# 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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### 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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### Relationship between real and imaginary part of a real-valued and causal system

I have one question about the real part of a real-valued and causal system with the imaginary part of its Fourier transform given by \textrm{Im}\big\{X(e^{j\omega})\big\}=3\sin(2\omega)-2\sin(3\...
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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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### 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 ...
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### Bin sizes for non-uniform discrete Fourier transforms

For a non-uniform discrete Fourier transforms, do the specified frequencies ā i.e., $f_k$ in ā refer to the midpoint of the bin or the lower bound? I read the answer here, but that stated that ...
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'...