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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Impulse response of a 3x3 PSF - how to find analytical expression for fourier transform of a 3x3 matrix?
I have a filter $\mu[n_1, n_2]$ with taps:
$$ (1/8) (1/4) (1/8)$$
$$ (1/4) (1/2) (1/4)$$
$$ (1/8) (1/4) (1/8)$$
How do I find an analytical expression for $\hat\mu(w_1, w_2) $?
Since it looks so ...
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Fourier transform 4 times = original function (from Bracewell book)
I was glancing through "The Fourier Transform & Its Applications" by Ronald Bracewell, which is a good intro book on Fourier Transforms. In it, he says that if you take the FT of a function 4 ...
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Is there any practical application for performing a double Fourier transform? …or an inverse Fourier transform on a time-domain input?
In mathematics you can take the double derivative, or double integral of a function. There are many cases where performing a double derivative models a practical real-world situation, like finding the ...
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STFT on time varying signal with good time and frequency resolution
I am trying to determine the main frequency of a noisy signal that varies in frequency over time. Ideally I want to detect changes in the frequency as rapidly as possible - say 50Hz update rate, but I ...
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1answer
680 views
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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1answer
243 views
Detection of Troughs and Notches in a PPG Signal
I'm working a project which tries to determine Blood Pressure from PPG signals.I'm trying to extract the features as shown below...
I'm having problem in finding the troughs and dicrotic notch for ...
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Two versions of Constant Q Transform (CQT) doesn't match each other?
To my knowledge, there's two major CQT papers, the one by Brown in 1991, and the one by Schorkhuber in 2010.
The 2010 paper claims to be a more computationally efficient implementation of the 1992 ...
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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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What are the statistics of the discrete Fourier transform of white Gaussian noise?
Consider a white Gaussian noise signal $ x \left( t \right) $.
If we sample this signal and compute the discrete Fourier transform, what are the statistics of the resulting Fourier amplitudes?
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Determining LTI system response to a scale change
We know that for an LTI system, if $y(t)$ is the output for $x(t)$ then the response for $x(t-2)$ will be $y(t-2)$ and so on.
But my question is what will be the system response for the input $x(-2t)$...
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Non Circulant Translation Using Fourier Transform
The translation property of Fourier Transform (FT) for a two dimensional image $f$ is as
$$
f(x-x_0, y - y_0) = F(u, v)e^{-j2\pi(ux_0/M+vy_0/N)}
$$
Using this equation, the following code (in Matlab) ...
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2answers
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How to reconstruct a sound from magnitude spectrogram?
I have an audio magnitude spectrogram but I don't have the phase, try to randomize the phases of each container and then make a reverse fourier, but only pure noise is heard
How can I reconstruct the ...
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How can I relate my amplitude from a FTT to the actual signal?
Sorry for disturb you guys, I've been playing with this the last days. I am computing signals of a wave produced with a wavemaker. Cause I have several sensors (wave gauges) I am sensing the same wave ...
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1answer
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Graph Fourier transform: the adjoint notation for the eigenbasis matrix
I already asked this question here but there is no response. I'd like to ask this question in signal processing domain.
It is well-known that for a real symmetric matrix $L$ (here, graph
...
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2answers
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Sinc interpolation in spatial domain
I have tried to perform sinc interpolation (in 1D) with the following Matlab code:
...
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How to Combine Low and High Frequencies of Two Images in MATLAB?
I would like to combine two images A and B in the following way:
1) I want to take a Fourier transform of both of them
2) For image A I want to apply a weighted filter, which gives more emphasis for ...
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What Are the Suggested Resources for Extensive Knowledge About the Fourier Transform (DFT, FFT, etc…)? [closed]
I would like to improve my knowledge about Fourier Transform related subjects.
What are the recommended resources in order to self study about it?
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how to reconstruct an phase information from the magnitude spectrogram
I need to recreate the phase of a spectogram of magnitude and when inverse fourier, that the sound is understandable and not pure noise
Observe these softwares
https://photosounder.com/
http://...
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How do I perform Spectral Analysis (FFT, Windowing, Detrending) on Sonic Anemometer Data?
I am having trouble with all of the forums that I have looked at thus far.
I have one day's worth of Sonic Anemometer data. I want to see the spectral analysis of this data. When the anemometer data ...
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1answer
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FFT and Power Spectrum Normalization
On many websites, including MathWorks, it was suggested to normalize the fft spectrum (MATLAB or numpy) by dividing it by the total number of samples ($N$). For a sinusoidal signal, for example:
$$x(...
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Is Fourier series a sampled version of Fourier transform?
I recently learned about dtft and how dft/dfs is the sampled version of dtft. I was wondering if Fourier series is also obtainable by sampling Fourier transform? I am a noob in the subject so sorry if ...
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Figuring magnitude and phase response
I've got a linear time-invariant system $$y[n]=\frac{8}{9}y[n-1]+x[n]$$
which I transformed into a transfer function $$Y(z)=\frac{8}{9}Y(z)*z^{-1}+X(z) =>\frac{Y(z)}{X(z)}=\frac{1}{1-\frac{8}{9}*z^{...
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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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Phantom harmonics when using cosine windows why do they appear and how to avoid them?
Given an L order cosine window, it is possible to show that the width of the main lobe is given by:
$$\omega_w = \frac{2 \pi L}{(2N+1)}$$
Where $L$ is the order of the window, $N$ is the maximum ...
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2answers
950 views
Problems Using FFT to Compute Impedance in a Model Neuron
I'm a neuroscientist currently investigating the resonance properties of a single neuron model that a colleague and I have constructed. The language we code in is Julia, which I hope is similar enough ...
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1answer
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Estimation / Reconstruction of an Image from Its Missing Data 2D DFT
Given the 2D DFT of an image i.e. a NxM matrix of complex numbers, with some missing lines (or even partial lines), considering we have zeros in the missing positions.
Any suggestions for an ...
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2answers
87 views
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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1answer
691 views
What's the difference between using DFT, IDFT or DCT to calculate cepstrum of a power spectrum?
I've seen different equations that calculate cepstrum from power spectrum, but the equations are not consistent. Some people use Fourier transform, some use the inverse Fourier transform, and some use ...
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2answers
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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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Is the whole data needed for the fast fourier transform with an ongoing signal?
I sample an signal with around 840k values a second, to check the spectrum around <400kHz. But i can't save the whole data as it is just to much for my microcontroller. I know that for the ...
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What effect does rotation in the spatial domain has on phase in Fourier transforms?
More precisely, let's say I apply a 45 degrees rotation to an image (in the spatial domain) say, in Matlab :
Ir=imrotate(myImage,45,'crop');
FT_I=fft2(I);
In the ...
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2answers
481 views
Separation of overlapping frequencies
I have a signal with multiple frequencies, and two of them, one of which is my main frequency, overlap.
Are there any techniques that could separate two frequencies that almost overlap?
I can ...
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1answer
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Is fft2 in MATLAB unitary? Some differences happen
I meet a problem when implementing fft2 in MATLAB.
The question is I try to simulate the realistic measurements $Y = |FCXF^H|^2$ - the intensity of Fourier domain of object $X$, where $F$ denotes ...
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What's the difference between the Gabor-Morlet wavelet transform and the constant-Q transform?
At a glance, the constant-Q fourier transform and the complex Gabor-Morlet wavelet transform seem the same. Both are time-frequency representations, based on constant-Q filters, windowed sinusoids, ...
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Fourier Transform of ECG signal in Python
I have an ECG signal which I am analyzing using Python, as opposed to the mainstream MATLAB. So, I have digital form ECG in .dat file with .hea (header file). Below is the Fourier transform
The ...
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1answer
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Fourier transform in Matlab and hermitian symmetry
According to the conjugate symmetry property of Fourier transform, shouldn't the following command not return 1 (=true):
...
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Implementing rotation in frequency domain and map it back to spatial domain
Please consider the following small example:
...
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“The Fourier transform cannot measure two phases at the same frequency.” Why not?
I have read that the Fourier transform cannot distinguish components with the same frequency but different phase. For example, in Mathoverflow, or xrayphysics, where I got the title of my question ...
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1answer
258 views
Normalized cross-correlation in frequency domain
I never worked with signal processing and never really used Fourier transforms before, still I am working on a project consisting on taking the output of an accelerometer to detect some movement ...
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1answer
111 views
Use samples of Fourier transform as DFT?
Consider the LTI system given by: $H(z) = 1 - \frac{1}{2}z^{-1}+\frac{3}{4}z^{-2}$
Let $x[n] = (\frac{1}{2})^nu[n]$ be the input to the system. We want to find the output for $n = 0,1,...,N_a$, using ...
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Fourier Transform Identities
We know the below,
$$
\mathscr{F}\big\{x(t)\big\}=X(f) \tag{1}
$$
$$
\mathscr{F}\big\{x(-t)\big\}=X(-f) \tag{2}
$$
$$
\mathscr{F}\big\{x^*(t)\big\}=X^*(-f) \tag{3}
$$
Now, if for some signal
$$
x(-...
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1answer
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Why does my plot of the Blackman window not match everyone else's in literature?
I've seen the plot for Blackman window as so in a bunch of books, as on this website:
But plotting the same equation on Wolfram Alpha yields a different plot:
Why is their graph not centered around ...
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1answer
39 views
Proof that DFT does not require more than N points
I'm trying to show how the discrete Fourier transform (DFT) arises from the equation for the continuous-time Fourier Transform. I've run into an interesting caveat which I can't seem to find an ...
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1answer
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Convolving with the frequency response of a filter
With scipy I can use signal.butter and signal.lfilter on a time signal.
Performing a Fourier ...
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1answer
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Approximating Lorentzian Fourier transform with FFT
I have a Lorentzian frequency distribution
$F(w) = \frac{1+iz}{1+z^2}$
Where
$z = \frac{w-\Omega}{R}$
With $\Omega$ being the peak frequency and R the decay constant. I know that analytically ...
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1answer
40 views
Continuity and its relationship with asymptotic spectral decay
The asymptotic decay of the magnitude of the Fourier transform of a function appears always to be determined by its continuity properties as follows, with examples given in Fig. 1:
Continuous ...
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1answer
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DFT of an audio signal stored as a multi-dimensional array
I'm using the Python scipy library to get the data of a particular .wav file into array format. Now, I'd like to find the Discrete Fourier Transform of that signal. The formula for the DFT is,
$X_k = ...
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Transform a complex impedance from frequency to time domain, and then back to the frequency domain again
I have a circuit which I can calculate the complex impedance by the normal methods to be
$$ Z(\omega) = \frac{1}{\frac{1}{R} + i \omega C_{1} +\frac{1}{i\omega L_{1}} + \frac{i\omega C_{2}}{1 - C_{2}...
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Difference between low pass/ high pass filter vs Discrete Wavelet Transform
In image processing, DWT is equivalent to apply a series of low pass filters and high pass filters to get the details (such as edges) and approximation (such as overall texture) coefficients . In this ...
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Is the FFT magnitudes of multiple audio sources additive?
Is the FFT magnitude of two audio signals when played together the sum of their individual FFT magnitudes across frequency bins? Note I'm talking only about the magnitude, ignoring phase.
For ...
