# 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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122 views

### Evaluate Fourier coefficients at arbitrary point using Python

Lets say I have a sinusoidal function $s$ that looks like ...
51 views

### Convolution of signals sampled on a logarithmic grid

Is there a practical accelerated algorithm or a theoretical discrete (Fourier) transform based method to convolve discrete-time signals sampled on a logarithmic grid? What I mean is representing a ...
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### Use samples of Fourier transform as DFT?

Consider the LTI system given by: $H(z) = 1 - \frac{1}{2}z^{-1}+\frac{3}{4}z^{-2}$ Let $x[n] = (\frac{1}{2})^nu[n]$ be the input to the system. We want to find the output for $n = 0,1,...,N_a$, using ...
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### What's the difference between using DFT, IDFT or DCT to calculate cepstrum of a power spectrum?

I've seen different equations that calculate cepstrum from power spectrum, but the equations are not consistent. Some people use Fourier transform, some use the inverse Fourier transform, and some use ...
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### What's spectral “tilt”?

I am looking at article Speech-in-noise intelligibility improvement based on spectral shaping and dynamic range compression. In paragraph 2.2 the article mentions "tilt" of the spectral envelope. The ...
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### Can you use Fourier transformations (or other) to read multiple superimposed barcodes?

If you printed bar codes on tracing paper/acetate etc. and then positioned several in front of one another, could you extract the individual codes from the aggregate overlaid image? I feel intuitively ...
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### Aliasing in the Short time Fourier Transform of a pulse

When attempting to take the Short Time Fourier Transform of a pulse, at the end of the pulse I'm running into problems. The signal looks like this at the end (it is a simple $sin^2$ pulse envelope, ...
124 views

### Understanding Walsh coefficients

I am working with Walsh coefficients. I know the intuitive understanding is almost that that they are the degree of connectivity, but it is there a better way of thinking about it? What is the ...
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### Discrete Fourier transform in a multidimensional space

I want to measure the frequencies at which a point oscillates in a multidimensional space, let's take the example of a point on a 2d-surface. For now, I naïvely split the signal in two, along the ...
109 views

### Global Transforms besides the DFT?

This is a simple question. Fourier analysis gives us the DFT, which is known as a global transform of a signal. In contrast, the Discrete Wavelet Transform (DWT) has a plethora of wavelets, all of ...
945 views

### Problems Using FFT to Compute Impedance in a Model Neuron

I'm a neuroscientist currently investigating the resonance properties of a single neuron model that a colleague and I have constructed. The language we code in is Julia, which I hope is similar enough ...
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### Two versions of Constant Q Transform (CQT) doesn't match each other?

To my knowledge, there's two major CQT papers, the one by Brown in 1991, and the one by Schorkhuber in 2010. The 2010 paper claims to be a more computationally efficient implementation of the 1992 ...
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### Non-Linear, Non-Stationary spectral analysis methods! When and where?

I have been reading about non-linear non-stationary signal analysis methods and it seems to do this type of analysis the go-to method is the Empirical Mode Decomposition (EMD), then Hilbert Transform (...
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### Multiply signal $x[k]$ with $\cos(2\pi\nu_0k)$, then given $X(\nu)$ draw resulting function in frequency domain?

Let $$y[k]=x[k]\cdot \cos(2\pi\nu_0k) .\tag{1}$$ Then, given a signal $x[k]$ with the DTFT $X(\nu)$ according to the following figure what will the frequency domain for $Y(\nu)$ look like for a ...
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### What is a correct way to find or “guess” a kernel which transforms an image into another image using Fourier Transformations?

Assuming I have two images, apple and orange; also assuming a filter kernel that transforms an apple image into an orange image possibly exists, how would some series of Fourier Transformations (and ...
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### Signal rescaling

Please help me out with this one. I think I've been given an impossible task. I'm working on a system that transmits an active signal and looks for strong reflections. The transmitter is actually ...
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### Fourier transform of a damped cosine wave with a linear frequency chirp

I want to take the Fourier transform of the following transient signal, $$f(t) = e^{-t/\tau} \cos((\omega_0 + m t)t)$$, where $m$ is some gradient parameter in units of $\rm{Hz}/s$. I thought this ...
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### Normalized cross-correlation in frequency domain

I never worked with signal processing and never really used Fourier transforms before, still I am working on a project consisting on taking the output of an accelerometer to detect some movement ...
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### Checking Parseval's Theorem for Gaussian Signal by Using Scipy

I'm trying to check Parseval's theorm for Gaussian signal. It's well known that fourier transform of $\exp(-t^2)$ is $\sqrt{\pi}\exp(-\pi^2 k^2)$. So I implement it by using quad and simps. I think ...
66 views

### Generate time domain signal from frequency domain filter

I am familiar with using the Fourier transform to take a signal from the time domain to the frequency domain. What I would like to do is the reverse: describe a signal in the frequency domain and then ...
64 views

### Burst Deblurring algorithm - Understanding the results

I've attempt to implement the algorithm from the paper "Burst Deblurring: Removing Camera Shake Through Fourier Burst Accumulation". The main idea is to take several frames of the same scene, each ...
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### Is it possible to recover the original signal from an LC circuit?

I'm using some photo detectors called Silicon Photo-multipliers (SIPMs) which produce a signal like the following: Now, I take this signal and pass it through an LC circuit to get the following ...
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### Determine 3 most dominant frequencies in a signal, PSD or just the absolute value of a Fourier transform?

I have a noisy ECG signal recorded for 5 minutes. My goal is to determine heart rate every 2 seconds. To find out 3 most dominant heart rates (Beats per minute) in a 2s-signal should I calculate its ...
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### How to calculate the Fourier transform of a mean filter in Matlab?

In Matlab, how can I calculate the discrete-space Fourier transform of a mean which takes the average of 4 adjacent points, with this kernel \begin{pmatrix} 0 &1& 0\\ 1 &0&...
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### Image zooming with Fourier transform

I want to go from this image into this one: So basically I need to scale the white square. The authors of the paper claim that this can be done in four steps: zero-padding in real space (image is ...
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### Creating realization of 2D Gaussian field in Fourier space

I want to generate a 2D Gaussian field with dimensions $L\times L$ with $N^2$ cells each of size $l = L/N$. I'm doing this by producing a realization of this field in Fourier space by producing ...