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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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97 views

How to set up a Fourier transform?

I am having trouble figuring out how to set up the Fourier transform to: ...
563 views

Fourier in Mathematica different from octave [duplicate]

First I create a table of sin(x) within 0, 10 ...
723 views

Using Periodogram to investigate the seasonality of the data

After asking how to get rid of the seasonality of this set of data, I'd like to ask how to investigate the seasonality in data using Mathematica. Which tool would you use to study seasonality? I.e. ...
191 views

Comparing ordinates between FourierTransform and Fourier

I have a test function ff[t_] := Exp[-t^2 - t]. I have calculated the Fourier transform with FourierTransform: ...
119 views

Filling in explicit zeros in a (x,y) list for nonexisting y values for discrete Fourier transform in Mathematica

I have a list of (x,y) values in Mathematica for various discrete x values, as in ...
323 views

Why the Spectrogram can't plot correctly?

The same data lead two different graph. Plot[E^(-Pi*(t - 5)^2), {t, -10, 10}, PlotRange -> All] The method to plot the spectrogram use the build-in function: ...
839 views

Animated Wave Propagation using Fourier & InverseFourier

This is a continuation off of previous help on the first part of my project: fourier issue arising from input miscommunication Now I want to go one step further in the current code. Here's the code ...
287 views

Fourier transformation of Hann window is wrong

From the documentation f = FourierTransform[HannWindow[x], x, w]; Plot[Log10@Abs[f], {w, -80, 80}, PlotRange -> All] which produces Now I was trying to do ...
1k views

Why Fourier transform is symmetric no matter what interval I choose? [duplicate]

I'm solving a vibration problem. After solving two systems of ODEs (one valid in 0-0.1 and the other in 0.1-1) I get the plot of 3 functions, one of them is this, the plot of the variable $y_w$ (Image ...
146 views

Decomposition of a time series into sinusoids

I've noticed this interesting study on metatrader 4; see the picture below: Where the financial timeseries is "decomposed" (deconvolved?) into a series of periodic sinusoidal functions. In the ...
2k views

Fourier transform of interpolating function [closed]

I want to get a Fourier transform of an interpolating function and plot that Fourier transform: ...
784 views

Phase in discrete Fourier transformation [duplicate]

I asked a question some days ago and it was very well answer. However, I have a new one. I don't understand why the phase of the discrete fourier transformation is not correct. It has the correct ...
831 views

Averaging over a circle from FFT to plot the amplitude vs wavelength

I am trying to calculate the amplitude of FFT vs wavelength for some experiments. I had put a question here previously on how to compute the FFT of an image. Thanks to everyone who provided the ...
147 views

Apparently incorrect Fourier Series

While trying to compute Fourier Series, i find that It doesn't evaluate both positive and negative parts and hence apparently giving wrong answer. Below is the code that i tried: ...
221 views

Asymptotic behavior of Fourier transform of $\exp(-x^4)$ at large $k$

I am computing the Fourier transform $$\int_{-\infty}^{+\infty}\mathrm{d}x\,e^{-x^4+ikx}$$ for large $k$. Since $e^{-x^4}$ is $C^{\infty}$ on the whole real line, I expect its Fourier transform to ...
659 views

NFourierTransform of an interpolating function

I have an interpolating function called rs22 - a solution from NDSolve - which is defined from 0 to about 1 ms. rs22 is a function that reaches a non-zero equilibrium value. (only shown here up to ...
522 views

Sampling a musical instrument (or re-tuning MIDI)

I'd like to try to convert a piece of MIDI music made with SoundNote to another tuning (not microtonal or even split-black-keys, just a slightly different tuning for each note). I searched for pitch ...
102 views

Is there a way to scale a graph from the command Periodogram?

Does anyone know if there is a way to scale a graph from the command Periodogram? More specifically in terms of the y axis. I am wondering if there is a way that I can make the highest value on the y ...
936 views

Finding the dominant frequency in a large dataset with Fourier + periodogramm

I know there are dozens of questions about how to extract the correct frequency out of data, however I probably don't interpret my data correctly, or do not apply those answers correctly. Problem I ...
3k views

Discrete Fourier Transform with x axis data?

Usually, Fourier Transform in mathematica is supplied by y data only, like the famous Sin[x] transform example. What if my data is a list of ...
821 views

Getting correct amplitudes with Periodogram

I'm having some trouble with the function Periodogram, mainly with getting it to produce correct amplitudes for the spectrum it returns. My question is how to fix ...
361 views

Constructing the spectral density of white noise

My goal is to find the spectral density $S_{XX}(f)$ from a time domain noise signal $X(t)$. The approach should work for general time series, but to illustrate what I've been doing I'll keep it simple:...
613 views

Help with Fourier analysis and filtering of an image

I am starting with the following image: For the curious, it is an STM scanned image of graphite. I am hoping to find some kind of periodic structure in the image related to the honeycomb structure of ...
7k views

Fourier Transform of Absolute Value

If you ask Mathematica to provide the Fourier Transform of a singular functions it is likely to provide an answer that while nearly correct, is technically incorrect and it will do so without a word ...
265 views

What are good/best practices to take the Fourier transform of an InterpolatingFunction?

I have a function which I have obtained from numerical integration of a differential equation, and I would like to take its Fourier transform. What are good practices for doing this? To make things ...
202 views

Fourier Transform to help guess with NonLinearModelFit

I imported some data in Mathematica which I cleaned a bit. This process went well. I also managed to plot it, and tried to take the Fourier transform of the data and plot it again. I'm not sure if I ...
529 views

NIntegrate not working after interpolation

I used linear interpolation between points: ...
3k views

Obtaining the Fourier transform of an operator

We know that if we have a function $f(x)$, and we call $g(\omega)$ its Fourier transform, then the Fourier transform of $x f(x)$ is $$\imath \frac{\mathrm{d} g(\omega))}{\mathrm{d}\omega}$$ and ...
128 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, ...
174 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 ...
751 views

Why doesn't Mathematica evaluate FourierTransform[Exp[-t], t, w]?

I am having trouble getting Mathematica to evaluate a trivial Fourier transform. I would like to be able to evaluate the Fourier transform of the right-sided exponential decay function as shown ...
134 views

Why do I encounter 1/0 expression

I am trying to write my periodical function $f(t)$ in Fourier Series $$f(t)=\frac{a_0}{2}+\sum_{j=1}^Na_j\cos(j 2\pi t/\tau)+\sum_{j=1}^Nb_j\sin(j 2\pi t/\tau)$$ and I know that there is a really nice ...
301 views

Discrete Fourier Transform - Inadequate precision and wrong peak positions

I have a small problem with a piece of code. I searched the site but was not able to find an answer to my specific question. I am trying a quick test of the Fourier capabilities (on lists) of ...
610 views

Fourier Analysis: How to get rid of a discontinuity

When I compute the phase error of a spatial series data using Fourier analysis in Mathematica there's a discontinuity @ parameter ...
2k views

108 views

Fourier cosine series of displacement

I'm trying to calculate a Fourier Cosine Series of displacement for general 4-bar mechanism. My code not working. I don't understand why. I need the result as this form ...
2k views

Fourier Transform on a Sound

I don't really know much above Fourier Transform , or how it's used in Mathematica but I want to know how I can find out, out of which Sin-waves a (static) sound is made of. So for example I take "G" ...
226 views

Fourier transformation of image in only 1 dimension

I have the following image: img = Import["https://i.imgur.com/Peu6mwd.png"] Each column shows the y coordinate of some objects (each row is 0.012 mm apart) and the ...
712 views

Changing Function Domain of Fourier Series

If I write FourierSinSeries[x, x, 10] Mathematica will output the first 10 terms of the Fourier Sine Series f(x) = x defined for 0 < x < Pi. How do I output the the Fourier Sine Series for ...
457 views

Approximate $h$ in $F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$

Consider $$F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$$ $$|z|\le L$$ $$0 \le \theta \le \pi$$ By having knowledge of $F(\theta)$, how can one approximate $h(z)$? In addition, ...
243 views