Questions tagged [fourier-transform]

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

1,204 questions
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Finite and Infinite support in time and frequency domain

It's known that signals with a finite support in time has an infinite support in frequency (talking about Fourier Transforms). A common example that is given for the claim is the triangle function ...
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Why is the second half of the FFT negative frequencies

There are lots of questions here about what the negative frequencies in fft mean, but I'm confused on why the second half of the fft calculation is the correct calculation for a negative frequency. ...
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Why MATLAB fft cos makes imaginary parts?

The cos fourier transform has no imaginary parts, but in this code it has imaginary parts that little big. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure(7); fs=128; t=-4*pi:1/fs:4*pi-1/fs;...
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Orthonormal Dictionaries for Band Limited Signals

If $\mathbf{x} = [x_0, x_1, \ldots, x_{N-1}]^T$ is the time sampled input signal and $\mathbf{Y} = [Y_0, Y_1, \ldots, Y_{N-1}]^T$ is the Fourier transform of the input signal, then a linear ...
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Understand Inverse DFT (FFT)

I was reading this article to understand the fft https://jackschaedler.github.io/circles-sines-signals/dft_walkthrough.html I understand that the fft takes a block (256 or 512) of the signal, ...
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Numpy fft2 frequency shift

I don't understand how to make frequency shift in fft2 or higher dimensions. Could anyone explain it, please? import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import ...
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What to do for the right FFT in Matlab (two peaks and incorrect amplitude)?

This is the FFT I'm using. But two peaks (did not expect the one in the beginning) are occurring and the amplitude is not as specified (expecting a value of 2). Any help is much appreciated! ...
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Why does the frequency in the DFT have to be an integer?

I don't know why the result of DFT and FFT in MATLAB like below images.. fs=128; t=0:1/fs:1-1/fs; x=cos(2*pi*3.5*t); X=fft(x); N=length(x); n=0:N-1; f=fs*n/N; plot(f,abs(X)/N); If I set the ...
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How does a cross-looking error profile arise in discrete fourier transform?

I am numerically computing a 2D NxN complex Hermitian matrix using a discrete fourier transform operation on an 2D MxM complex Hermitian matrix. The phases of the output 2D NxN matrix elements are ...
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how to guess what the interference source it could be

At work, we are in an industrial area, and there is always a signal that I receive inside my office which interferences with my tests. This signal is in the 433 MHz and when I see the spectrum, ...
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Creating realization of 2D Gaussian field in Fourier space

I want to generate a 2D Gaussian field with dimensions $L\times L$ with $N^2$ cells each of size $l = L/N$. I'm doing this by producing a realization of this field in Fourier space by producing ...
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I want to get impulse response of causal system

I want to get impulse response of this causal system on first photo. So I got frequency response on second photo from this system. and now I am trying to transform this frequency response to impulse ...
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PHAT filtering for cross-correlation yields wrong results while simple cross-correlation does OK (Python)

I work with two signals, the second being perfectly delayed and attenuated, with no reverberation. I implemented cross-correlation algorithm, which yields me these results: Here is my code for these ...
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Graph signal processing

What's the intuition behind a ''Graph fourier transform'' ? I'm not so much interested in mathematical details or technical applications. I'm trying to grasp what a graph fourier transform actually ...
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DFT (FFT) of a Real Even Function Doesn't Yield Real Only DFT Signal

There are a lot of similar questions already, but I can't find one answering this problem. I used the following MATLAB code to perform the FFT on a Lorentzian input signal ...
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Accuracy of time domain signal when one frequency is absent

Suppose the known frequency spectrum of a signal is: $$G(n\Delta f)=9,4,3,5,1,6,...$$ where $n=0,1,2...$ and $\Delta f=1$ Hz If, for some reason, we cannot sample $G$ at $n=0$ (i.e. $G(0)=9$ is not ...
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In a periodogram, why is the modulus squared of the DFT taken rather than the DFT itself? [duplicate]

Why can't you just take the DFT itself? And how accurate is this method in spectral density estimation? Are there cases in which it is very accurate?
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How to Calculate the number of DFTs taken in a STFT

Given variables of window size (W), overlap (O), and length of the Signal (S) (in my case, length of a song) and I am trying to determine an equation that gives me the number of DFTs that would be ...
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Cross-correlation, sharp peak at 0?

First of all, I have to stress that I am not a professional of coding, no more than a professional of signal processing. I am a chemist that happen to be working on a project involving both. So in ...
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STFT amplitude normalization, librosa library

So librosa.core.stft returns a complex single sided spectrogram. My question is: What normalization of the amplitude values should I perform afterwards? I believe I have to multiply the amplitude ...
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I know that time shifting property of discrete-time Fourier Transform states that $x[n]\leftrightarrow X(e^{j\omega})\implies x[n-n_0]\leftrightarrow e^{-j\omega n_0}X(e^{j\omega})$ So given a signal ...
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Bandwidth of Information Signal

I have trouble finding the bandwidth of a signal. Say I have an info bearing signal m(t)=sinc(2t/pi). I found the fourier transform of the sinc function and found that the angular frequency was 1/pi. ...
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Discretization of Sinusoidal Signals

How do I should sample two continuous sinusoids of $f_1$=1/4 Hz and $f_2$=1/2 Hz at a 1 Hz rate? Can i recover both if i bandlimit after sampling at a 1/2 Hz limit?
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Should scipy.signal.coherence be 1 for single input and output signals?

I am trying to calculate the coherence between input and output signals. I thought I could work with a single input and a single output time series and calculate the coherence $\gamma^2$ between them. ...
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Signal squared in time domain

In some publication I have found a formula that for some reason squares signal in time domain. I am analyzing it now. What should be the Fourier transform of a signal that was squared in time domain? ...
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CMV: COLA constraint is not necessary

In the literature on the short-time Fourier transform (STFT) it is often stated or implied that the constant overlap-add (COLA) constraint must be satisfied in order for the STFT to be invertible. ...
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Wikipedia equation for DFT seems to be bad?

I was writing a simple fourier transform implementation and looked at the DFT equation on wikipedia for reference, when I noticed that I was doing something differently, and after thinking about it ...
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Understanding Magnitude Spectrum of Images [closed]

I am facing problem in reading Fourier domain of a given image. I don't understand what to interpret from it. For instance, consider this image. Ok, so there is a dot in the middle, with some ...
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Why Derivative/Integration in time domain act as Highpass/Lowpass filter in frequency domain respectivly? [closed]

It is one of Fourier transform properties
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Demonstrate that $x(t)$ and $\hat{x}(t)$ are orthogonal

I have to demonstrate that a function $x(t)$ and his Hilbert's transform are orthogonal, it is said: $$\int^{\infty}_{-\infty} x(t) \cdot \hat{x}(t) dt = 0$$ I have tried the exercise using Parseval'...
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Why is the size of the output of the FFT of a signal is same as the size of the input signal?

I am kind of new to the DSP domain. I was trying to get the frequencies associated with a signal by performing FFT over it. I used numpy.fft.fft for this. ...
Understanding where the constant $2/N$ comes from in Fourier transformation
I'm implementing Fourier transformation in my analysis and I wanted dig a bit deeper on the reasons why the absolute value of Fourier transformation is usually multiplied by the constant $2/N$ to get ...