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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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How to utilize product graphs in graph signal processing?

I'm working with dynamic graph signal processing. How to plot time variation and spatial variation separately and take the cartesian product of those two graphs? Any relavant Matlab codes?
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Why Does This Sliding Window Goertzel Filter Trick Work?

I'm reading an analog signal at a constant interval on an embedded device, and I want to extract a specific frequency component. Since the signal is continuously being read I want to constantly scan ...
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Sinc droop in a simple sampling mixer

This question is about the conceptual interpretation of a track-and-hold mixing operation implemented conceptually below, where an output $y(t)$ tracks an input $x(t)$ for half of a period $T_{LO}$ ...
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How does MATLAB's edgetaper function work?

MATLAB has a function edgetaper that does something I haven't seen before: J = edgetaper(I,PSF) blurs the edges of the input ...
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For the square wave signal, why does a narrower square wave correspond to more spread in the frequency domain?

Consider the square wave. As we decrease the pulse width $T_1$, it seems that the positive Fourier coefficients (located in the central area/lobe) are spreaded out across more frequencies. In fact, if ...
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How do I properly compute a convolution kernel given the convolved and initial signal?

I'm trying to for solve for $ b $ in the equation $C = a*b$ where $C,a,b$ are 1D arrays of size $k$. $F(b)$ is also $= \frac{1}{|F(a)|}$. I have tried doing the following procedure in order to isolate ...
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Is the analytical fourier transform of an exponential decay the same as the FFT of a time series of the same signal?

Analytical Fourier Transform of $e^{-t/2}$: FFT of a time series representation of $e^{-t/2}$: I'm trying to find the decay coefficiencts in tri-eponential decay signals, and as a logical starting ...
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Fourier Transform of product of sinc function and its raised powers

Is it possible to find the fourier transform of $$\left(\frac{\sin(x)}{x}\right)^3$$ and $$\frac{\sin(x)}{x} \frac{\sin(x^2)}{x^2} $$
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How should I go about completely decorrelating a digital signal?

So I'm working on real time signal compression, and I need to come up with the best convolution to minimize the entropy of incoming data (which I will then compress), which I understand is achieved by ...
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Problem observing the correctness of a Fourier transform property

I'm studying "Signals & Systems" by Oppenheim et al. On page 391, for a real-valued $x[n]$ whose Fourier transform is $X(e^{j\omega})$: $$x[n] \leftrightarrow X(e^{j\omega})$$ $$\...
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Rigorous derivation of autocorrelation of white noise

It is said that the autocorrelation of white noise is the dirac delta function $\delta(\tau)$, but I don't know how to derive that... Since white noise is a function with constant power spectral ...
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Comparing Spectral Leakage in Sine and Cosine Functions

I am not from a signal processing background, kindly excuse me for my vocabulary. When I compute the power spectrum of a periodic function, where the "real" space variables are generated by <...
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Why is white noise uncorrelated for any two different samples?

Consider white noise with spectrum density $N_0/2$, it is known that the autocorrelation is given by: $$R(\tau) = \frac{N_0}{2}\delta(\tau)$$ Meanwhile the definition of delta function in the ...
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Can I get a resonance frequency from FFT power spectrum result?

I'm going through vibration analysis of cantilever by using FFT device but impact hammer input data isn't showing for some reason. So instead, I'm trying to get the resonance frequency by acceleration ...
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FFT comparisons between g.USBamp software vs BCI2000 software

Update: I followed the instructions in g.USBamp Demo how to download the codes into Matlab (btw the product page is at https://www.gtec.at/product/gusbamp-research/ ) Here is the exact Matlab code ...
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very basic confusion about the bandwidth of constant signal function

I have a very basic question about bandwidth of constant function $f(t) = K$. As the Fourier transform of a constant pulse is a delta-function centered at zero frequency, the bandwidth (maximum value ...
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Taking an FFT of a signal that wraps around

I have an embedded application that does some phase modulation and streams back the phase offsets it's applying over UDP. I now want to take the FFT to see the spectrum of the applied modulation. ...
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Decay of the impulse response for poles contained in the unit circle

I've been struggling with the following exercise in Ljung's "System Identification: Theory for the User" (Problem 3G.1): Given a rational transfer function $G(z)$ such that its poles are all ...
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Fourier Transform and Audio Processing

Most audio capturing software automatically distills the audio into distinct frequencies with Fourier transform. This makes audio editing much easier. I have a project where I want to show the ...
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Fourier series - finding its period from frequency representations

I’ve been given the following signal: $$X^F(\omega) = \sum_{n=-\infty}^{\infty} 2\pi a[n] \delta(\omega - \omega_0 n)$$ and I was asked to: find it’s period given $|X^F(\omega)| \ne 0$ only at $|\...
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Morlet wavelet convolution

I use a simple formula (without normalization) from Mike Cohen's "Analzying neural time series data" book. \begin{align} \psi \left( t \right) &= e^{-\frac{t^2}{2 s^2}} \cdot e^{2 \...
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Border effects / artifacts for spectral filtering of images

I am working on a spectral filtering problem as follows: I'm given an image with a periodic distortion pattern (see below), and I want to remove the distortion pattern while preserving the main ...
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realistic sampling - where am I wrong?

I’m given a signal $x(t)$, it's convolved with $h(t)$ and sampled at rate T=1. The result is called $\tilde{x}[n]$. For $$h(t) = \begin{cases} 1 & -0.5<t\le 0.5 \\ 0 & \text{else} \end{...
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Expressing Frequency Bins as Period Bins

I'd like to change the x-axis of a Fourier transform frequency domain bar chart from frequency bins to period bins so that instead of displaying Hz or cycles/sec, I'm displaying sec/cycle; however, I ...
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Why the Discrete time fourier series coefficients of a real discrete time periodic signal are not symmetric about y axis?

If the signal is something like cos(πn/3) , we get the two DTFS coefficients that are symmetric about y axis and the resulting frequency spectrum is an even function . Now take the example given in ...
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Signal response amplitude depends on the time interval in simulation

I have already tried to look for an answer, but I do not find existing answers satisfactory. I am interested in the absolute value of the response function of a damped oscillator (or any time series). ...
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What Are the Units of a Fourier Transform? [duplicate]

I know that a Fourier transform (FT) outputs a distribution of how much of each frequency is present in a signal, but what would be the units of that distribution? It's not a proportion or a percent ...
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FFT2 to RFFT2 Fourier plane and similarities

I'm trying to understand how Python's fft2 is different from irfft2. Basically, I have some continuous Fourier 2D samples that I need to put in a (n,n) grid (this can be done by a simply count-in-cell ...
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Is the magnitude spectrum of the Discrete Time Fourier Series of a Discrete Time periodic Signal , an even Function?

We know that the magnitude spectrum of a continuous time fourier series representation of a real periodic signal is an even function (i.e. symmetric about y axis). Does this hold true for discrete ...
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Real-world examples of unweighted directed graphs

Social Networks, Internet Traffic, Citation Networks, Transportation Networks, and Biological Networks exemplify real-world instances of unweighted directed graphs. Within these domains, the Graph ...
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Comparing custom Welch periodogram with Julia's Welch periodogram

I wrote my own PSD struct in Julia for practice purposes. It involves two type of constructors: a "direct" PSD and a <...
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What factors could affect the scale of PSD estimation?

I was required to program a function in R to estimate power spectral density of EEG data. The function I created is, I think, rather standard, and estimates the PSD of a signal by computing $$ \frac{2|...
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transform time series different length and sampling rate with frequency domain

i want to transform my time series (each same scale) to frequency domain. There are 2 things to conside: some time series are longer then the other i have different measuring intervals which means e....
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Effects of Hanning window on power

I have written this function in R to compute the power spectrum density (PSD) of a signal: ...
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How do you properly cut out negative frequencies from FFT of a real signal if it reduces sample size?

If a real time signal has $N$ samples, then the magnitude of its FFT will also have $N$ samples--half of which will have positive frequencies and half of which will have negative frequencies. The ...
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Fourier transform processing of iq data

I want to perform fourier transform on the iq data that is taken from spectrum analyzer. The purpose is to estimate phase noise from iq data.
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Channel impulse response (CIR) and OFDM relationship

In Chapter 3 of the [Goldsmith book] (https://faee.sut.ac.ir/Downloads/AcademicStaff/1/Courses/7/Andrea%20Goldsmith-Wireless%20Communications-Cambridge%20University%20Press%20(2005).pdf) we can see ...
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Looking for an online course

I work for a company with expertise in electromagnetics physics, specifically dealing with time domain-based simulation software. We routinely need to transform our results into frequency domain, ...
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Extracting Musical Notes from two audio samples, then providing feedback to the second one based on first one, weekend project or need to learn more?

I am a second year Electronics student attempting to make a mini project in audio analysis. I am thinking about using FFT to convert and then compare the two audio signals, first one being the "...
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Why i am not getting same convolution plots?

I am trying to implement convolution using fourier transform property but i am not getting exactly same shape of output that i get by using conv command First portion of graph obtained using conv ...
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Need help understanding FFT for timeseries analysis?

I am studying the seismo-ionospheric anomalies associated with the Japan earthquake using total electron content derived from a GPS signal. I am trying to detect acoustic-gravity waves in the signal ...
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Frequency response

in 2.104 he put a condition that x(t) must be an exp to use this result ,but in 2.108 he did't even know what the value of x but use the result to get y i know that he decompose x(t) to group of exp ...
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Axis Units for Discrete and Continuous Fourier Transform

Hello I have the following question in regards to what the units should be for the y axis for a continuous time Fourier transform and that for a discrete time Fourier transform. In my understanding if ...
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Why in 2D Fourier Transform phase seems to be more "useful" than magnitude?

In 1D signals f(t) (e.g. a sound signal - independent variable t-->time) when we want to use informations from the Fourier transform F(ω) in order to reconstruct the signal, using the magnitude |F(...
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Since harmonics only generate at multiples of the center freq, is it for this reason that the left part of a FT (like sinc) has no physical meaning?

If we have a rectangular pulse function, we know that after a Fourier transform we obtain a sinc: We know that the left part (negative frequencies) has no physical meaning and it's just specular. It'...
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Predicting the "amplitude" of a damped sine wave from FFT

For a sine wave, $A \sin(\omega_0 t)$, with an amplitude $A$, after FFT and calculating the magnitude spectrum we can get a single peak with a height also equal to $A$. This requires proper scaling. ...
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How am I supposed to acquire/measure vertical and horizontal effective resolution from my images?

I apologize first for some questions that might be dumb. Unfortunately, I am only a bachelor student (writing my bachelor thesis in physics) and have almost zero image processing experience. And I ...
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Combining Three Images into One Output Image Python

I have to combine three images that are inside one single image into one output image in Python. This has to be done using Gamma corrections, Histogram equalization, filters convolutions (gradient, ...
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Fourier Coefficients of Sawtooth Wave

Following this link, we can see that the magnitude of the $n^{th}$ harmonic of a sawtooth wave is equal to: $$ V_n = \frac{Vpp}{(n*\pi)} $$ Converting that Matlab code (the code at the end of the page,...
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How can I denoise this signal?

I have data captured by a wireless sensor that is noisy. It randomly jumps in value frequently, and I want to know what this signal will look like without these jumps. I am looking for an elegant ...
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