# 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 utilize product graphs in graph signal processing?

I'm working with dynamic graph signal processing. How to plot time variation and spatial variation separately and take the cartesian product of those two graphs? Any relavant Matlab codes?
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### Why Does This Sliding Window Goertzel Filter Trick Work?

I'm reading an analog signal at a constant interval on an embedded device, and I want to extract a specific frequency component. Since the signal is continuously being read I want to constantly scan ...
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### Sinc droop in a simple sampling mixer

This question is about the conceptual interpretation of a track-and-hold mixing operation implemented conceptually below, where an output $y(t)$ tracks an input $x(t)$ for half of a period $T_{LO}$ ...
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### How does MATLAB's edgetaper function work?

MATLAB has a function edgetaper that does something I haven't seen before: J = edgetaper(I,PSF) blurs the edges of the input ...
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### For the square wave signal, why does a narrower square wave correspond to more spread in the frequency domain?

Consider the square wave. As we decrease the pulse width $T_1$, it seems that the positive Fourier coefficients (located in the central area/lobe) are spreaded out across more frequencies. In fact, if ...
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### How do I properly compute a convolution kernel given the convolved and initial signal?

I'm trying to for solve for $b$ in the equation $C = a*b$ where $C,a,b$ are 1D arrays of size $k$. $F(b)$ is also $= \frac{1}{|F(a)|}$. I have tried doing the following procedure in order to isolate ...
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### Is the analytical fourier transform of an exponential decay the same as the FFT of a time series of the same signal?

Analytical Fourier Transform of $e^{-t/2}$: FFT of a time series representation of $e^{-t/2}$: I'm trying to find the decay coefficiencts in tri-eponential decay signals, and as a logical starting ...
1 vote
65 views

### Fourier Transform of product of sinc function and its raised powers

Is it possible to find the fourier transform of $$\left(\frac{\sin(x)}{x}\right)^3$$ and $$\frac{\sin(x)}{x} \frac{\sin(x^2)}{x^2}$$
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### How should I go about completely decorrelating a digital signal?

So I'm working on real time signal compression, and I need to come up with the best convolution to minimize the entropy of incoming data (which I will then compress), which I understand is achieved by ...
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### Expressing Frequency Bins as Period Bins

I'd like to change the x-axis of a Fourier transform frequency domain bar chart from frequency bins to period bins so that instead of displaying Hz or cycles/sec, I'm displaying sec/cycle; however, I ...
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### Why the Discrete time fourier series coefficients of a real discrete time periodic signal are not symmetric about y axis?

If the signal is something like cos(πn/3) , we get the two DTFS coefficients that are symmetric about y axis and the resulting frequency spectrum is an even function . Now take the example given in ...
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1 vote
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### Signal response amplitude depends on the time interval in simulation

I have already tried to look for an answer, but I do not find existing answers satisfactory. I am interested in the absolute value of the response function of a damped oscillator (or any time series). ...
1 vote
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### What Are the Units of a Fourier Transform? [duplicate]

I know that a Fourier transform (FT) outputs a distribution of how much of each frequency is present in a signal, but what would be the units of that distribution? It's not a proportion or a percent ...
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### FFT2 to RFFT2 Fourier plane and similarities

I'm trying to understand how Python's fft2 is different from irfft2. Basically, I have some continuous Fourier 2D samples that I need to put in a (n,n) grid (this can be done by a simply count-in-cell ...
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### Is the magnitude spectrum of the Discrete Time Fourier Series of a Discrete Time periodic Signal , an even Function?

We know that the magnitude spectrum of a continuous time fourier series representation of a real periodic signal is an even function (i.e. symmetric about y axis). Does this hold true for discrete ...
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### Real-world examples of unweighted directed graphs

Social Networks, Internet Traffic, Citation Networks, Transportation Networks, and Biological Networks exemplify real-world instances of unweighted directed graphs. Within these domains, the Graph ...
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### Comparing custom Welch periodogram with Julia's Welch periodogram

I wrote my own PSD struct in Julia for practice purposes. It involves two type of constructors: a "direct" PSD and a <...
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