# 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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### DTFT based Frequency Sampling

H($e^{jw}$)= 1, |w| < $\pi/2$ and 0, $\pi/2$ <= |w| <= $\pi$ I took M equally spaced frequencies from 0 to $2\pi$. If we assume h[n] to be causal, $H(e^{jw})$ should have some phase and it'...
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### Why does an anti-symmetric function has zero amplitude at the center of an even length window

I am performing FFT on a real odd function and the resultant transform has zero amplitude in the last bin. Essentially if Y= rfft(X), then Y[-1] is always zero. I stumbled on this answer which says ...
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### Real Fast Fourier Transformation (FFT) in 2D changes with changing the axes order

I am using Python to calculate the real FFT for a 2D array. I found that the real FFT function does not return an array with the same size as the input array, rather, it returns an array with the same ...
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### Multitaper F statistics

I'm having some problems interpreting the F-statistics output from multitaper analysis. To illustrate, the following code-snip in R performs multitaper analysis on the same sine-frequency but with ...
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### Scaling factor for comparing spectrums obtained via Continuous Fourier Transform and Discrete Fourier Transformation?

Essentially I am trying to calculate the Bremsstrahlung spectrum numerically for magnetized plasma and want to compare the resultant spectra with the standard textbook spectrum formula for ...
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### Apodization in the Fourier (frequency) domain on discrete experimental data

Let us assume we had time domain signal as a raw data R (Window 1) and we wish to perform the deconvolution process on R using another set of raw data G (window 2). This is accomplished dividing FT of ...
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### How to find fundamental frequency of two signals?

I am facing difficulty with finding fundamental frequency of signals I mean by fundamental frequency=(1/Time period) Correct me if I am wrong consider two continuous time signals with Time period ...
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### Is it possible to extract peak locations in the time domain using help from fourier/wavelet analysis?

The signal I'm studying has fundamental frequencies of 20 and 60 cycles per minute (shown in the Periodogram graph). It is straight forward to extract the peaks in the time domain belonging to the 20 ...
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### Detecting changes in signal due to server delay

I'm currently working on an application that can be used to determine when a signal changes due to a server delay. Essentially, I have an API that is used to output data to a UI. However, for reasons ...
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### What's the significance of lomb-scargle power?

What is the significance of Lomb-scargle power (y-axis)? I have two data sets. For each plot, above plot is Lomb-scargle periodogram of the lower plot (original data). The first data set has an ...
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### Python FFT outptut

I have a (real) array of data and am trying to analyze its frequency components. I've been using NumPy's FFT routines, but I realized there is something I don't quite understand: why does the output ...
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### How to normalize PSD to get the same magnitude as FFT peak

I am trying to use FFT and power spectra density estimation with python (np.fft.fftand scipy.signal.periodogram). And trying to ...
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### Symmetry in Lomb-Scargle transformation

I'm observing weird symmetry and repeating pattern on my unevenly sampled time series data after Lomb-Scargle transformation. I used astropy lomb-scargle. ...
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### Correlation/anticorrelation as a function of frequency

I am tracking the values of two fluctuating quantities as a function of time and am trying to analyze possible correlations between the two as a function of frequency. The application is experimental ...
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### inverse discrete fourier transform with plain python

I am trying to calculate inverse discrete fourier transform for an array of signals. I am using the following formula: $$x[n] = \tfrac1N \sum\limits_{k=0}^{N-1} X[k] \, e^{j 2 \pi k n/N}$$ And my ...
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### Plot Frequency Spectrum of Binary Sequence in Matlab

I am new to Matlab and I am trying to implement a section of a published paper, the basic idea of the part that i am implementing is to show the frequency spectrum of camera aperture. The shutter ...
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### Overlapping in real time fourier transform?

I have an algorithm and I need to record audio and perform short time Fourier transform to obtain which frequency is the most common. I am using a Hanning window to try and reduce spectral leakage as ...
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### Matlab FFT not producing symmetric spectrum

I am plotting a FFT of a sampled RC pulse but my resulting spectrum isn't symmetric - it's offset. ...
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### Fourier transform pair for $ln(ln(…))$ cascade?

I need to analyze real signals $y_i$ in the frequency domain. $y_i$ are defined like: $y_1 = ln(ln(x))$ $y_2 = ln(ln(ln(x)))$ $y_3 =~ ...$ $...$ Are there Fourier transformation pairs for this ...
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### Using MATLAB to plot the input and the magnitude spectrum of the signal

I have an aperiodic signal $v_{out} = e^{-t} u(t)$ (real exponential signal) from discharging capacitor. I was trying to plot using MATLAB 15 seconds of this signal in time domain? I am thinking how ...
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### Low pass filter transfer function

I am calculating the transfer function of a low pass RC filter and I have gotten $\frac{1}{1+jωRC}$ which is correct. But somehow it seems $ωRC = \frac {ω}{ω_0}$ that refers to the cutoff freqency ...
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### How to find Fourier series coeffecients of convolution of two periodic continuous functions with different time periods?

Above given is my solution Plz check if it is correct and I got struck at last step .Plz help
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### On the spectral representation of deterministic and random signals

I went back to many references in order to fix some of the confusions that I have on many concepts in signal spectral representation. I concluded that: 1) Deterministic signals may be represented ...
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### Seperating two (image) signals in Fourier Space / Denoising

i have a problem here which is not so easy to solve. I have a measurement system which provides me two signals: -The "contrast" channel" - this is the main channel on the object -A second channel ...
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### Finding n Amplitudes by DFT, what is correct normalization

Please forgive me if this has already been asked. Let us assume an example with $x(t) = \sum_{i=1}^N A_i \sin(2\pi f_i t)$ under a given sampling frequency $f_s$, frequencies $\omega_i$ and ...
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### Is there a way to find a picture inside another picture, using only 2D Fourier Transforms of both images?

Can Fourier Transforms of both images tell anything about "likeliness" of two pictures? If yes, how precise? Can it still work if only several pixels are different or can it tell they are same if one ...
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### Why are patterns repeated in the frequency-power graph of a periodic signal?

The original question was posted here. I have a signal, which I'd like to treat as a non-continuous function now, let it be $signal(t)$. It looks like this: Zoomed in a bit: I create a Lomb-Scargle ...
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### Artifacts observed in STFTs computed with C++ library FFTW3 or NE10

In one of my projects, I have to compute stfts with audio signals coming either from a microphone or a .wav file in a C++ based program. However, I am observing different artifacts due to my stft ...
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### Wide-Band Lorentzian FDTD Algorithm

I want to convert a simulated gain/absorption of a material, which can be understood as a discreet (dispersive?) function $g_i(f_i)$ ($f$ is for frequency) or $g_i(\lambda_i)$, into $\tilde g(t)$ for ...