Discrete Walsh-Hadamard Transform in Signal Processing

The Walsh-Hadamard transform (WHT) is an orthogonal transformation that decomposes a signal into a set of orthogonal, rectangular waveforms called Walsh functions. The transformation has no multipliers and is real because the amplitude of Walsh (or Hadamard) functions has only two values, +1 or -1.Therefore WHT can be used in many different applications, such as power spectrum analysis, filtering, processing speech and medical signals, multiplexing and coding in communications, characterizing non-linear signals, solving non-linear differential equations, and logical design and analysis. An orientation on the use of Hadamard matrix and Walsh matrix for the computer assisted signal processing of a particular signal is proposed here. The structure of the Walsh matrices and Hadamard matrices are briefly discussed.