# 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 identify the frequencies of periodic peak signals in a noisy time series?

Suppose to have two time series with peak signals at different frequencies, like these two: ...
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### Cepstrum of white gaussian noise

What are the statistics of the cepstrum of gaussian white noise? \begin{align}\newcommand{\Nfft}{ {N_{\mathrm{FFT}} }}\DeclareMathOperator{\FFT}{FFT}\DeclareMathOperator{\IFFT}{IFFT} x_i &\sim \...
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### $2\pi$ Periodicity is not working for me for Fourier of Discrete Time Signal

please help me find the error in the following counter example. Consider we take sinus with period of $2\pi$. We sample it many time, and more than 3. We make convolution with rectangle of height 1 ...
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### STFT of ISTFT in the Griffin Lim Algorithm

The Griffin-Lim algorithm for phase recovery (based on the magnitude of an STFT) involves a step that is: STFT(Inverse STFT(...)). This seems to be the key iteration in the algorithm. This Quora ...
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### How will magnitude and phase spectrum of an imaginary function would look like? Like if $x(t)=j \text{rect(t)}$. Is phase spectrum even or odd?

I am confused between when a phase spectrum is odd and when it is an even function of $\omega$(angular frequency, Fourier transform variable).
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### Finding the frequency response $H(\omega)$ of a shifted sinc function

Given $$h[n]=\frac{\sin\left(\frac{\pi}{3}n-\frac{\pi}{3}\right)}{\pi n-\pi}\text,$$ use the table to find the frequency response $H(\omega)$. I don't have any clue that how to deal with the ...
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### Rule of thumb / Best practice for Audio (voice) data normalization for use in Classification

TRIVIAL QUESTION: I am currently working with some audio data of speech utterances. I am attempting to perform classification on the data based on the phonemes. This means that I manually label the ...
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### How to apply FT to real-life signal that labeled in seconds, not radians

In training examples we always do a transformation on signals which have t-scale in labeled in radians. I understand that Pi is just a number, but I still have some troubles to understanding how to ...
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### Time domain to frequency domain conversion of audio signals to extract 1/3 octave frequencies

I am writing first time in this forum and I am not expert in programming and FFT. We have developed an android app (Noise Tracker) for noise measurement using smartphones. It displays noise levels in ...
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### Resources to understand DSP visually in 2020

I know you have been asked several times but the questions are old, and I would like to know if there are new intuitive web pages of applets or interactive DSP animations (Filters, FFT, Wavelets)
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### non-consistent normalization problem in fft

I have a csv file of data sampled with Ts=1ns which looks like this: This signal is a step response of some system which responds to a step of value 1. I'm trying to get the impedance profile of the ...
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### Deriving expression for the DTFT of a rectangular window

Looking at the picture above, how did the author get from point A) to B)? My Approach: Multiply A) by $e^{j\omega/2}/e^{j\omega/2}$. Now I am stuck with simplying the numerator.
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### Partial column approximation error

Can someone help me understanf how to plot the next partial column in MATLAB: while N=2001 |M|<700 ak =
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### Fourier transform of t*rect(t)

In my previous post I asked for help for a Fourier transform of $$t \text{rect} ( t- \frac{1}{2} )$$ and I think I’ve understand the process. Now I’ve 2 another similar Fourier transform to do , I ...
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### Scalable gaussian window

I would like to determine fractional fourier transform of scalable gaussian window function Can I get help on implementing g(t,u) in MATLAB?
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### Why is my Fourier descriptor not rotation invariant?

I am trying to implement a simple contour based Fourier descriptor to classify some MNIST images. Nothing fancy. As expected, if I discard the first coefficient, I achieve translation invariance. ...
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### What is the relationship between a signal's Marginal Hilbert Spectrum and Fourier Spectrum?

I am looking at the differences between Marginal Hilbert spectra and Fourier spectra and I was wondering what the mathematical relationship is between them and under what conditions they become ...
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### Energy of a sinc signal

My book give me two signals to demonstrate that the temporal translation does not alter the energy and area. It gave me $$x(t)=\operatorname{sinc}(t)$$ and $$s(t)=x(t-T)$$ and I found that ...
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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 ...
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### 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 ...
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### 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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Suppose you have an LTI system for which the (complex) frequency response $H(j\omega)$ has been measured in some frequency window $[\omega_1,\omega_2]$. Now imagine that you want to provide an input $... 0answers 17 views ### Formula for PSD across an axis of a 2D output Consider a 2D stationary input$e(x,y)$and a 2D real convolution function$h(x,y)$. Let$S=h*e$be the result of the convolution of$e$by$h$. If needed, we may assume$e$is isotropic (spectrum ... 0answers 26 views ### I want to invert my fourier transform components to waves again Hi I am using R to analyze some data I basically did fft(data) and got a vector of complex numbers but from that now I want to remove certain harmonics from my actual wave but how do I convert one of ... 1answer 41 views ### Fourier transformed acceleration from Fourier Transform of velocity and position using Omega arithmetic Let's say the position of an object is given by simple sine function. By elementary calculus, I can calculate the acceleration in the time domain and find its Fourier transform. I can also calculate ... 0answers 81 views ### Convolution of a non-symmetrical window function by a cosine signal in the frequency domain A have a time signal: The associated DFT spectrum of this signal: The time signal can be considered as a non-symmetrical rectangular window function multiplied by a cosine signal with a frequency$...
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 ...