Analog Wavelet Transformer Draft #

This paper describes the theory and implementation in CMOS technology of a circuit which performs analog wavelet decompositions of a one-dimensional (e.g., sound) input. The circuit is based on the Analog VLSI techniques described by Carver Mead in Analog VLSI and Neural Systems 1]. The analog wavelet outputs are the output of a logarithmically scaled set of bandpass lters; each band is sampled at a rate proportional to the Nyquist rate of the highest frequency content of that band. The result is a matrix of discrete points describing the input signal as a function of both frequency and time. The lter function of each band is gaussian shaped in order to best resolve the uncertainty relation between time and frequency at each sampled point. This chip has been designed by Tim Edwards under the direction of Michael Godfrey, and fabricated by MOSIS. Zilog Corporation of Campbell, California, provided the funding for this project. 1 Overview This paper describes the Analog Wavelet Transform chip, a CMOS subthreshold circuit design intended for use in an experimental speech compression system. This chip was built as an alternative to using a computer or DSP system to perform the same calculations; the advantages of this approach are reduced size and power consumption. The resulting analog implementation is innexible in terms of ability to reprogram the function performed, and requires dealing with the problem of temperature sensitivity, variable process parameters, and noise injection throughout the circuit. However, we believe that the circuit will be eeective for speech signals and will be smaller and cheaper than the digital alternatives. The Wavelet transform performed by the chip is an analog ltering function and is similar to what is known as the Gabor spectrogram (and is not to be confused with the Discrete Wavelet Transform))2], which divides a signal into a set of frequency bands (in this case, six), often on a logarithmic scale, using a gaussian-shaped lter as the bandpass function. We have used complex demodulation so that the center frequency of each lter band is zero 3]. Two outputs for each lter band preserve phase information about the signal in order to provide the ability to reconstruct the signal from its decomposed outputs. The total combined bandwith of the outputs is approximately equal to the bandwidth of the original signal. The original version of this paper, for the rst-generation chip, accurately describes the theory behind the continous …