Time-sequency-limited signals in finite Walsh transforms (Corresp.)

The relation between time-limiting and sequency-band-limiting in finite Walsh transforms is considered. It is found that optimum solutions (energy ratio equal to unity) are a nontrivial linear combination of
[TM/N]
successive orthogonal block pulses of duration
R = NM^{-1}
. Optimum solutions for bandpass signals are pointed out. Extension to the continuous-time domain is also discussed.