Analog circuits that are calibrated using digital-to-analog converters (DACs) use a digital signal processor-based algorithm for real-time adaptation and programming of system parameters. In this paper, we first show that this conventional framework for adaptation yields suboptimal calibration properties because of artifacts introduced by quantization noise. We then propose a novel online stochastic optimization algorithm called noise-shaping or ΣΔ gradient descent, which can shape the quantization noise out of the frequency regions spanning the parameter adaptation trajectories. As a result, the proposed algorithms demonstrate superior parameter search properties compared to floating-point gradient methods and better convergence properties than conventional quantized gradient-methods. In the second part of this paper, we apply the ΣΔ gradient descent algorithm to two examples of real-time digital calibration: 1) balancing and tracking of bias currents, and 2) frequency calibration of a band-pass Gm-C biquad filter biased in weak inversion. For each of these examples, the circuits have been prototyped in a 0.5-μm complementary metal-oxide-semiconductor process, and we demonstrate that the proposed algorithm is able to find the optimal solution even in the presence of spurious local minima, which are introduced by the nonlinear and non-monotonic response of calibration DACs.
Jump-resonance is a phenomenon observed in non-linear circuits where the amplitude of the output signal exhibits an abrupt jump when the frequency of the input signal is varied. For [Formula: see text] filters used in the design of analog auditory front-ends (AFEs), jump-resonance is generally considered to be undesirable and several techniques have been proposed in literature to avoid or alleviate this artifact. In this paper we explore the use of jump-resonance based hysteresis in [Formula: see text] band-pass filters for encoding speech formant trajectories. Using prototypes of silicon AFEs fabricated in a 0.5 μm CMOS process, we demonstrate the benefits of the proposed approach for extracting speaker discriminative features. These benefits are validated using speaker recognition experiments where consistent improvements in equal-error-rates (EERs) are achieved using the jump-resonance based features as compared to conventional features.
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