# 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 aren't negative frequencies folded in reconstruction of the aliased signal?

I'm working on the problem 1.9 from the book Introduction to Signal Processing by Sophocles J. Orfanidis. The pdf version and solution is freely available here. This is the solution for part a of the ...
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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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1 vote
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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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1 vote
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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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