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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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1answer
97 views

### How to set up a Fourier transform?

I am having trouble figuring out how to set up the Fourier transform to: ...
1answer
563 views

### Fourier in Mathematica different from octave [duplicate]

First I create a table of sin(x) within 0, 10 ...
2answers
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. ...
1answer
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: ...
3answers
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 ...
1answer
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: ...
1answer
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 ...
1answer
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 ...
1answer
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 ...
1answer
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 ...
1answer
2k views

### Fourier transform of interpolating function [closed]

I want to get a Fourier transform of an interpolating function and plot that Fourier transform: ...
1answer
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 ...
1answer
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 ...
1answer
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: ...
1answer
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 ...
1answer
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 ...
1answer
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 ...
2answers
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 ...
1answer
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 ...
1answer
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 ...
1answer
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 ...
0answers
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:...
0answers
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 ...
0answers
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 ...
0answers
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 ...
2answers
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 ...
3answers
529 views

### NIntegrate not working after interpolation

I used linear interpolation between points: ...
2answers
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 ...
1answer
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, ...
2answers
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 ...
1answer
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 ...
2answers
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 ...
2answers
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 ...
2answers
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 ...
1answer
2k views

1answer
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 ...
1answer
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" ...
1answer
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 ...
1answer
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 ...
1answer
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, ...
1answer
243 views

1answer
44 views

### How does the Fourier transform take its input?

I'm using the Fourier command and I'm wondering how does it take its imput. I know that it takes a list of numbers representing a function of time and it gives back a list of numbers representing a ...
2answers
161 views

### Fourier transform of a bivariate normal distribution

I can define a Multinormal distribution by p = PDF[MultinormalDistribution[ {mu1, mu2}, {{sig11^2, ρ sig11 sig22}, {ρ sig11 sig22, sig22^2}}], {x, y}] I would ...