Demonstrations

\(z(t)=Ae^{i(\omega t+\phi)}\)

\(\operatorname{Re}\{Ae^{i\phi}e^{ikx}e^{i\ell y}\}\)

\(\operatorname{Re}\{E(x,t)\}=E_0\cos(\omega t-kx)\)

Python + NumPy + WebAssembly

Programming task 1 · Fourier series

\(\mathcal{F}^{-1}\{|I_1|e^{i\angle I_2}\}\)

\(x_N(t)=T^{-1}\sum_{k=-N}^{N}e^{i2\pi kt/T}\)

Listen to sparse Fourier reconstruction

\(x_N(t)=\frac12+\frac{2}{\pi}\sum_{m=0}^{N-1}\frac{\sin((2m+1)2\pi t/T)}{2m+1}\)

\(\left|\operatorname{STFT}\{x(t)\}\right|\)