A new waveform analyzer based on the Walsh transform is developed and is applied to a real-time filtering of fast pulse signals, and the linear filterings of time signals through the Walsh transform is discussed. The analyzer converts a solitary waveform during 16 μs into the 16 Walsh amplitude spectra in a hybrid manner: it has the sequency band from 62.5 kzps to 500 kzps. The spectra are parallelly held during 16 μs by analog integrators, while serially displayed by the CRT, and one of them is digitally read out. The spectra of the test waves are measured within the error rate of several per cent. The analyzer is applied to the correlative detection of the photoelectric pulse signals in a gasspectroscopic system using a pulse laser, and there composes the matched filter, which is useful for measuring the signals superposed by Gaussian noises with a high accuracy. For the real-time filtering of fast signals, the arithmetic convolution and the frequency power spectra are approximated using the complex Walsh transform.
These approximations are of practical use in 16 or 32 dimensions. Then, the matched filters for pulse peaking are given by the approximate convolution and by the dyadic convolution.