# 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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### 2-d circularly symmetric low-pass filter

For a square pixel grid, the ideal 2-d low-pass filter with a horizontal and a vertical cut-off angular frequency $\omega_c$ in radians has an impulse response (kernel) $h_{\small\square}(x, y)$ that ...
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### Applicability of Fourier transform to periodic signals? [duplicate]

Can we use Fourier Transform for periodic signals or only we can use fourier series with periodic signals? I am asking this question because I read on page 301 of alex palamides as shown highlighted ...
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### Difference between CTFT and DTFT?

I have tried to read different articles but still confused in difference between continuous time Fourier transform and discrete time Fourier transform?
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### Intuitive understanding of Fourier transform of images [duplicate]

I am trying to have an intuition about the Fourier transform of images For example the image on the right is the Fourier transform of the image on the left, my question is : 1)Why are the ...
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### Why am I not getting the intended coefficients in this 2D Fourier demonstration?

I am trying to demonstrate how the 2D Fourier decomposition of an image works with Matlab and a very, very simple example. I create a 4 x 4 pixel image with cosine basis vectors as such: ...
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### What is the type number of a discrete time system given $H(z)$?

Given a continuous time impulse response $h(t)$, if I take the Laplace transform and count the no. of poles at origin, that gives the type number of the system. For e.g., $$H(s) = \frac{2}{s(s+2)}$$ ...
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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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### What is the interpretation of Fourier Transform containing only imaginary part?

The FT of a unit step function is taken as: $$X(\omega) = \int_0^\infty e^{-j\omega t}dt = \frac{-1}{jw}e^{-j\omega t} \Biggr |_{0}^{\infty} = \frac{j}{\omega}$$ The transform only has the ...
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### Why is the ROC of Laplace transform independent of imaginary part of s?

An integral is defined as converging if it yields a finite value upon application of limits of integration. It is divergent otherwise. Now sticking to the mathematical notation of Laplace transform, ...
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### Why Does 2D FFT of Gaussian Looks More Sharper than Gaussian Itself?

I am trying to understand why 2D FFT is done on a Gaussian process in a particular code. From my understanding from these posts: https://www.researchgate.net/post/...
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### How to get descrete fourier tarnsfom [closed]

Could anyone explain me please how to produce descrete fourier transform of such signal? There are no anymore information besides the picture in this task.
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### Reconstructing a signal from FFT by adding individual signal components

I'm attempting to reconstruct a signal from the DFT of the signal. I tried to do it by extracting the individual sinusoids and adding them up, but the answer I get is incorrect. ...
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### From Fourier transform to Laplace Transform

It's well known that you can estimate the Fourier Transform $X(f)$ of a signal $x(t)$ via its Laplace Transform $X(s)$, just by setting $s = j2\pi f$ to the latter, as long as the region of ...
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### Fourier Transform of Alternating Periodic Rectangular Pulse

I'm having trouble determining Fourier transform of signal. I have 2 ideas on how to solve this problem. Given the signal is periodic I could use formula for Fourier transform of periodic signals: ...
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### Applying frequency-domain filters on a centered Fourier transform

I understand why we shift the Fourier transform such that the 0-frequency is centered for visualization. In the shifted DFT(u,v) of an M*N 2-dimensional image, the top-left corner of the 4th quadrant ...
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### Finding the input from the impulse response and output

I have $y,h,x$ which are all vectors. From $y[n]=x[n]*h[n]$ which is basically how I got $y[n]$. I also know $h[n]$. I put this through a Fourier transform. Let's assume that the capitalized ...
Suppose we're given the following: $x[n] = 2 + (-1)^n$, and are given the impulse response $h[n] = u[n] a^n$, of an LTI system where $|a| < 1$. We're asked to find the output $y[n]$, if $x[n]$...