# 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 do you apply a filter after DFT on an image?

Let's say size of the image is 100 x 100 and the kernel matrix is 5x5. I took the DFT of both the image and the kernel. But how do I multiple these two matrices? And which parts involve in these ...
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### Fourier transformations of discrete time signals [closed]

How does one Fourier transform the following signals? $$x[n]=[0,9,0]$$ and $$y[n]=[9,0,19,0,9]$$ I've tried to get it along the way of $$X[\omega]=e^{-i\omega n}$$ but this seems incorrect. I'm not ...
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### How to get general projection of rect function?

To be more clear I want to get a general expression for PƟ(t)= ∫∫rect(x)rect(y)δ(xcosƟ+ysinƟ-t)dxdy I also want to find particular projection for Ɵ=0 and Ɵ=45 and also Fourier Transform of the ...
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### Discrete inverse Fourier transform

I have a question regarding discrete inverse Fourier transform, and no answer I found on the internet seem to be satisfying. This might be because I do not fully get some of them, so please excuse my ...
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### Sampling with an alternating impulse train

The have the following question: A signal $m(t)$ with bandwidth 500Hz is first multiplied by a signal $g(t)$ where $\displaystyle g(t)=\sum_{k=-\infty}^{\infty}(-1)^k \delta(t-0.5*10^{-4}k)$. The ...
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### Partial Fraction Expansion for Inverse Fourier Transform

In many textbooks, I've seen the application of Partial Fraction Expansion (PFE) to find an inverse Fourier Transform. Let's stick to the discrete time case, and let me give you an example. Let's say ...
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### How to do DFT of this signal

I am trying to get $X[k]$ when $x[n]$ is equal to $$x[n] = \cos\left(\tfrac{\pi}{4}n-\tfrac{\pi}{4}\right)$$ I'm using this equation: $$X[k] = \sum_{n=0}^{N-1}x[n]e^{-j \frac{2 \pi}{N}kn}$$ but ...
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### Signal in frequency domain with OpenCV dft

I am experimenting with cv::dft: a 1HZ sinus signal is generated, and displayed in the frequency domain. But for some reason it hasn't got the maximum component at ...
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### Fourier transform and impulse function $\delta(\omega)$

Why does impulse function $\delta(\omega)$ keep occurring in the Fourier transform expression of standard functions like $\sin(t)$, $\cos(t)$, constant function, unit step $u(t)$ etc? (can someone ...
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### While finding the ESD/PSD of a signal why we always prefer to find it via Auto-correlation function then the square of the FT of the signal? [closed]

In a video i saw that while calculating ESD or PSD of a signal time auto correlation function was used when it can be also done by the square of FT of the signal.Why we followed that approach even ...
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### trying to understand fast fourier transform in matlab

Y = fft(X); P2 = abs(Y/L); P1 = P2(1:L/2+1); P1(2:end-1) = 2*P1(2:end-1); 1) I dont understand what lines 2-4 are acheiving, why must lines 2-4 be ...
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### Scaling property of Fourier Transform

Problem 4.6(b) from Oppenheim, Wilsky & Nawab (2nd ed) reads: Given that $x(t)$ has the Fourier transform $X(j\omega)$, express the Fourier transform of $x(3t - 6)$ in terms of $X(j\omega)$. The ...
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### How to get around the circular shift property of Discrete Fourier Transform?

I understand that when we introduce a linear time shift using DFT on a finite sequence, the algorithm assumes that the signal repeats itself outside of the given range. Here is an example explaining ...
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### Maximum of cross-correlation not moving

I already asked this question here yesterday, but it was very poorly worded I think. I made a much more detailled post explaining my problem of stackoverflow, as it might also be a code problem. Here ...
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### graph display problem [closed]

I have a problem with the end of my code. I would like to display the last two curves, the problem is that at the beginning the size of YY is 288 and then after the equality with diff, my size goes to ...
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### Orthogonal signals in frequency and time domains [closed]

I have 3 orthogonal signals obtained by Fourier transformation. But when I do the inverse Fourier transform in Matlab, my signals are no longer orthogonal in the time domain. Here is my question: ...
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### What frequencies are present in the Fourier transform of the Dirac impulse?

When I do the Fourier transform of the Dirac impulse I get a pure sinusoid (or complex exponential, however you wanna call it) but I read in several places that all frequencies are present in the ...
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### How to understand the relationship between the filter time constant and the half-power cutoff frequency

I learned that the time constant can be computed as $\frac{1}{2 \pi f_0}$, where $f_0$ is the half-power cutoff frequency of a high-pass filter. However, I was wondering how the time constant and the ...