# 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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### Impact of STFT window function and FFT length on computation time

I have been doing a study which part of it includes a comparison of computation time vs window type and length (among some other things in the computation time, however I speak in terms of relative ...
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### Phase extraction from Fourier transform

Is it possible in principle to correctly extract the phase from Fourier transform? I just tried to do so using Python, here some attempts: ...
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### FFT of a gaussian signal in Python

I've been trying to get the FFT of a gaussian in Python. When I use the following parameters, the FFT goes hand in hand with the theoretical FT of the gaussian, but if I increase $\sigma$ they rapidly ...
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### Sinc function Energy [closed]

I am struggling for days trying to compute the energy of the follow sinc function. Any help appreciated ! Thanks. -(sin(π(t-2)/2))/(π(t-2)/2))
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### understand short time fourier transform

I am reading this paper for signal denoising. In the paper, the authors says The core concept in this paper is to compute a regression between a noisy signal frame and a clean signal frame in the ...
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### Can the Fourier Transform of the unit step be used as a filter?

Using the FT of the step function we have $H(\delta)=\pi\delta(\omega)+\frac{1}{j\omega}$, and it's magnitude is $\infty$ at $\omega=0$ and approaches $0$ as $\omega$ goes to both positive and ...
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### What is the magnitude response and phase of this function?

Given the system/filter $H(\omega)=\frac{1}{5-j\omega}$, find $h(t)$, it's magnitude response and phase and identify what type of filter it is. Now clearly given it's form, $h(t)=e^{5t}u(-t)$, but I'm ...
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### Inferring shape of information signal from its DFT?

I came across this question recently, and I am very confused by (b)(ii). b(i) gives $x_n$ = [0.5, 0, -0.5, 0]. My approach to (ii) was to recognise that $X_m$ represents the frequency content of the ...
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### FFT and spatial frequency basic knowledge

Using the following website: on how the Fourier transform works (Interested in the Basic Principle part). I found out that if you have 3 pixels closer in the spatial domain you'll get more spaced ...
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### Why does fourier transforming an analytic signal gives me negative frequency components?

I consider an array: import numpy as np from scipy.fft import fft from scipy.signal import hilbert a=np.random.rand(5) First I manually compute the fourier ...
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### Spectrum of triangular pulse - MATLAB

I am new in matlab.I was given the code for spectrum of rectangular pulse of amplitude 1V and duration 1ms, and now I have to find the spectrum of a triangular pulse of amplitude 1V and duration 1ms ...
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### How to inject a 2D plane sine wave to the array of seismic sensors?

I've several sensors positioned at various points in the $X$,$Y$-Cartesian coordinate system, and I've experienced a problem to inject a planar Sine wave to the spatially positioned sensors, the ...
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### What is the Fourier convolution theorem range of application (example of Dirac comb times rectangular window)?

$\DeclareMathOperator{\sinc}{sinc}$ I have questions regarding the Fourier transform of the product of functions or distributions and the range of application of the convolution theorem. Context When ...
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