A fast digital hardware system far signal analysis and synthesis is presented. This system, combined with data compression or information rate reduction techniques, which are also discussed in the paper, provides a powerful tool for a variety of control, corn munication and signal processing applications. An illustrative 163 example is given. 1. INTRODUCTION Walsh functions constitute a family of binary orthogonal functions and find important applications in both the control and communication fields [lj-[8]. Among the various processes that can be accomplished using Walsh functions we mention sequency filtering, spectros-COPY. two-dimensional image transformation, optimal controller implementation, system identification,sysrerr state reconstruction (observer-design), and speech processing. The salient features of Walsh function expansions (transforms) which make them attractive in the abave applications are: (i) (ii) (iii) The Walsh coefficients are computed by simply adding and subtracting sampled values Of the signal waveform at hand. The signals can be reconstructed with good accuracy using only a few Walsh transform components (coefficients). Due to property (ii), fast algorithms can be designed in system and control applications, and a cansiderahle "data compression" OF "bit rate reduction" can be obtained in signal transmission applications. Our purpose in this paper is to present a new hardware system for processing (analysing and synthesizing) analague signals using Walsh functions, which can be easily implemented using LSI components. Actually signal analysis and synthesis with Walsh function transforms can be accomplished using software means, but the hardware method, which is cheap and fast, is preferable in on-line processing applications where dedicated special purpose equipment is required. The results reported in [6]-[a] were obtained using general purpose computing facilities (CDC-1700, PDP-15). Although the performance of Walsh-Hadamard transform in terms of bit rate reduction is not as good as that of the Fourier transform 01) the Karhunen-Lodve transform [6], it gives good results, in speech signal coding, if II to 8 dominant Walsh-Hadamard coefficients are used b]. Actually, in trying to reconstruct a sequency (Walsh frequency) band-limited signal using the Walsh function transform one must be campatible with the following sampling theorem which states [9]: "A signal x(t), sequency-band-limited to Z zeros/sec can be completely reconstructed from samples at every T=l/Zktl seconds, where k is an integer such that ZksZ. In particular: x(t)=x(i/P ktl 1, i/2 k+$t<(i+l)/2k+1.,t The present Walsh function processing system makes "se of the Walsh function generator and analyzer presented in [10],[11]. Some work making "se of microprocessors for converting the Walsh coefficients to Fourier coefficients or for simulating speech signals may be found in [12], 1131. Before presenting our signal processing system a short account of the basic digital processing theory "sing orthagonal transforms, followed by a review of some important experimental results, is given.