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To be really good :
Math :
Fourier transforms
Laplace transforms
Discrete fourier transforms
Z transforms
Convolutions
Fourier series
Linear algebra
Wavelets
Random processes and noise
Numerical analysis
Matlab or python or c++
EE
Filters, amplifiers, etc,
Waveguides and transmission lines
Dsp texts
Machine learning (for if you want to apply it to stuff)
Stochastic processes
Probabilistic graphical models
Statistics stuff that might be of use
