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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Malaysia Flight 370 Image Processing

I wish that all those people on that flight were with us, and maybe they still are, as I like to think they are on an island somewhere waiting to us to find them ... however, it does not look good... ...
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Fourier Transform Computer Vision Textbook

I am required extremely fast to fill the gap and learn Fourier Transform with application in Computer Vision. It was easy to find mathematical aspects of Fourier Transform, but I am more interested ...
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How to get coefficients for sine/cosine function from complex FFT?

I'm working on a control system that measures the movement of a vibrating robot arm. Because there is some deadtime, I need to look into the future of the somewhat noisy signal. My idea was to use the ...
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How to do Frequency Scaling on an Audio File

Please excuse me if my terminology is wrong. I'm from a music production background and have no experience in signal processing. I was wondering if it was possible to stretch out the overtones (...
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Checking Parseval's Theorem for Gaussian Signal by Using Scipy

I'm trying to check Parseval's theorm for Gaussian signal. It's well known that fourier transform of $\exp(-t^2)$ is $\sqrt{\pi}\exp(-\pi^2 k^2)$. So I implement it by using quad and simps. I think ...
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Calculating SPL from pressure signal - Amplitude vs Power method

I have a pressure signal from a Fluent FFowcs-Williams Hawkings acoustics analysis. I converted this pressure signal into the frequency domain in order to get SPL values, using Matlab. I used the ...
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disadvantages of FFT, it can not extract enough frequencies without enough samples

Let's say sampling rate is $Fs = 44\mathtt{kHz}$, now I have $N = 2048$ samples, then I can get $N/2 + 1 = 1025$ frequencies. I'm confused by Matlab's FFT documentation that says the frequencies are ...
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FFT method input argument have to be $2^n$ ?

Does FFT method input argument have to be power of 2, i.e, $2^n$ I just realized there are many algorithm for FFT implementation,...
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Determining the period of a discontinuous function

I'm new to the field of DSP. I'm trying to determine the period and shift of the function. I've tried using FFT, but haven't had much luck. Seems like it should be simple. Signal (pastebin of ...
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Find h[n] using DTFT properties

Using the DTFT property, find h[n] of a system where: Is it an FIR or IIR system?
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Convolution in frequency domain

Simple math question. The convolution theorem states that multiplication in time domain is equal to convolution in frequency domain and vice versa. There is a condition that the signal has to be ...
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I was watching a youtube video for the duality property for continuous time Fourier transforms, which shows that if Fourier transform of $x(t)$ is $X(\omega)$ then Fourier transform of $X(t)$ is $2\pi ... 4answers 385 views What is Frequency Resolution? Im trying to tackle the following problem while still not having a firm idea on what "frequency resolution" means : Suppose we sample a continuous time signal with sampling period Ts = 1/2000, and ... 2answers 1k views Are the FFT coefficients symmetric in image processing? On page 11 of Fundamentals of Image Processing by Ian T. Young, Jan J. Gerbrands, Lucas J. van Vliet (pdf) the results of the Fourier transform are shown (Figs 4a and 4b) and it appears to me (please ... 3answers 3k views Centered Fourier transform What is the difference between the non-centered and centered Fourier transforms? In other words, when should you use one instead of the other? Non-Centered:$\quad \displaystyle X_1(f)=\sum\limits_{n=...
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My understanding of DFT is as follows For a signal $x[n]$ of finite-length, the DFT is DFS of the periodic extension, $\tilde{x}[n]$, of that signal $x[n]$ and also another way to view DFT is that itā...
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Fast Hartley Transform Implementation in MATLAB

I want to implement Fast Hartley Transform (Specifically Discrete Hartley Transform) in a script file in MATLAB. Does anyone know have a reference implementation of this in MATLAB or another language ...
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Can you decimate / downsample a signal in frequency domain just like you can interpolate / upsample it?

To interpolate a signal I can just zero pad it in the frequency domain. If I want to decimate the signal, can I just discard some part of the frequency domain? So in MATLAB this works: ...
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Fourier series expansion of $\exp[-j2kA\sin(\omega t)]$

I've been going through this paper where we exploit the well known Fourier expansion of the model signal as shown in the image below. I've never come across this well known fourier expansion before. ...
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How to Flip Spectrum Around DC?

Is it possible to flip a signal's spectrum around DC? I have a simple spectrum that I made up (MATLAB code): ...
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Regarding Bode plots; $H(s)$ and $H(j\omega)$

In circuit analysis, I understand the use of Laplace Transforms to obtain the impedance of a linear RLC circuit, ie transforming from the time domain to the frequency domain. In most texts I have seen ...
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Why do we have to rearrange a vector and shift the zero point to the first index, in preparation for an FFT?

I am trying to learn how to implement the FFT as a way to approximate the continuous-time Fourier transform, and as a "nice easy example" I have chosen to test it with a simple Gaussian pulse in the ...
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Why Does 2D FFT of Gaussian Looks More Sharper than Gaussian Itself?

I am trying to understand why 2D FFT is done on a Gaussian process in a particular code. From my understanding from these posts: https://www.researchgate.net/post/...
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Is there a name for the procedure of taking the FT over separate consecutive small time-blocks?

Suppose we have a continuous time-interval $I=[a,b]$, and a signal $x \colon I \to \mathbb{R}$. A procedure that is sometimes carried out (e.g. when doing bispectral analysis) is to partition $I$ ...