# 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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### Identifying sounds patterns from wav file

I have an audio recording stored as a .wav file. My goal is to identify exact sounds patters from it using Python. The problem I'm facing is there's a clear "ting" sound in the audio file, ...
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### Image Restoration by Solving Constrained Least squares in Frequency Domain (Frequency Domain Filtering)

I am trying to implement the constrained least squares filtering as described in Rafael C. Gonzalez, Richard E. Woods - Digital Image Processing 3rd Edition Section 5.9. The equation (...
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### Finding the equivalent filter H(u,v) in the frequency domain of a 3x3 spatial mask

I'm trying to find the equivalent frequency domain filter, $H(u,v)$, of a 3x3 spatial mask that averages all neighbours of a point $(x,y)$ in said 3x3 neighbourhood excluding the point itself. So far, ...
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### Why DFT is used for approximating CTFT when you can approximate CTFT-integral itself?

I was using MATLAB for approximating FTs. Why DFT is used if we can approximate the transform-integration using summation.
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### Impulse invariance vs. DT representation of a CT system: Where is the inconsistency?

Suppose you have a continuous-time (CT) system $h_c(t)$, bandlimited to $B$. Your goal is to represent the system as a discrete-time (DT) system $h[n]$, sampled at $f_s \leq 2 B$. Clearly $h[n]$ won't ...
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### DFT of pure sinusoidal wave

I'm writing a program in which you can synthesize waves by adding to a sound's Fourier transform, and then inverse the transform to get the modified sound. In order to do this, I need to know what to ...
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### How do I calculate the correct amplitudes of a discrete Fourier transform (DFT)?

I have a set of samples values in time domain. I know they are uncorrelated and I have to extract the correct amplitudes. However, the values are only ~88% of what they should be. As a test see the ...
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### How is signal to noise ratio actually measured by receiver equipment?

This sounds like quite a basic question but it surprised me, how is SNR actually measured? You have the incoming signal: It seems like the SNR is just the visual comparison of the peak signal '...
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### Why is Fourier space not adequate for (theoretical or digital) filters?

As far as I have seen, almost all theoretical filter design occurs in Laplace or Z-space. Also, there is a pervasive connection to real life analog filters in the design. If one is just thinking in a ...
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### DFT algorithm designed for a “sample-by-sample” senario

Suppose I have a system that wants to take an input signal (audio in this case) and wants to output a Discrete Fourier Transform of it in real time (ie every sample). My initial thought is that if you ...
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### Find CT Fourier transform of $\left[ \frac{ \sin(\pi ~ t) }{\pi ~t} \right] \left[ \frac{ \sin(2\pi ~ (t-1)) }{\pi ~(t-1)} \right]$using properties

Use properties of Fourier Transform to solve the question. The question is in the imgur link below. I got $f_t$ of $\frac {sin(pi \cdot t)} {pi \cdot t}$ as rectangular pulse with value $1$ from -pi ...
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### What is the DFT of $[x_1 -x_2 x_3 -x_4…x_n]$

If DFT of $[x_1 x_2 x_3... x_N]$ is $Y(k)$, what is the DFT of $[x_1 -x_2 x_3 -x_4,....x_N]$ in terms of $Y(k)$? I have tried to formulate it but I cannot get a simplified expression for DFT of ...
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### finding power spectral density from a vector

I have been given a vector: \begin{equation} v= \:\begin{pmatrix}\frac{1}{\sqrt{2}}&\frac{1}{\sqrt{2}}\end{pmatrix} \end{equation} my job is to find the power spectral density from this vector \...
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### Bandwidth of a bandpass signal

If the Fourier transform of an aperiodic continuous time signal has signal components between the minimum frequency w1 and the maximum frequency w2, but not all the frequencies between w1 and w2, is ...
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### Why is the continuous time Fourier series of DC signal an impulse?

In case of continuous time Fourier transform(CTFT), I can easily calculate the Fourier transform of DC signal by using Fourier duality or inverse CTFT. But I don't know how to calculate the continuous ...
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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 ...