# 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 simplify multiple addition and convolution operations into one convolution kernel

I need to perform such a conversion to simplify my image processing problem (sharpening, in green are the knowns, in red the unknowns): \begin{align} y(n,m) &= \color{green}{x(n,m)} * \left[ \...
1answer
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### How to understand the sum of all “fourier frequencies”?

I got the data of an acceleration sensor to analyze. It consists of special terms of 30 Hz, 60 Hz and 120 Hz. In the following you can see in the first plot the 60 Hz data and in the second one the ...
1answer
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### Evaluating the continuous Fourier transform of a constant, and matching it up with the FFT result

I am following my optics textbook (Optics, by Eugene Hecht), throughout which are given various exact analytical results for the diffraction patterns that result from light passing through differently ...
0answers
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### Create 2-d Dirichlet kernel for use in image processing

I am working on frequency domain CNNs for image classification task, in which I initialize complex kernels of size (k*k). For performing point-wise multiplication between the kernel and the Fourier ...
1answer
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### Quadrature signal acquisition simulation

Bottom-line: how to create a 90 degrees out of phase signal from the real part of the fourier transform of a 1D signal (i.e., fft of a line of an image). ? *(I *(I think the Fourier shift thm can help ...
1answer
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### How to make low pass filter using frequency sampling method?

https://www.allaboutcircuits.com/technical-articles/design-of-fir-filters-using-frequency-sampling-method/ So there is two main equation: I wish to filter out frequency $\le 10000Hz$, for example. So ...
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### How to do the Fourier Transform of bounded function?

I was trying to solve a Fourier transform of a function using the properties of Fourier transforms. The function is given as: $\frac{At}{2}$ for $-2<t<2$ and $0$ for all other $t$. Doing the ...
2answers
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### Window functions and the Fourier transform

I want to clarify the 'correct' way to use windowing and Fourier transforms. My question is somewhat related to this one, but I have a few additional queries. I have some real, non periodic signal ...
2answers
123 views

### Why am I not getting a flat phase for a Gaussian pulse when doing a Fourier transform in Python?

I have been trying to obtain a spectrum and a spectral phase of a Gaussian pulse using the Fast Fourier Transform provided with numpy library in Python. Here are ...
0answers
33 views

### Linearity of Fourier Transform [closed]

Given the CTFT pair above, I am trying to find a Fourier transform of I thought I could multiply both sides(time domain and frequency domain) by to get the CTFT pair in the following form: But that ...
1answer
56 views

### Torque signal fft

I have the following torque signal picked up with a 10.240Hz sampling rate from a testbench. I am studying its fft which I create on Octave with the following code: ...
1answer
80 views

### A Delay Between Two Filtered Chaotic Signals

it is a common practice to use a shift of cross-correlation peak to evaluate a group time delay of two signals (chaotic signals are included). Can one synchronously and equally filter these chaotic ...
0answers
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### average value of modulated signal with Fourier Analysis

I am using an instrument that uses a modulated heating program. The instrument returns an average heat flow signal calculated from the modulated heat flow. I would like to understand how this average ...
1answer
86 views

### Subtract background from 2D signal using spectral methods

I have a 2D signal, with intensity as a function of two angles (alpha and beta), as shown below. This contains a background, which makes the signal's base-surface locally convex-concave. I would like ...
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1answer
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### Discrete Fourier transform - Norms of complex input signals and their transformation

Given a signal $\mathbf{z} \in \mathbb{C}^n$ and its Discrete Fourier transform $\hat{\mathbf{z} }$, does $||\mathbf{z}|| = ||\hat{\mathbf{z} }||$ hold? The question is given to me like this with ...
1answer
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### Discrete Fourier Transform in Signal Processing - Interpreting graphs of transformed signals

Given above are the real parts of the signals I to IV. Which of the following statements are correct? (i): Signal III is the result of the discrete Fourier transform of signal I. The associated ...
3answers
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### Poisson summation formula and periodic summation of Fourier transforms

One of the forms of the Poisson summation formula is $$\sum_{n=-\infty}^{\infty} T\cdot x(nT)\ e^{-i 2\pi f T n}\; {=} \; \sum_{k=-\infty}^{\infty} X\left(f - k/T\right),$$ where $x(nT)$ are ...
0answers
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### Cancelling effect of a system on a signal

I have a signal $A(t)$ and it's been transformed using an unknown system to a signal $A'(t)$. I also have another output signal $B'(t)$ from the same system and I want to retrieve the corresponding ...
1answer
266 views

### Power Spectral Density (PSD) from autocorrelation

I have a 1D fractional Brownian motion (fBm) signal, $u(x)$, of size $N$, generated through a random number generator with a gaussian mean, $\mu=0$, and standard deviation, $\sigma=\sqrt{N}$. I want ...
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267 views

### Power spectral density vs. Fourier Transform

I am trying to understand the difference between the Power Spectral Density and the Fourier transform. Specifically, I am trying to understand why the power spectral density is useful and in what ...
0answers
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