This paper presents design algorithms for hybrid filter banks (HFB's) for high-speed, high-resolution conversion between analog and digital signals. The HFB is an unconventional class of filter bank that employs both analog and digital filters. When used in conjunction with an array of slower speed converters, the HFB improves the speed and resolution of the conversion compared with the standard time-interleaved array conversion technique. The analog and digital filters in the HFB must be designed so that they adequately isolate the channels and do not introduce reconstruction errors that limit the resolution of the system. To design continuous-time analog filters for HFB's, a discrete-time-to-continuous-time ("Z-to-S") transform is developed to convert a perfect reconstruction (PR) discrete-time filter bank into a near-PR HFB; a computationally efficient algorithm based on the fast Fourier transform (FFT) is developed to design the digital filters for HFB's. A two-channel HFB is designed with sixth-order continuous-time analog filters and length 64 FIR digital filters that yield 086 dB average aliasing error. To design discrete-time analog filters (e.g., switched-capacitors or charge-coupled devices) for HFB's, a lossless factorization of a PR discrete-time filter bank is used so that reconstruction error is not affected by filter coefficient quantization. A gain normalization technique is developed to maximize the dynamic range in the finite-precision implementation. A four-channel HFB is designed with 9-bit (integer) filter coefficients. With internal precision limited to the equivalent of 15 bits, the maximum aliasing error is 070 dB, and with the equivalent of 20 bits internal precision, maximum aliasing is 0100 dB. The 9-bit filter coefficients degrade the stopband attenuation (compared with unquantized coefficients) by less than 3 dB.
This paper presents a novel approach to high-speed, highresolution analog-to-digital (A/D) conversion using a hybrid filter bank with an array of slower speed A/D converters (ADCs). The hybrid filter bank is a new class of filter bank that employs continuous-time analysis filters to allocate a frequency band to each ADC in the array and discrete-time synthesis filters to reconstruct the digitized signal. The filter bank improves the speed and resolution of the A/D conversion by reducing the effects of mismatches between the ADCs in the array. This paper presents a filter design algorithm which minimizes mean-squared reconstruction error for the M-channel hybrid filter bank. A near-perfectreconstruction, two-channel hybrid filter bank which introduces 0.00095 dB average deviation from 0 dB distortion and -108 dB average aliasing is developed.
Backscattered energy from a medium with nearly constant velocity measured by an omnidirectional source-sensor comes from spherical shells centered at the source-sensor location. If source and sensor locations differ, the energy comes from ellipsoidal shells. To image the scattering potential or reflectivity of the medium, backscattered energy must be projected onto ellipsoids with a weighting factor dependent on the eccentricity of the ellipsoid. Eccentricity is the ratio of the separation of source and sensor to the path length from source to scatterer to sensor. Because path length changes with time, this weighting factor is, in general, time-dependent. It is consistent only if the source and sensor location are the same, in which case its value is unity. To estimate scattering potential or reflectivity at a given site, the backscattered signal which could have arisen from that site as measured by a given source-sensor pair is weighted by that pair's time-dependent ellipsoidal factor, then the weighted backscattered signals are averaged over all available source-sensor pairs.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.