Grade 9General Physics
How do I compute the eigenfunctions of the Fourier Transform?
1 Answer
Vikas TU
By definition, to calculate the eigenvalues of the Fourier transform, solve the equation Ff(x)=λf(x) or ∫∞−∞f(x)e−2πiXxdx−λf(x)=0.
To decompose a function into Hermite-Gaussian functions HGn(x), i.e. find cn in f(x)=∑ncnHGn(x), take the inner product of f(x) with each Hermite-Gauss function: cn=∫∞−∞f(x)¯HGn(x)dx.
To decompose a function into Hermite-Gaussian functions HGn(x), i.e. find cn in f(x)=∑ncnHGn(x), take the inner product of f(x) with each Hermite-Gauss function: cn=∫∞−∞f(x)¯HGn(x)dx.
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