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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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771 views

How to deal with highly oscillatory integrand when using “NIntegrate” and have a precise result

FTw][n_][w_]:=NIntegrate[ax[n][1][t]/.sol2]Exp[i w1 t],{t,0,600}] Plot[Abs[FTw[1][w1]],{w,1,3}] Here I'd like to calculate the Fourier transform of a complicated ...
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1answer
217 views

Discrete fourier transform vs analytical fourier transform [duplicate]

I have a function (myfun): scale = 3; fun[x_] := E^(-(x^2/2))/\[Pi]^(1/4) myfun[x_] := fun[x/scale]/Sqrt[scale] that is normalized: ...
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1answer
155 views

Numerical Integration With Many Singularities

Is possible a solution to this Numerical Integration? The constant values are as follows: ...
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1answer
1k views

How do I perform an FFT on a .wav file?

I've been trying all day to figure out how to do this. I have been able to import the data without any problem and have been able to also plot just the data. However, I keep getting error messages ...
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150 views

create a table of values for a Fourier series

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281 views

Plotting finite series with Bessel functions and Bessel zero's [closed]

I would like to plot the Nth partial sum of the Fourier series of $f(x) = 1$ with the 0th order Bessel function as the eigenfunctions. This sum corresponds to: $$\sum_{n=1}^N \frac{2 J_0(x \lambda_{...
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1answer
141 views

Smoothing of oscillatory function

I have a pretty gruesome expression of which I need to do the inverse Fourier transform twice (over two coordinates ($\omega$ to $t$ and $q$ to $r$)). $f(q,\omega)= \frac{ 2 \sqrt{\pi} \sqrt{\frac{...
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1answer
143 views

Using Fourier for periodicity and spike analysis

I am trying to look for significant peaks/spikes and periodic changes or fluctuations in about 60 time series of synthetic data. For example, in data1 below, there ...
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1answer
67 views

Why am I getting unexpected result while implementing Fourier Transform?

I have considered five signals of different amplitude, frequency and phase components and applied Fourier Transform using the code given below: ...
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1answer
85 views

An numeric Inconsistency in mathematica

Here are my mathematica command and output: ...
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1answer
98 views

Reorganise expression as trigonometric polynomial [closed]

I have this expression (obtained with Expand): ...
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1answer
480 views

Fourier series of the odd extension of a function [duplicate]

Using Mathematica to make a plot, I noticed that the interval it's defined over must be changed in order to do the Fourier series. How do I change the interval to be on an interval of $[-{\cal l}, {\...
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239 views

Error messages when using NInverseFourierTransform

I have two functions that I need to inverse Fourier transform and I was trying to get Mathematica to help me. I tried simply using theInverseFourierTransform ...
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37 views

Finding Fourier transform of a quantity v/s theta (0 to 360 degrees)

I have a physical quantity (experimentally measured) lets say T whose variation I have measured with angle (theta in degrees). I want to find out the Fourier components of this quantity with respect ...
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18 views

Plotting DiracDelta series

I'm dealing with the Fourier Transform of the following signal: ...
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46 views

What is the representation of the Harmonic Number being used by Mma in this result?

The Fourier Transform of the function F[x_] = (m/Sqrt[\[Lambda]])*Tanh[(Sqrt[x^2]*m)/Sqrt[2]] where all variables are real, and $m>0$ is given by (Mma 11.0) ...
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49 views

Fourier Transform and Inverse Fourier Transform of Lists

I am trying to compute the Fourier transform of a list, say an array of the form {{t1, y[t1]},.....{tn, y[tn]}}; apply some filters in the spectral components, and then back transform in time domain. ...
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34 views

Fourier transform of a 3D list {x,y,value}

I have a list of x and y coordinates and values corresponding to it. (Note: I don't have a function). ...
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49 views

How to solve integral equation involving Fourier Series

I have a set of equations involving two anti periodic functions $f(t+T)=-f(t)$ and $g(t+T)=-g(t)$ \begin{cases} f(t)&=J^2g(t)^3 \\ \mathcal{F}[g](\omega_n)&=\frac{1}{-i\omega_n-\mathcal{F}[...
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40 views

Harmonic amplitude spectrum

I have simulated an electrical machine in mathematica in discrete calculus. One of the results is three phase currents. My plotted answer is like below: Now I'm looking for harmonic amplitude ...
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27 views

Using `Integrate` and or `FourierTransform`

I have some general questions about Integrate and FourierTransform. Firstly with ...
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1answer
55 views

Integration not working

Can't seem to get this integration to work. s, n, b, b, l are all constants. ...
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45 views

Trouble with computing a Fourier transform

I am able to compute the Fourier transform of the general form Exp[-Sqrt[t]] as shown here: ...
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48 views

Discrete convolution power

In my previous question we have discussed the posibility of various definition of convolution of power function within Mathematica. Now the question is "How to define convolution power in Mathematica ?...
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38 views

Fourier on chosen dimensions

I have a data set DATA in 4 dimensions $A \times B \times C \times D$ and I want to use the Fourier function net only on the 2 ...
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35 views

Evaluating Fourier coefficients when Exponential terms are present

I am trying an analytical solution for a 3D Laplace equaition, and just wanted to know if I could use the symbolic calculation capabilities of Mathematica to calculate the Fourier coefficients ...
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28 views

Problem with symmetry and anti-symmetry of the fourier coefficients

let's say that I have a set of data ...
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55 views

Is there a way to find the Region of Convergence along with the Laplace Transform?

This is what I've tried so far. Is the inequality of the conditional expression the Region of Convergence? Why doesn't LaplaceTransform Generate conditions here? ...
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66 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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60 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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61 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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61 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 ...
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103 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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219 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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1answer
89 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? ...
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1answer
315 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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1answer
587 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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216 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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61 views

Prevent running out of memory when doing SpectrogramArray?

I was using SpectrogramArray[Import@"myFile", 22050, 22050]to transfrom a piano mp3 file so that I can (probably?) generate a midi file from that mp3. The step size ...
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452 views

Fitting by Fourier series and their coefficient [duplicate]

I have two arrays contain $y$ and $k$,respectively. However, the exact function relationship is not clear. What I what to do is to fit $y(k)$ by Fourier series $\qquad y=\sum_n c_n \cos(nk)$ up to $...
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75 views

Numerical error or mistake when filtering using Fourier?

I am comparing the filtering method using a recurrence filter with filtering using Fourier. I think both methods should give the same answer but they differ by a small amount that could be numerical ...
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103 views

Multidimensional DFT of function

Assume that we have a well-defined real-valued functionf[x,y,z] whose (inverse) Fourier transform is impossible to solve for symbolically and numerically using ...
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0answers
93 views

Help with Frequency Identification with Fourier? [duplicate]

Note: This question has been marked as a duplicate of What do the X and Y axis stand for in the Fourier transform domain?. While the answer will likely have an overlap, so the question should be ...
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67 views

(Naive) Manual implementation of DFT results in long sum which is very inefficient to plot, can my approach be saved?

I will do my best to keep this question as short as possible, I am afraid though that I wont be able to get my issue across if I don't elaborate on the background and provide my code as an example. ...
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85 views

Identify frequency components

I try to perform data analysis on wind power production. Data consist in 17520 points, corresponding to the production averaged over 30 minutes over the 365 days of the year. I somehow expect to see ...
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0answers
81 views

Problems with sampling

Let $t\ge 0$ and let $f_{s}(t)$ be the sampled version of $f(t)$. If $$f(t)=\begin{cases}\int_{0}^{t}\exp\left(-\frac{1}{1-s^{2}}\right)\,ds,&|s|<1, \\ 0,&\text{otherwise}.\end{cases}$$ I ...
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93 views

FourierTransform a differental-equations [duplicate]

I want to use the command FourierTransform to transform a differential equations from time - domain to complex frequency domain but it don't works. My code is ...
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0answers
310 views

Engineering spectral densities using filtered white noise

My goal is to create time-spectrum noise signals with spectral densities $S_{xx}(f)$ for pretty much arbitrary spectral densities (think white noise, lorentzian, $1/f$). In finding advice on how to do ...
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84 views

Fourier-style solutions to differential equations, not piecewise polynomials

NDSolve returns piecewise polynomials. Is there any way I can get a single (non piecewise) function consisting of sines and cosines instead? Sort of a "Fourier approximation" to the solution of my ...
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36 views

Why I am not getting the same frequency when sampling a waveform? [duplicate]

I am trying to simulate the sampling of a waveform to then apply FFT Analysis to it. Here is the sample code I have now using a square wave: ...