# 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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### 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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### Need to find Fourier series of the following graph

Need to find Fourier series of the following graph.....question is also written in figure.
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'...
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 $(-\frac{1}{2},\frac{1}{2})$:- ...
64 views

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-... 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 ... 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 ... 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: ... 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 <... 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 ... 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 ... 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): $$\... 1answer 213 views ### Re and Im relationships without Abs among Fourier, FourierTransform, InverseFourier, and InverseFourierTransform Is there a way to make Fourier's Re and Im components separately track the results of ... 3answers 711 views ### Find Fourier Series/Coefficients with Mathematica Hello I want to find the Fourier series and/or the coefficients for a function like the following: or or For the first one I did the following: ... 1answer 160 views ### Fourier Transform of a symbolic expression Hello I would like to do the Fourier Transform of H1'[t - L2[t]/c - L2primo[t]/c] I know that its transform has to be: ... 1answer 86 views ### Plot the graph of the square wave function defined as f(t)=\sum^{\infty}_{n=0}(-1)^n h_{n}(t) on the interval t>0 and find its Laplace transform Plot the graph of the square wave function defined as$$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/... 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, ... 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 ... 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 ... 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 ... 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 ... 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-... 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 ... 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 ... 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? 1answer 404 views ### How to find the Fourier Transform of a list? I have a list (list) in the form of {x,y} as ... 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 ... 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 ... 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? 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} $$So at first, I tried to evaluate a fancy MMA ... 0answers 235 views ### 2D Fourier transform of a diffraction pattern Mathematica vs FourierPainter We are trying to make sense of the numbers provided by the PC program FourierPainter for a 2D Fourier Transform of a diffraction pattern. We would like to evaluate the ratio of the zeroth harmonic ... 0answers 66 views ### 2d vs 1d FourierTransform According to the documentation, the multidimensional Fourier transform is defined as$$ \frac{1}{(2\pi)^{n/2}} \int_{-\infty}^\infty \int_{-\infty}^\infty \cdots f(t_1, t_2, \dots, t_n) \mathrm e^{\... 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 ... 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 ... 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 ... 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 ... 1answer 57 views ### Passing arguments correctly to FourierTransform I'm trying to define the functionalT$on test functions$f$and$g$in Mathematica 11, where $$T(f,g) = \int_{-\infty}^\infty\hat{f}(x)\hat{g}(-x)\,dx$$ So I have written: ... 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 ... 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 ... 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? ... 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 ... 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 ... 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 ... 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 ... 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: ... 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. ... 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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### 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: ...