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Questions tagged [fourier]

281 questions
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Fast Fourier transform- non-integer number of cycles in the FFT aperture

There are a few excellent discussion threads and answers on this site (eletronics.se) on the theory of Fourier transforms. I tried implementing the same in a simulation tool (MS Excel :)). I have a few interpretation and implementation issues…
Vaibhav Garg
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Fourier transform 4 times = original function (from Bracewell book)

I was glancing through "The Fourier Transform & Its Applications" by Ronald N. Bracewell, which is a good intro book on Fourier Transforms. In it, he says that if you take the Fourier transform of a function 4 times, you get back the original…
sambajetson
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“The Fourier transform cannot measure two phases at the same frequency.” Why not?

I have read that the Fourier transform cannot distinguish components with the same frequency but different phase. For example, in Mathoverflow, or xrayphysics, where I got the title of my question from: "The Fourier transform cannot measure two…
Antoni Parellada
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Deriving the Fourier transform of cosine and sine

In this answer, Jim Clay writes: ... use the fact that $\mathcal F\{\cos(x)\} = \frac{\delta(w - 1) + \delta(w + 1)}{2}$ ... The expression above is not too different from $\mathcal F\{{\cos(2\pi…
pyler
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Fourier series of cycloid

What is the Fourier series representation of a cycloid? The parametric representation of the curve is as follows. $$ t=\dfrac{\theta-\sin\theta}{\pi}\\ x=\dfrac{1-\cos\theta}{\pi} $$ The period is $2$, so the coefficients of the complex exponential…
tfpf
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Fast & accurate convolution algorithm (like FFT) for high dynamic range?

It seems that FFT-based convolution suffers from limited floating-point resolution due to evaluating everything around the roots of unity, as you can see in the $10^{14}$-factor error in this Python code: from scipy.signal import convolve,…
user541686
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Fourier transform artifacts

My starting point in what follows is a radially symmetric random field. Taking the Fourier transform of this (and plotting it in logarithm to highlight the patterns), I obtain the following image in Fourier space: As you can see, there is a…
user1991
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For an LTI system, why does the Fourier transform of the impulse response give the frequency response?

I know that for a given system, the Fourier transform of its impulse response gives its frequency response. I want to find where this property comes from, but haven't been able to find if it's a definition or if there's a mathematical proof…
Florian Castellane
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8
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The Number of Sine and Cosine Waves in an $ N $ Point DFT

This is bound to be an embarrassingly simple question, but here it goes... I was reading the chapter on discrete Fourier transforms (DFT) of this really didactic online book, The Scientist and Engineer's Guide to Digital Signal Processing, by Steven…
Antoni Parellada
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About Fourier transform of periodic signal

In Fourier transform for periodic signal, I checked different books and I found a different explanation in each book. Let's take the explanation in Signals and Systems by Rajeshwari & Rao: The resulting Fourier transform for a periodic signal…
Aadnan Farooq A
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Example of Fourier Transform not existing for real-life signals?

I got curious based on this question here, but basically, is there ever a real-life signal that exists where its Fourier transform does not exist? If a signal is not finite energy, then its Fourier Transform does not exist, so what might be an…
TheGrapeBeyond
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What do colored noises look like in the time domain?

I understand that the time domain representation of white noise looks like impulses. How do colored noises like brown, pink etc. look like when we perform an inverse Fourier Transform on them ? What could be some sources of colored noise that may…
Prateek
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Fourier Transform of Alternating Periodic Rectangular Pulse

I'm having trouble determining Fourier transform of signal. I have 2 ideas on how to solve this problem. Given the signal is periodic I could use formula for Fourier transform of periodic signals: $$X(j\omega) = \sum\limits_{k=-\infty}^{\infty} C_k…
Aleksandar Simonović
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Filter design to realize Cauchy product

I come from Computer Science so please pardon for my possibly wrong terminology. I need to design a filter which has coefficients $$h_0, h_1, \ldots, h_n, \ldots \quad\text{such that}\quad h_0 > h_1> \ldots > h_n > \ldots$$ The input is $x_n$. The…
Ngoc Anh Huynh
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Frequency Analysis (DFT / FFT) of a Signal Without a Constant Sampling Frequency (Non Uniform Sampling in Time Domain)

I'm a stack exchange user for some time and now I'm registering to ask a simple question (I think!). I have a vibration signal with an amplitude and time (sampling frequency not constant) in a $10000\times 2$ double variable. The data is available…
Pedro
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