The ratio spectrum: Theory, applications and analog implementation

The power spectrum is fundamental to signal analysis and understanding and has found many applications in communications, speech, and radar. One of the disadvantages of using the power spectrum is that the estimate of the power spectrum is inconsistent, meaning that the variance of the estimate does not approach zero even when the data length grows infinitely large.; Lim and Harris have developed a simple analog IC for Ratio Spectrum (RS) computation. The RS is formed by computing the ratio of the power of a low-pass filtered signal to the power of the original un-filtered signal for all possible filter cutoff frequencies. The RS has many advantages over the traditional power spectrum, particularly in terms of improved feature extraction and efficient implementation in analog circuitry.; We first study the important result that the integrated spectrum and the ratio spectrum are consistent estimators unlike the widely used power spectrum. This property makes the integrated spectrum and the ratio spectrum more useful for some applications than the conventional power spectrum. In addition, we derive the mean and variance of the ratio spectrum and obtain an approximate closed-form solution. As a result, the ratio spectrum estimate is asymptotically consistent, which is verified by the simulations.; We next propose a detection algorithm for unknown signals using the RS. In the algorithm, we sample the ratio axis to enhance the signal to noise ratio such that the detection performance can be improved. We also analyze the detection performance. Furthermore, we show that the performance of the algorithm is better than the conventional GLRT for bandlimited signals with fewer assumptions made. In addition, we propose a RS domain based algorithm for parameter estimation. Using the consistency property of the RS, we show that improved performance can be achieved.; An improved analog IC for the analog implementation of the RS has been designed, implemented and tested. In the chip, a tenth-order Butterworth g_m-C LPF is designed, and the cutoff frequency of the LPF can be widely adjusted from 100Hz to 5KHz. We describe the circuits and discuss their design considerations, such as the cascade sequence issue for the filter. In the implementation of the RS, we analyze the convergence performance and steady state error, which are important issues for any adaptive system. Using piecewise linear techniques, we derive equations for computing the convergence time, which are verified by simulations and chip measurements. The power computation circuit consists of a square and a LPF. We also discuss the selection of the cutoff frequency in the LPF. One of the advantages of using this design is that the short time window needed for non-stationary signal can be achieved by the design.; Finally, we conduct the chip test for both assumed signals and real speech signals. In the chip test, 1% deviation is achieved for a pure sinusoid signal input, and less than 7% deviation is achieved for the real speech signals. As a result, the main features can be recognized by using the RS obtained from the chip. We believe that the analog ratio spectrum offers an alternative to conventional filter banks for signal processing applications.