C++ library for signal processing

Question

I wrote a research project in matlab that uses quite a few functions which I do not want to re-implement in C++, so I'm looking for libraries to handle these for me. The functions I need are: (by order of importance)

1. Hilbert transform
2. Matrix functions(determinant, inverse, multiplication...)
3. Finding roots of polynomials(for degrees greater than 5)
4. FFT
5. Convolutions
6. correlation(xcorr in matlab)

Answer 1

I don't know about most of those, but FFTW is the 'fastest Fourier transform in the West'. It is used in the MATLAB implementation of fft().