Questions tagged [fourier-analysis]

Questions on the discrete and continuous Fourier analysis functions of Mathematica, as well as the FourierSeries` package.

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30 views

Result from FourierCosCoefficents does not appear to be linear [closed]

f3 and f4 below produce the same output (more or less) but the coefficient in f3 does not appear to be the sum of f2 and f1 (which it should, uiam).' ...
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0answers
91 views

Need to find Fourier series of the following graph

Need to find Fourier series of the following graph.....question is also written in figure.
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1answer
112 views

Unexpected behaviour of PowerSpectralDensity

I recently wanted to calculate the power spectral density of a surface profile. I was happy to find out that there is a built in PowerSpectralDensity[] function in Mathematica (version 10). However, I'...
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0answers
44 views

How to force the output to be in terms of a specific function?

I have a rectangular function rect[t], which is a window function with values of $ 1 $ in the interval $ (-\frac{1}{2},\frac{1}{2}) $:- ...
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64 views

For Fourier Transform with $ x(t) $, how to obtain result in terms of $ X(f) $?

I have a function $ x(t) $ and I denoted its Fourier transformation as $ X(f) $. I want to get the Fourier transformation of $ x(t)\mathrm e^{2\mathrm i \pi f_0 t} $, and I know the result is $ X(f-...
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1answer
277 views

Get frequency axis in Fourier transform (and save them)

I am trying to get the Fourier transform of a light-curve (with an even number of points, 300, and equally spaced in time, 6.9 seconds) and my problem is to get the frequency on the x-axis. I can ...
2
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1answer
138 views

Discrete Fourier transformation from ASCII (for noob)

I am not familiar with Mathematica (I am a physicist programming in Fortran) and my knowledge of it is very limited, unfortunately. I would like to perform the Fourier trasform of a lightcurve which ...
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1answer
168 views

is there a way to avoid the Dirac Delta in the fourier transform?

I would like to compute the fourier transform of H1[t], as you can see the output of mathematica gives the the dirac delta: ...
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0answers
64 views

Frequencies for Fourier coefficients [duplicate]

I have been given the task of calculating the frequencies to which the fourier coefficients correspond. So my input is a discrete signal [1,4,0,1], which gives me <...
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1answer
130 views

Spectrogram of low-frequency data

I generate the following data data = Table[Sin[2 π*100*t] + Sin[2 π*140*t], {t, 0, 10, 1/1023}]; and the spectrogram, as expected, shows two horizontal lines ...
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1answer
200 views

How to use fast Fourier transforms (FFT) to calculate derivatives of a function?

Suppose we have a function numerically defined at pseudospectral collocation points ...
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1answer
153 views

Inverse Fourier transformation discrepancy between Wolfram|Alpha's solution and mine [closed]

I searched for the inverse fourier transformation of $$ \mathcal{F(\omega)} = \frac{2}{(1+i\cdot \omega)^2 +4} \rightarrow i^2=-1 $$ My solution (compliant with the solution from my textbook): $$ \...
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1answer
213 views

Re and Im relationships without Abs among Fourier, FourierTransform, InverseFourier, and InverseFourierTransform

Is there a way to make Fourier's Re and Im components separately track the results of ...
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3answers
711 views

Find Fourier Series/Coefficients with Mathematica

Hello I want to find the Fourier series and/or the coefficients for a function like the following: or or For the first one I did the following: ...
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1answer
160 views

Fourier Transform of a symbolic expression

Hello I would like to do the Fourier Transform of H1'[t - L2[t]/c - L2primo[t]/c] I know that its transform has to be: ...
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1answer
86 views

Plot the graph of the square wave function defined as $f(t)=\sum^{\infty}_{n=0}(-1)^n h_{n}(t)$ on the interval $t>0$ and find its Laplace transform

Plot the graph of the square wave function defined as $$f(t)=\sum^{\infty}_{n=0}(-1)^n h_{n}(t)$$ on the interval $t>0$ and find its Laplace transform. The http://mathworld.wolfram.com/...
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1answer
153 views

Indeterminate result from Sinc

I have an impulse train given by (1 + Csc[(π x)/(1 + R)] Sin[(π (1 + 2 R) x)/(1 + R)])/(2 + 2 R) Because of the Csc, ...
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0answers
94 views

Shift a signal in time using Fourier Transform and Inverse Fourier Transform

I am trying to time-shift a signal x, which is a sine wave with 10 sec time-period, by t=2 seconds to get shifted version ...
2
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0answers
89 views

Use List convolve for aligning images

I am trying to align images of point spread functions using a convolution. Before doing it on real data, I wanted to try on simulated data. I have no problem with the 1-D case where I create 2 ...
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2answers
383 views

Frequency of ticks in mechanical watches

I'm looking to find the frequency of a relatively large dataset (or a relatively short audio file) of a repeating sound, like so: Here are the original files, for those willing to play. :) eta2412 ...
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1answer
147 views

Implementation of discrete Fourier Transform in Matrix Form

I am trying to gain an in depth understanding of how discrete fourier transforms work, and consequently I am trying to implement the discrete fourier transform myself in the form of a matrix. First ...
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1answer
774 views

Fourier Parameters

I need to use the built-in function Fourier, to get the Fourier transformation of a list of numbers. Unfortunately, I would need to set the second argument of the FourierParameter option to a non-...
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1answer
309 views

Fourier transform of a complicated function

This question is related to "Numerical Fourier transform of a complicated function" from 2012. I have pretty much the same problem: I have a function $f(x)$ which is complicated to evaluate, and want ...
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2answers
195 views

How to make this higher resolution transform as fast as Fourier?

Given a table of data, the Fourier command gives the discrete frequency content of the data, where the resolution in frequency space is equal to 1/N, where N is the number of data points. Higher ...
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1answer
604 views

Problem with Fourier transform

How to define a top hat function with plot also at opening and closing value? and How to plot a Fourier transform of the function?
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1answer
404 views

How to find the Fourier Transform of a list?

I have a list (list) in the form of {x,y} as ...
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1answer
274 views

normalization of convolution product when using Fourier transform

I'm trying to calculate the convolution of two probability density functions (PDFs) defined on the real axis: a normal distribution (with \[Sigma] > 0 and ...
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1answer
454 views

Package for fast spherical harmonic transform in Mathematica?

Mathematica's implementation of the Fast Fourier Transform is, naturally, much faster than computing the discrete transform yourself using Sum. The analog of the ...
47
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1answer
18k views

How can I draw a Homer with epicycloids? [duplicate]

You may have seen this video: https://www.youtube.com/watch?v=QVuU2YCwHjw. How does this work, and how to do it with Mathematica?
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0answers
90 views

Fourier Cos coefficient vs Integrate vs common sense

I was trying to find out what the (discrete) Fourier transformation of the following function is $$ f(\nu, u) = \frac{\sinh \nu}{\cosh \nu - \cos u} $$ So at first, I tried to evaluate a fancy MMA ...
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0answers
235 views

2D Fourier transform of a diffraction pattern Mathematica vs FourierPainter

We are trying to make sense of the numbers provided by the PC program FourierPainter for a 2D Fourier Transform of a diffraction pattern. We would like to evaluate the ratio of the zeroth harmonic ...
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0answers
66 views

2d vs 1d FourierTransform

According to the documentation, the multidimensional Fourier transform is defined as $$ \frac{1}{(2\pi)^{n/2}} \int_{-\infty}^\infty \int_{-\infty}^\infty \cdots f(t_1, t_2, \dots, t_n) \mathrm e^{\...
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1answer
75 views

Evaluating a Fourier integral

Is it possible to evaluate the following integral? $$\int \frac{(x-x_0) \: dx \: dy \: e^{i k_x x + i k_y y}}{((x-x_0)^2+(y-y_0)^2+4 h^2)^{\frac{5}{2}}}$$ As a first try, I evaluated ...
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0answers
121 views

Fourier Scaling Issue

First a little background: I’ve looked at the following discussions on StackExchange and still racking my head on Fourier What are the most common pitfalls awaiting new users? Discrepancy between ...
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0answers
283 views

How to perform local Fourier Transform of an image?

Consider an image (img) as A nice explanation of the Fourier transform of an image can be found here. However, I want to perform the Fourier transform locally. For ...
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0answers
157 views

Fourier transform of imaginary exponential with absolute value argument [closed]

When asked to compute FourierTransform[Exp[(-I*Abs[x])], x, k, FourierParameters -> {1, 1}] Mathematica returns ...
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1answer
57 views

Passing arguments correctly to FourierTransform

I'm trying to define the functional $T$ on test functions $f$ and $g$ in Mathematica 11, where $$T(f,g) = \int_{-\infty}^\infty\hat{f}(x)\hat{g}(-x)\,dx$$ So I have written: ...
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3answers
348 views

DFT: Fourier Plot Not Giving Expected Result

I'm trying use Mathematica to compute the Discrete Fourier Transform (DFT) of a table of data points and then plot the result. As a test run, I took values from the function $x=f(t)=\sin(2\pi t) $ for ...
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2answers
163 views

FourierParameters default differs from documentation?

Running Mathematica 11.2.0 I see in the documentation that FourierParameters defaults to {0,1}, yet when I try a Fourier transform with the default options, vs those values explicitly, I get different ...
0
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1answer
98 views

Plotting a sum for a series of sine and cosine all within the same height on the x-y axis? [closed]

The limits of the graph should be (0,1) on the x and y axis but mine is [1,11] on x-axis and [0,7] on the y axis. Any idea what to do? ...
0
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1answer
414 views

Problem plotting partial sum of a Fourier series

I'm new to using Mathematica, and I have a problem with plotting Fourier series partial sums. In particular, my target is to plot the Fourier series of my piecewise function and with that function ...
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0answers
161 views

Fourier | Examples | Applications | Frequency Identification: high resolution: what trick is this?

My question is regarding one of the examples in the Documentation Center for the built-in symbol Fourier: Fourier | Examples | Applications | Frequency Identification Fourier is used to find the ...
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2answers
208 views

frequency shift in Fourier transform

Have a bit of an analysis issue with Fourier transform of a sinusoidal signal: I have a piece of signal that represents spatial scanning of a pattern. xcoordinate is distance and y is amplitude. I'm ...
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4answers
1k views

How fast is my fidget spinner spinning? A sound experiment!

I would like to measure how fast my 6-bladed fidget spinner spins. To do so, after giving it a hard spin, I gently touch the spinner with a wooden stirring stick to create a buzzing sound which ...
2
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1answer
742 views

Fourier Transform plot of a piecewise function

I'm working with financial data. I used "Find Formula" to find an approximate function and then I applied FourierTransform to it. Here are the function and the Fourier Transform: ...
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0answers
238 views

How to realize the contribution of each row in the Fourier Transform of an image?

Let me first show you what I have done so far. ...
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1answer
125 views

Fourier transform of $1/\sin(\pi x)$ - a quest to find the sign function!

While performing the following (presumably) correct manipulations in Mathematica, I obtain a result that is missing a sign function. Is there a mistake in my code, or is there some bug in Mathematica? ...
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1answer
70 views

Integrating problem using interface

lately I tried to develop an interface that will plot the furier sum of a given function up to a given number of terms. The code is here: ...
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4answers
2k views

Circular Aperture Diffraction Pattern

I am unsure if this is even possible in Mathematica, but my optics professor assigned a project to me on circular apertures and Fourier transforms. I have found plenty on the Airy function, but I am ...
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1answer
282 views

Ideal/Brick wall Low/High-pass filters: Fourier approach not working

I am trying to take a signal (as a list) and separate it into the low frequency and high frequency parts around some split frequency f. Given that what little signal processing I ever studied is now ...

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