# 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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### Does zero-padding distort the spectrum?

It's said to "sample the DTFT", revealing what "DFT fails to see". And I fail to see how this sampling isn't distortion. The "spectrum" aims to provide the sinusoidal ...
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### Find the length of the impulse response for the given output and input

Homework Question: Consider a signal $x[n]=\alpha e^{j \omega_{0} n}+\beta e^{j \omega_{1} n}+\gamma e^{j \omega_{2} n} .$ What is the length of impulse response $h[n]$ of a system (non-trivial) such ...
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### Is there anyway to find the frequency of DFT eigenvectors (basis) from its eigenvalues?

I've read this document which talks about the DFT. It describes that DFT bases are the eigenvectors of a circulant matrix. I know that every basis has a frequency in it, but I don't know what is it? ...
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### Zero Padding in image reconstruction

I need to zero-pad the image for a better reconstruction but according to my project details, I will be given a Fourier-transformed image so can someone tell me how to pad the image in such a ...
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### Heterodyne modeling confusion in SDR

I've been reading this lab sheet which explains the signal processing math of the RTL-SDR radio dongle. http://www.eas.uccs.edu/~mwickert/ece4670/lecture_notes/Lab6.pdf In pages 5 and 6, the local ...
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### How to determine the sine Fourier coefficients of discrete data?

The following relation gives me the measurements of interest $w$ at equally distanced locations $x_j$ in space: $$w_j=\sum_{m=1}^{11}A_m\sin\left(\frac{mĻx_j}{L}\right)$$ where $A_m$ are the Fourier ...
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### How to plot thermal noise in the ātime domainā?

$P = 4kT$ (where $k$ = Boltzmannās constant, and $T$ = temperature of the instrument ($K$)) And the mean voltage is thus, of course, $V^2/R = 4kT$ And the voltage is distributed as a Gaussian around ...
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### How much zero padding I should do to an audio signal before fft?

I was working on project and I need to do fft to my audio signal. I was going through a code and found following line. Can anyone explain me the line of code. ...
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### how to plot fft with imaginary and real part in 3d or calculate the degree of rotation

I would like to make a plot like 1 and see the real and imaginary part in a 3d space. I dont want to make exactly the same plot. for me it is okay if i see the peak for both signals shifted. it is ...
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### Applying fourier transform twice (DSP course)

I stumbled upon a question in a DSP course (coursera) which I don't understand, shown below is a screenshot of the question and answer. The part which I don't understand is circled. Why is it equal ...
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### The impact on the frequency of adding zero samples and non zero samples

Can someone give me a brief explanation of what is going on in here? I struggle to understand the full differences between the impact on the frequency of added zero samples and adding samples which ...
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### Cosine of amplitude 1 but GNU Radio shows FFT has amplitude > 30,000

I am doing an FFT on a cosine wave which has an amplitude of 1. The FFT is amplitude is not 1 but over 30,000. What am I missing here? It's from the GNU Radio FFT wiki page:
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### Calculate displacement from acceleration signal data using Fourier transformation

I recorded acceleration data from an accelerometer attached to a vehicle, and I want to calculate displacement using the Fourier Transformation Integration method. I used software called vibration ...
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### Why does MATLAB's dualtree3 function not return the lowpass subband of the imaginary tree?

MATLAB has a function named dualtree3 which computes 3-D dual-tree complex wavelet transform. This function only retains the last low-pass coefficients/subband of ...
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### Adding zeroes in between the samples of a discrete frequency domain leads to both zero padding and scaling

I wonāt show ALL the calculations, but Iāll describe the problem fairly enough to understand. Weāve been taught that upsampling on one domain leads to padding zeroes or added time period which is zero ...