# Questions tagged [fourier-transform]

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### Least Squares and Fourier Series

I have a little bit of problem figuring out the relation between Fourier series and Least Squares. As far as I understand, LS is a way of minimizing the quadratic error between a measured value $y_i$ ...
2k views

### Fourier Transform of function in Spherical Harmonics

I have a function $f(r,\theta,\phi)$ which I am expressing in terms of spherical harmonics $$f(r,\theta,\phi) = \sum_{l=0}^{\infty} \sum_{m=-l}^{l} g_{l,m}(r) d_{l,m}(\theta,\phi)$$ where $d_{l,m}$...
15k views

### C++ libraries for Fast Fourier Transform in high precision

I am looking for a C++ library for Fast Fourier Transform (FFT) in high precision (e.g., using high precision real data types similar to mpfr_t in MPFR or ...
339 views

### How to obtain values in physical space for a given spectrum?

My question falls under purview of turbulent flows. I want to add an initial perturbation, for which I have a given energy spectrum (say$E(k)=ak^4e^{-bk^2}$). The steps involved in getting these ...
375 views

### How to calculate efficiently and accurately the Fourier transform of a radial function in Fortran

As my question states, I want to calculate the Fourier transform $F(q)$ of a radial function $f(r)$ (defined on $[0,\infty)$ and which decays like an exponential $\exp(-Ar+b)$ at large $r$) as ...
88 views

### Calculate integrals using numpy.fft

Good evening, I would like to understand why I do not get the correct result: I assume that I know my function on discrete data points and expand it as a discrete Fourier transform: \$\text{sin}(x)=\...
776 views

### My calculated laser pulse duration is too large. Where am I wrong?

I am currently writing a small Python script to estimate the pulse duration from the optical spectrum. At the end, the idea is to observe the effects of the spectral phase on the pulse duration and ...