function. By elementary calculus, I can calculate the acceleration in the time domain and find its Fourier transform. I can also calculate ...
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### Why the unilateral Laplace transform?

Why is the Laplace transform commonly taught as the unilateral Laplace transform? I mean, for the Fourier transform, we commonly have the bilateral transform... if the signal is 0 for $t<0$, then ...
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### DTFT based Frequency Sampling

H($e^{jw}$)= 1, |w| < $\pi/2$ and 0, $\pi/2$ <= |w| <= $\pi$ I took M equally spaced frequencies from 0 to $2\pi$. If we assume h[n] to be causal, $H(e^{jw})$ should have some phase and it'...
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### Why does an anti-symmetric function has zero amplitude at the center of an even length window

I am performing FFT on a real odd function and the resultant transform has zero amplitude in the last bin. Essentially if Y= rfft(X), then Y[-1] is always zero. I stumbled on this answer which says ...
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### Real Fast Fourier Transformation (FFT) in 2D changes with changing the axes order

I am using Python to calculate the real FFT for a 2D array. I found that the real FFT function does not return an array with the same size as the input array, rather, it returns an array with the same ...
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### Multitaper F statistics

I'm having some problems interpreting the F-statistics output from multitaper analysis. To illustrate, the following code-snip in R performs multitaper analysis on the same sine-frequency but with ...
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### Scaling factor for comparing spectrums obtained via Continuous Fourier Transform and Discrete Fourier Transformation?

Essentially I am trying to calculate the Bremsstrahlung spectrum numerically for magnetized plasma and want to compare the resultant spectra with the standard textbook spectrum formula for ...
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### How to visualize high-pass filtered images?

When I try visualizing a high-pass filtered image, all I see is gray, similar to the middle subfigure in the attached figure from a related paper. The authors claim they normalize the image to have ...
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### Confusion in deriving formula for fourier tansform of impulse train

I was trying to derive fourier transform for impulse train : I know how to solve for this using using properties of fourier transform. But now I wanted to use a brute force approach to it so I did ...
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### Understanding the FFT phase spectrum with a simple example

I'm trying to compute the DFT using scipy's functions. I don't understand why the phase spectrum of a simple sine wave with 2 Hz frequency doesn't show $\pm\pi/2$ at the $\pm 2Hz$ frequencies. Instead,...
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### Is it possible to reduce the complexity of radix-2 FFT if the input vector contains identical elements?

my question is about reducing the complexity of radix-2 FFT when the input vector has a specific structure. For an input vector of x with N elements, the complexity is given by O(N log2 N). My input ...
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### Orthogonal Basis for a 2D Signals (Compressive Sensing)

I have a 2-D signal that is (1536x128) and that is sparse in the Fourier domain (after applying fft2). I want to apply compressive sensing to recover the signal using fewer random elements, but I am ...
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### Complex output after inverse FFT of a real signal

I have a real one dimensional signal s (light absorbance in a flow cell), which has significant noise and some periodic noise after performing a deconvolution of $S$ from $S_o$. Basically fft($S$) was ...
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### Advantages of the Rotation Translation Operation Before Doing FT Smoothing

I was reading a relatively old paper from the 1970s on smoothing by FT methods (chemistry applications), where the authors show that if we do rotation translation operation on the signal (y- values) ...
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### Finding the impulse response of a system

I have the following transfer function. $$H(j\omega) = \frac{1+0.5 e^{-j\omega}}{1-1.8 \cos(\frac{\pi}{16}) e^{-j\omega}+0.81 e^{-j2\omega}}$$ I'm trying to find the impulse response of the system. ...
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### Is it possible to recover the time-domain signal after manipulating it in the frequency-domain? [duplicate]

I've worked a fair amount with EEG signals, though I've never had formal training in signal processing, so please excuse my ignorance. The problem is this: my signal has noise at many, many ...