Syllabic-companding log domain filters

Abstract

Abstract-A general theory for companding log domain filters is proposed which combines not only exponential mappings, but also a new translational mapping approach which guarantees suitable operating conditions in any log domain filter. The filter equations resulting from the use of the theory ultimately contain translinear terms which are known to be realizable using translinear techniques. A discussion of the design of the companding filters, regarding the economical use of translinear loops and the convenient selection of system parameters, is offered which leads to first-and second-order circuit designs. Finally, the noise performance of an example design is investigated using a carefully crafted large-signal simulation technique, showing clearly the advantage of the companding filter approach.

Perceptual features for automatic speech recognition in noisy environments

“…The concept of companding has been applied in other fields of speech processing, particularly for improving the signal-to-noise ratio in cases where the dominant noise occurs after the compression block. It has also been applied in novel analog filtering circuits (Dolby, 1967;Frey et al, 2001). Fig.…”

Noise analysis of externally linear systems

“…The goal of the transformation in (35) and the extra equation (36) is to dynamically change the bias current of certain BJTs in the circuit implementation of (34) in terms of the envelope of measured by . Substantial amount of power can be saved in this way (see [26] and [27] for further details) compared to using constant bias currents.…”

“…The remaining parts of the analysis is straightforward. Using (33) to determine for each BJT, then applying superposition of the contributions of the eighteen noise sources, each contribution being given by an equation in the form of (15), the total output noise PSD can be written as The time averages in (52) can be computed easily, since if the main input is known, then is also known [as it was mentioned before, is related to the envelope of ] in a specified manner [26], [27]. In this case, and are determined as the output signals of the LTI systems defined by (34) and (36), respectively.…”

“…This will be illustrated in Section IV. Syllabic companding filters (e.g., those in [1], [10], and [27]) are typical examples of extended dimension systems. A detailed discussion of this material (excluding noise analysis) can be found elsewhere [23], [24].…”

“…We now analyze the noise of the circuit presented in [26], [27]. Assume that the first-order prototype system (34) is to be realized by an ELIN circuit with the mapping (35) where is the saturation current, is the thermal voltage of a BJT [see (32)], and the frequency are design parameters, and is governed by the first order differential equation (36) where the frequency is given and is a known function of time related to the envelope of .…”