# 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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### Image zooming with Fourier transform

I want to go from this image into this one: So basically I need to scale the white square. The authors of the paper claim that this can be done in four steps: zero-padding in real space (image is ...
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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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### 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 ...
222 views

### 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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### When Is a Power of 2 FFT Slower than Smaller Sized Non Power of 2 FFT in MATLAB

Knowing that computing an FFT is faster if the amount of samples is a power of 2 I have always tried to pad the inputs to Matlab's FFT with zeros until the next power of 2 is achieved. Matlab's ...
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### Problem identifying the analytic expression of such determined signal

I came across this problem I am supposed to find the Fourier transform of $g(t)$, but I am not able to find the analytical expression of such signal. The teacher suggests that I should consider ...
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### Normalised magnitudes in sliding dft

I am new to signal processing. I am trying to use the output of a sliding DFT to analyse frequency peaks. Take for instance this implementation: https://github.com/bronsonp/SlidingDFT/blob/master/...
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### Compute hilbert transform from DCT- FFTW3 REDFT00

My problem is similar to this but not the same. Edit: Here is a description of Neumann boundary conditions for differential equations: Neumann-type boundary conditions means derivatives are ...
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### Fourier transform of attenuated propagating pulse

I am studying the optical properties of a medium by looking at how a Gaussian pulse is deformed as it propagates through the medium. The initial Gaussian pulse signal and Fourier transform are : \...
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### How to calculate the spatial frequency of an image in cycles per image

I have been attempting to calculate the spatial frequency of a colour image. I first converted it to grayscale and used a Fast Fourier transformation (fft2) that codes the quantity of each spatial ...
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### Determining periodic pattern when there is pattern which period is multiple of former

I have periodic signal, say, it has year period, yearly pattern. I want to check if also has quarterly pattern. Event if there is no visible quarterly pattern, Fourier Transform of this signal has ...
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### How to get the phase offset from the instantaneous phase

The phase components of a signal that they are got from the Fourier Transform, are simply, the phase offset of each sinusiod. Which is the $\phi$ in equation $1$. However, in case of Hilbert transform,...
495 views

### Window size and DFT size

I am using pwelch function of Matlab which returns the power spectral density (PSD) estimate. This got me confused about DFFT size and Windows size. Here my code: ...
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### Fastest way to subtract known music tracks from live videogame audio stream

I want to isolate video game "action" sounds from the video game soundtrack. Given all ~20 songs, I'd like to filter them out from any live audio stream during gameplay. What is a fast and robust way ...
756 views

### Relationship between Wavelet transform and Fourier Power Spectral Density

Is there anyway to obtain the Fourier Power Spectral Density from a wavelet transform of a time series? I am particularly interested in this problem because I was wondering if there is any ...
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### How to get the scale bar of an FFT for a 2d image

I've been analyzing some images from a transmission electron microscope, including their FFTs, and I'm not sure how to apply a scale bar to the FFT images. I have calibrations for the real space image,...
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### Regressing/interpolating between quasi-periodic sinusoids

This is a cross-post (on recommendation) from CV. My problem is very simple. I currently intend on using Kriging (Gaussian process regression) to perform regression between the trajectories marked ...
58 views

### amplitude at exact frequency in wide band signal

Could anyone suggest the most computationaly efficient method for finding amplitude of exact frequency having a noisy wide band signal. To be more specific about a task. I have some physical ...
252 views

### Transfer functions from wavelet transform

So I have this problem where I need to measure the phase of a signal and correct for a delay associated with the travel time of the signal while simultaneously determining the transfer function of my ...
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### How to convert a spatial frequency in a 2D-DFT into the units radians per pixel?

Let's say I have a 2D image, and I take the discrete Fourier Transform (via FFT) of that image. In the frequency domain, I get the following image: In this image, let's just assume all the spatial ...
376 views

### Discrete Fourier Transform for text analysis?

I would like to determine the number of text-blocks verifying a roughly similar pattern. I have the intuition that I could do it using some Discrete Fourier Transform (DFT)-like methodology. Example: ...
1k views

### How do we calculate Power Spectrum Density (PSD) which is given in dB/Hz and not just dB?

I found many definitions for this quantity, PSD. In a document on signal analysis by National Instruments say that it is the amount of power in a unit bandwidth. Let's say P(f) is the power of the ...
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### Fourier transforms of random processes

In the Wikipedia article on Brownian noise, the Fourier transform of Brownian noise is determined. How is that Fourier transform defined? It seems it is a non-random quantity there, so it is not ...
329 views

### Realization of IIR resonator

The measure of a given frequency $\omega$ in a signal $x(t)$ is: $\frac{1}{N}\sum\limits^N_{t=0}x\left(t\right)e^{^{-i \omega t}}$ This is basically an average of the correlation between the signal ...
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### Implementation of the constant Q transform + property questions

I'm reading up on fourier theory, especially the transforms. I implement the math as spectrograms in C++ to get a better understanding of what is going on. I've made an implementation of the short ...
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### inverse discrete FFT in python, multiple times?

I was wondering what really happens when taking the inverse discrete FFT on some set of numbers, for 3 times? Because looking at it, it looks like we're getting an output that is identically with the ...
54 views

### Fourier Transform of the full Morlet wavelet

In 2014 someone asked here the Fourier transform of the Morlet wavelet; link below: Fourier Transform of Morlet wavelet Function? However, it was the approximated Morlet wavelet not written with the ...
89 views

### Getting different spectrum from velocity, and position data using Omega arithmetic

I am solving a very long problem and one part of it requires me solving an ODE and computing FFT of the resultant data. Essentially I have a differential equation$\frac{dz}{dt}$ for velocity, from ...
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### turn circular convolution into linear convolution by zero padding: A special case

We know that, multiplying a kernel and signal spectrum in Fourier domain will lead to a circular convolution and not a linear convolution, so in order to it become linear convolution we must zero pad ...
For a non-uniform discrete Fourier transforms, do the specified frequencies – i.e., $f_k$ in – refer to the midpoint of the bin or the lower bound? I read the answer here, but that stated that ...