A robust O(N log n) algorithm for optimal decoding of first-order Σ-Δ sequences

Abstract

An exact recursive formula is derived to describe the structure of an ideal first-order 6-1outputsequenceasafunction of its input. Specifically, it is shown that every 6-1 sequence generated by the constant input [0 1] can be decomposed into a shorter 6-1 subsequence whose input [0 1) may be used to recover that of the original sequence. This formula is applied to develop an (log) algorithm for decoding an-length sequence. Without knowledge of the modulator's initial state, it exhibits an average improvement, over all initial states, of 4.2 dB in output signal-to-noise ratio (SNR) compared with a near-optimal linear finite impulse response (FIR) filter. The regularity of the ideal first-order 6-1 structure with constant inputs permits the algorithm to be extended to bandlimited and noise-corrupted data. A simple error correction procedure is demonstrated, and it is shown that the recursive algorithm can outperform FIR filters on sequences of length 64 having input SNRs as low as 30 dB.

High Dynamic Range adaptive ΔΣ-based Focal Plane Array architecture

“…Reset Noise: Since there is no extra reset required in the integration period, the reset noise should be the same as conventional architectures.σ 2 reset = KTC int /q 2 electron; (12) Shot Noise: Again, the same as conventional architectures.…”

High dynamic range adaptive ΔΣ-based focal plane array architecture

“…Filter Design: Sophisticated filters such as triangular, zoomer [19], recursive [12], optimal [20], etc. can enhance the SNR performance at the low end of Photo-diode current, at the cost of more circuit complexity and higher power consumption [13].…”

On incremental sigma-delta modulation with optimal filtering

“…The optimal filter in the form of "Zoomer" implementation was derived in [18]. In [19] McIlrath developed a nonlinear iterative filter that achieves significantly better performance compared to linear filters. We are now ready to introduce our framework for studying incremental Σ∆ quantization systems.…”