# 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 Find "pitch" from Fourier Series

The end goal of my project is to create an autotune program, But the problem I'm trying to solve right now concerns finding the pitch of someone singing a note. I have written some code that performs ...
1 vote
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### Why use sinc function to downsample an image in fourier domain?

I'm very confused about downsampling in image processing and the use of sinc function to do it. I read this post : 2D Fourier downsampling some time ago that talked about my own doubt, that is to ...
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### Need help with DTFT problem

Prepping for exam and this is one of the practice problems: I just want some clarification on some of the steps my professor took. This is the answer in the answer sheet Only thing I dont understand ...
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### Fourier transform why can I convert one of the axes into an imaginary number?

Contextualizing This question is inspired by the following video: https://www.youtube.com/watch?v=-qgreAUpPwM&t=60s&ab_channel=3Blue1Brown I own a sign, a drawing of a square with 200 points ...
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### What are some approaches / algorithms for reducing size of numerical data of large size with redundancies?

I'm dealing with bunch of .asc(ascii) files that are the output of continous monitoring of various electronic equipments for certification purposes. We monitor various parameters of the equipments ...
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### Time domain to frequency domain conversion of audio signals to extract 1/3 octave frequencies

We have developed an android app (Noise Tracker) for noise measurement using smartphones. It displays noise levels in Leq sound pressure levels. I want to implement A & C weighting. As per my ...
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### Removing once per revolution variation from data

I’m looking for help to find a robust technique to remove a once per revolution variation in some vehicle test data. The data is collected by driving a vehicle around a circular path at increasing ...
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### Rayleigh Bandwidth Calculation-Radar

I am trying to generate a simple Gaussian pulse that has a 1 ns pulse width. However, when I generate the pulse, I realized that I did not meet the condition that calculates Rayleigh Bandwidth (1/...
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### Fourier transform of periodic functions

The Fourier transform is derived from the Fourier series by considering a non-periodic signal, thinking of it as a infinitely long periodic signal, putting it into the Fourier series and making this ...
1 vote
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### Effect of overlapping percentage on STFT output

I know STFT is generally applied to non-stationary signals but I tried to apply it to a stationary signal to get a working knowledge. I created a stationary signal composed of three frequencies as ...
1 vote
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### How do I generate the approximate Fourier Transform of the signal using Principle of Stationary Phase?

The following excerpt is taken from the textbook "Digital Processing of Synthetic Aperture Radar" by Ian G. Cumming The Principle of Stationary Phase (POSP) can be briefly explained as ...
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### Fourier transform of modulus of sum of weighted sines

$$x(t) = |a \cos(\omega_0 t) + b \cos(\omega_1 t)|$$ with $a, b \geq 0$, $\omega_0, \omega_1 > 0$, but $a, b > 0$ or all $a, b$ (negatives included) is also acceptable, or replacing $\cos$ ...
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### pocketfft delivers wrong values

does anyone understand how to use the pocketfft by martin reinecke? Link: https://gitlab.mpcdf.mpg.de/mtr/pocketfft Basically it's just this snipped of code: ...
1 vote
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### Fourier transform of the energy

If I have the time history of the energy, Does it make sense to do the fourier transform of this energy? or if I want to see the energy in frequency the PSD is the only tool? and Why
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### Why does Hilbert filter distorts the shape of the signal?

If all the harmonics composing a the signal are shifted by the same amount, this would be the same as sampling later or earlier in time. I think. Take a simple pulse train as an example. If Fourier ...
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### What are the criteria for a change-of-basis transform to be doable in $O(n \log(n))$?

The Fourier basis is a common choice for transformations, but a lot of times, it's not the best for a specific application. For instance, wavelet bases give us better spatial / temporal locality than ...
783 views

### Purpose of Phase Information

I am learning Fourier Transform from many days but till now I am not able to understand what does phase angle image show us or tell us? They say that MAGNITUDE tells "how much" of a certain frequency ...
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### Estimate phase using STFT in Matlab?

My signal oscillates back and forth on the interval [-1, 1] at varying frequencies, with some added higher frequency noise components (example data shown below). I want to to estimate the phase of the ...
1 vote
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### Spacing between gaussian windows for STFT

I'm computing discrete short time Fourier transform. Data is split into overlapping chunks and gaussian window is used for each chunk. However, I'm not sure how much overlap there should be between ...
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### General question about DFT

I am learning Fourier analysis and without any teacher, just trying to read books on my own. I think I have made some decent progress but they are a couple of points which are still very unclear to me ...
412 views

### 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 ...
1 vote
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### Bring two Fourier transforms to same range to add them

I have Fourier transforms of two images which I wish to add (Basically I have an input Fourier transform which I mask, reconstruct the underlying image using an algorithm, and then try to replace the ...
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### Multiply and divide by the same function in convolution

I am calculating the convolution of two functions $F(x), G(x)$ in $\mathbb{R}^{n}$, n-dimensional space. I have another function $h(x)$ that is a Gaussian. What effect does multiplying $F(x)$ by $h(x)$...
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### Finding a periodic signal knowing its period, mean value and power

I've found an interesting exercise which I have been trying to solve for a couple days, without success. Let $x(t) \in \mathbb{R}$ be a periodic signal with fundamental period $T_0 = \tfrac{1}{4}$, ...
1 vote
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### My fft gives always gives the correct frequency or double the correct frequency

I will do anything to get help. Please help me find a solution. I can safely say that my fft algorithm, implemented with pyfftw, works as intended when a sine wave with a certain frequency is passed. ...