# Fast Walsh-Hadamard Transform frequency spectrum?

Can the Fast Walsh-Hadamard Transform be used to find a Walsh-Hadamard frequency spectrum which some how relates to a Fourier frequency spectrum?

Is the Fast Walsh-Hadamard Transform more accurate than the Fast Fourier Transform when analyzing signals with very low bit resolution?

Below are the different Walsh-Hadamard harmonic signals stored in the matrix's columns ordered from lowest frequency to highest frequency across the matrix's rows with a lot of phase variation degeneracy in the mid-range frequencies. The matrix is symmetric.

octave:56> ifwht(eye(16)) .+ 1
ans =

2   2   2   2   2   2   2   2   2   2   2   2   2   2   2   2
2   2   2   2   2   2   2   2   0   0   0   0   0   0   0   0
2   2   2   2   0   0   0   0   0   0   0   0   2   2   2   2
2   2   2   2   0   0   0   0   2   2   2   2   0   0   0   0
2   2   0   0   0   0   2   2   2   2   0   0   0   0   2   2
2   2   0   0   0   0   2   2   0   0   2   2   2   2   0   0
2   2   0   0   2   2   0   0   0   0   2   2   0   0   2   2
2   2   0   0   2   2   0   0   2   2   0   0   2   2   0   0
2   0   0   2   2   0   0   2   2   0   0   2   2   0   0   2
2   0   0   2   2   0   0   2   0   2   2   0   0   2   2   0
2   0   0   2   0   2   2   0   0   2   2   0   2   0   0   2
2   0   0   2   0   2   2   0   2   0   0   2   0   2   2   0
2   0   2   0   0   2   0   2   2   0   2   0   0   2   0   2
2   0   2   0   0   2   0   2   0   2   0   2   2   0   2   0
2   0   2   0   2   0   2   0   0   2   0   2   0   2   0   2

• The answers are basically "No, there is no relationship between the Walsh-Hadamard spectrum and the Fourier spectrum", and "It depends on what you are looking for in your analysis". – Dilip Sarwate May 8 '14 at 13:53
• To avoid nitpickers, let me add to my previous comment by saying that if $N=2$, the Walsh-Hadamard transform and the DFT are one and the same. – Dilip Sarwate May 8 '14 at 14:04
• @DilipSarwate I was playing around with Octave's Fast Walsh-Hadamard Transform and its default Order is Sequency. The different signals generated from different Walsh-Hadamard frequency components are ordered from what I believe appears to be lowest frequency to highest frequency? – linuxfreebird May 8 '14 at 14:15