Allen Gersho

Theory of the photoacoustic effect with solids

When chopped light impinges on a solid in an enclosed cell, an acoustic signal is produced within the cell. This effect is the basis of a new spectroscopic technique for the study of solid and semisolid matter. A quantitative derivation is presented for the acoustic signal in a photoacoustic cell in terms of the optical, thermal, and geometric parameters of the system. The theory predicts the dependence of the signal on the absorption coefficient of the solid, thereby giving a theoretical foundation for the technique of photoacoustic spectroscopy. In particular, the theory accounts for the experimental observation that with this technique optical absorption spectra can be obtained for materials that are optically opaque.

Photoacoustic Effect with Solids: A Theoretical Treatment

Chopped light impinging on a solid sample in an enclosed cell produces an acoustic signal within the cell. A derivation for the acoustic pressure supports the experimental observation that optical absorption spectra may be obtained from the acoustic signal even when the sample is completely opaque to transmitted light. The complete solution for the temperature has the form A(x) + B(x)ejw in each medium, neglecting transients. Applying the boundary conditions of temperature and heat flux continuity at the sample surfaces (x = 0 and x = -1) and an ambient temperature To at the cell walls (x = -I -lb and x = lg), we can obtain the full temperature distribution throughout the cell. In particular, the a-c component of the gas temperature distribution is given by a=c(x, t) Oeg4x+it where 0 represents the complex amplitude of the time-dependent temperature of the solid sample at the solid-gas boundary (x = 0). The explicit expression for 0 is where y is the ratio of specific heats, P0 and VO are the ambient pressure and volume, respectively, and -6 V is the incremental volume. Thus we get

Charge-transfer filtering

Linear discrete-time (sampled-data) filters can be implemented in monolithic form on an MOS chip using a variety of recently developed and newly emerging techniques without requiring analog-to-digital conversion. An analog signal sample can be represented by an isolated quantity of charge and such packets of charge can be stored, transferred, and manipulated in other ways to perform signal processing operations. Best known of these techniques is the use of a charge-coupled device (CCD) to operate as an analog shift register. A simple modification of the CCD shift register allows the realization of transversal filters. Other techniques can implement recursive filter operations offering a great flexibility for filter design. The possibilities and limitations of charge-transfer filtering are reviewed and examined.

A Simple Growth Model for the Diffusion of a New Communication Service

The diffusion of an innovation such as a new communication service is modeled using a randomly generated network of interpersonal influence between members of a social system. Each member decides to adopt the innovation when K out of his particular set of L influencers have already become adopters. A discrete-time recursion is obtained which describes the evolution in time of the fraction of adopters. The model exhibits a critical mass effect, where the number of initial adopters must exceed a critical value for the diffusion to saturate the population, otherwise the diffusion ends prematurely without substantial growth. Also exhibited is a bandwagon effect, which explains a sudden upsurge in growth following an initial period of slow diffusion. Both phenomena are amply corroborated by Monte Carlo simulations for a population of 10 000 people.

Coefficient inaccuracy in FIR filters

Coefficient inaccuracy in FIR filters is known to degrade the frequency response particularly in stopband regions. The magnitude of the stopband degradation increases with the number of stages N, the length of the impulse response. A widely used formula for the error in frequency response is proportional to sqrt{N} . Recently, we have found that for random additive coefficient errors with variance σ2, the maximum error in frequency response for large N is given by sigmasqrt{NlogN} . This result is applied to an empirical formula relating the minimum number of stages, N, to specified lowpass filter performance parameters. The results lead to absolute bounds on attainable stopband rejection for band-select FIR filters. The realization of transversal filters with charge-coupled devices (CCDs) is particularly relevant to this study.