# 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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### beam pattern are fourier transform of the beam weight, is it true ? if it's true how?

what i understood is the equation of AF looks similar to DFT equation as we are multiplying with exponential term
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### The Discrete Fourier Transform (DFT) decomposes any signal into four orthogonal signal components

Let $F=\frac{1}{\sqrt{n}}(w^{kl})_{k,l=0}^{n-1}$ be the discrete Fourier matrix of size $n$ where $w=\exp^{-\frac{2\pi i}{n}}$. It is a well-known that $F_n^4 = I_n$ where $I_n$ represents the ...
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### Orthogonal signals basics [closed]

Suppose we have 2 orthogonal signals $x_{1}(t)$ and $x_{2}(t)$ and we add them up. Can we always say that the resulting signal will be of this form: $$x_{3}(t)=x_{1}(t)+jx_{2}(t)$$ ? If that is true ...
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### Constraints on choosing the frequency axis when Fourier transforming non-uniformly sampled data?

Does anyone have a reference that specifically discusses choosing the frequency scale for a simple 1D data for non-uniformly sampled time-domain data when performing the discrete Fourier transform. In ...
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### How to know if a continuous function can be represented by a finite sum of sinusoids?

I have a lack of mathematical knowledge, and notably in mathematical vocabulary, so maybe a similar question exists but with a different wording. What I want to know, is actually how to know if a ...
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### How to feed multi-channel spectrograms to Deep Neural Network?

I am using a 14 channel EEG device. To do away with the need for any handcrafted features, I wish to implement an ML classification task with the EEG data collected using deep neural networks (such as ...
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### Debug the difference between two Frft implementations

I need help to understand the difference between two fractional Fourier transform implementations. On this website two different implementations for the fractional Fourier transform are presented (...
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### Are complex exponentials real thing?

Is there any physical significance of complex exponentials. I mean can we produce them like how we can produce sinusoidal signals using a signal generator? OR are they just pure mathematical ...
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### How are the results of a fourier-transform interpolated to cover the entire frequency range?

Say we have an audio signal and we do a Fourier transform with block size 2048. Now the outputs correspond to 1024 different frequencies. A spectrum analyzer however doesn't just display 1024 discrete ...
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### Can someone explain me how the phase spectrum of trigonometric fourier series is related to phase spectrum of exponential fourier series of a signal?

Suppose we take a periodic signal and perform fourier analysis over it . Now we have two ways of representing the fourier series of this particular signal , one is trigonometric fourier series and ...
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### (graphic) Relation between FFT and complex signal

I have a complex signal with a frequency between 0 and 16 (16 not included). I have made four plots (in python) to show four examples. For each example I provide the signal, its FFT in both real, imag ...
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### Why do singularities on the imaginary axis affect the Fourier transform differently than the Laplace transform?

(Please note that I'm aware there are already several questions asking about the difference between the two transforms. However, none of them that I could find touch on this specific issue of the ...
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### Radix-4 DIT Inverse Transform Reordering Issue

I am trying to implement a radix-4 DIT FFT. It looks like the forward transform is working correctly, but the backward transform output is not in the correct order. I'm pretty sure that the ...
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### why fourier transform multiplies $e^{-i\omega t}$ not $e^{i\omega t}$?

I think that difference between $e^{-i\omega t}$ and $e^{i\omega t}$ is only the direction of rotation. Is there any reason why Fourier Transform multiplies $e^{-i\omega t}$ and Inverse Fourier ...
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### Does the length of DFT points (duration of a signal) affect the "amplitude" of the power spectral density?

For example, performing a DFT on a 10-second-long and 20-second-long signal with the same sampling frequencies will change the "amplitude" of the power spectral density (PSD) at each ...
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### Compare Discrete Fourier Transform for multiple signals

I have heart rate data from a wearable sensor (no ECG). I want to perform Discrete Fourier Transform to see if some patterns are present. I have over 200 signals, as each individual has heart rate ...
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### What is the Fourier Transform integral equation for a 1D signal and how can it be expanded into 2D, 3D, and 4D?

I know that is the 1D Fourier Transform (FT), and the 2D FT is and 3D FT is , but I am not sure whether these expressions are in fact Fourier transform integral equations for a 1D signal, expanded ...
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### FOURIER TRANSFORM: How can i find the index of data points

I am a senior in high school and am currently trying to conduct an exploration of Fourier Analysis, specifically using the Discrete Fourier Transform to analyse a chord played on my piano. Basically, ...
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### Estimating acoustic sound signal energy radiated

Im recording sound generated by a drilling machine against an object. I have the recording of following : Ambient noise with drilling machine switched off. Drilling machine on+ambient noise Drilling ...
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