# 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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### Fast Hartley Transform Implementation in MATLAB

I want to implement Fast Hartley Transform (Specifically Discrete Hartley Transform) in a script file in MATLAB. Does anyone know have a reference implementation of this in MATLAB or another language ...
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### Instantaneous frequency vs fourier frequency [closed]

Lets consider a pure sine signal at $\nu$ that is chopped using square pulses (like a burst mode on signal generators). My understanding is that instantaneous frequency is $\nu$ when oscillations are ...
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### FFT for a single frequency

I was looking for a more efficient way of finding the magnitude and phase of a signal at a certain frequency without performing an FFT because it produces more information than I need and I came ...
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### Online DFT Algorithm

I have a discrete audio stream $x$ that needs to be processed in real-time. Specifically, as the each new sample is received, I would like to compute a Fourier transform of the last $n$ samples of the ...
398 views

### Cross-correlation, sharp peak at 0?

First of all, I have to stress that I am not a professional of coding, no more than a professional of signal processing. I am a chemist that happen to be working on a project involving both. So in ...
217 views

### Fourier transform 4 times = original function (2D and higher)

The Signal Processing SE post linked below shows how the Fourier Transform applied 4 times to a 1D function returns the original function, i.e. F{ F{ F{ F{ g(x) } } } } = g(x) Link to 1D case: ...
76 views

### Impulse response of a time scaling system

Assume a bandlimited signal $X(t)$. Given that the output for this signal is $X(t/2)$, what will be the impulse response $h(t)$ of such a system? \begin{array}{l} X( \omega ) \ =\ \int ^{\infty }_{-\...
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### Expression to represent alternating pulse train?

I have a question regarding an alternating pulse train signal, $p(t)$, and a system which looks like this: Immediately, I'm supposed to be able to extrapolate that $$P_t = P_1(t)-P_1(t-\Delta)$$ ...
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### FFT method input argument have to be $2^n$ ?

Does FFT method input argument have to be power of 2, i.e, $2^n$ I just realized there are many algorithm for FFT implementation,...
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### Fourier transform with periodicity at the harmonic frequency

Let's suppose I have a signal $F(t)$ that is periodic, with two periodicities $P1$ and $P2$, with $P1>P2$ Suppose that I know the values of the two periodicities. Using the Fast Fourier transform ...
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### IDFT of $Y[k]=2X[k]$ for even $k$

If the 16-point DFTs of $x[n]$ and $y[n]$ are given as $Y[k]=\begin{cases}2X[k], & k=0,2,4,...,14 \\ 0, & k=1,3,5,...,15\end{cases}$, where $x[n],y[n]=0, \forall n<0, n>15$, how can I ...
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### Significance of modular arithmetic in DFT?

In what ways does modular arithmetic plays a part in DFT? Why is it a so integral part of DFT?
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### What is the role of complex exponential?

What is the role of complex exponential $e^{jθ}$ in Fourier Transform? Is it different in the continuous and in discrete time domain?
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### Fourier Transform of Morlet wavelet Function?

As you know the Morlet wavelet function is given by: $$\frac{1}{\sqrt{\pi f_b}}e^{\frac{-t^2}{f_b}}e^{j2\pi f_c}$$ The Fourier transform of this equation is: $e^{-\pi^2 f_b(f-f_c)^2}$ (is it right)? ...
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### Can I study continuous time Fourier Transform and treat the rest as special cases

Say I learned the theoretical result of continuous time Fourier transform. And I want to extends some results(say "convolution rule") to Lapace transform, Z transform, DTFT, DFT, Fourier sequence ...
I am reading this paper about density estimation (Appendix A), where the authors apply a Fourier transform to the estimated probability density (the $X_j$ are a sample of $N$ data points drawn ...