Noise-shaping Quantizer Research Articles

Sigma-Delta and distributed noise-shaping quantization methods for random Fourier features

Abstract We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs—even in the case of $1$-bit quantization—allow a high-accuracy approximation of the underlying kernels, and the approximation error decays at least polynomially fast as the dimension of the RFFs increases. We also show that the quantized RFFs can be further compressed, yielding an excellent trade-off between memory use and accuracy. Namely, the approximation error now decays exponentially as a function of the bits used. The quantization algorithms we propose are intended for digitizing RFFs without explicit knowledge of the application for which they will be used. Nevertheless, as we empirically show by testing the performance of our methods on several machine learning tasks, our method compares favourably with other state-of-the-art quantization methods.

An 81.6 dB SNDR 15.625 MHz BW Third-Order CT SDM With a True Time-Interleaving Noise-Shaping Quantizer

This work introduces a time-interleaved architecture to tackle the speed-resolution bottleneck of the noise-shaping (NS) successive approximation register (SAR) quantizer in a continuous-time (CT) sigma-delta modulator (SDM). A critical insight is that introducing a delay in the NS quantizer feedback loop enables complete parallelization of the NS quantizer operations. The extra time from parallelization greatly relaxes loop filtering and residue integration and enables a high quantizer resolution. Furthermore, the extra time in the feedback loop allows data weighted averaging (DWA), which eliminates the need for calibration. The prototype comprises a second-order CT front-end and a fully interleaved first-order NS quantizer. The prototype is fabricated in a 28 nm process, occupies 0.072 mm2 and consumes 6.4 mW. The peak signal-to-noise ratio (SNR), signal-to-noise-distortion ratio (SNDR), and dynamic range (DR) are 83.9, 81.6, and 84.8 dB, respectively, in a 15.625 MHz bandwidth. The corresponding Schreier SNDR figure of merit (FoM) is 175.5 dB.

A Hybrid-Loop Structure and Interleaved Noise-Shaped Quantizer for a Robust 100-MHz BW and 69-dB DR DSM

A continuous-Time delta-sigma modulator (CT-DSM) excels at high-bandwidth (BW), high-dynamic-range analog-to-digital conversion. However, CT-DSMs suffer from PVT variation, high sensitivity to timing errors, and are restricted in sampling rate. This work proposes a hybrid-loop (HL) DSM architecture to mitigate the disadvantages of CT-DSM while providing similar performance. This work also introduces a bandpass time-interleaved noise-shaping (TINS) successive-approximation (SAR) architecture, which increases the sampling rate of TINS SAR. A prototype HL-DSM with bandpass TINS-SAR quantizer is built in 28-nm CMOS and occupies a die area of 0.09 mm². The measured peak SNDR is 67.5 dB for a 100-MHz BW. The total power consumption is 13.4 mW at a sampling rate of 1.6 GS/s. The resulting Schreier FoM of 166.2 dB is comparable to state-of-the-art CT-DSM converters.

Delta-sigma ADC modulator for multibit data converters using passive adder entrenched second order noise shaping

This paper introduces a multi-bit data converters (MDC) modulator of the 2nd order delta-sigma analog-to-digital converter use the passive adder proposed. The noise shaping quantizer can provide feedback that has generated quantization noise and perform additional shaping noise first-order by coupling noise method.Thus, two Integrator's with ring amplifier and the MDC is shaped by noise coupling quantizer know the 2nd-order noise coupled with somewhat of a DAC modulator. At a summing point, the inputs are summed and then filtered with a low pass filter. A cyclic second order response is generated with a data weighted averaging (DWA) technique in which the DACs ' outputs are limited to one of two states in the noise shaping responses. Mainly as a result of the harmonic distortion in circuits of amplifier. Transistor rate is equipped for the fully differential switched condenser integrator used, a comparator and DWA. The modulator with proposed DWA design, almost quarterly improved timing margin. A simulated SNDR of 92dB is obtained at 20 MHz sampling frequency; while a sinusoidal output of 4.112 dBFS is tested at 90µs besides 20 MHz as the bandwidth. The power consumption is 0.33 mW while the voltage of the supply is 1.2V.

A fourth‐order incremental ADC in three‐step

This letter presents a second-order incremental ADC (IADC) operated in three steps, which extends the performance of a second-order IADC close to that of a fourth-order IADC with only two amplifiers. It performs a second-order noise-shaping quantization in the first step operation. Reusing the same hardware, the circuit is reconfigured to perform fine quantization as a first-order IADC in the second and third step. Within a conversion time of 60 clock periods (oversampling ratio OSR = 60), 35 dB signal-to-quantization-noise ratio is boosted. The proposed topology is very suitable for low-bandwidth high-resolution data conversion.

Design of Noise Shaping Quantizers for Data Compaction of Neural Networks

Design of Noise Shaping Quantizers for Data Compaction of Neural Networks

A 4th-Order Continuous-Time Delta-Sigma Modulator Using 6-bit Double Noise-Shaped Quantizer

This paper presents a continuous-time delta-sigma modulator using a double noise-shaped quantizer (DNSQ), which not only provides 2nd-order noise shaping but also generates a 6-bit quantization in the modulator. The proposed DNSQ efficiently extracts the quantization error in the time domain from a noise-shaped integrating quantizer (NSIQ), and directly applies it to a gated ring oscillator-based quantizer, hence achieving a 2nd order of noise shaping on its own. By incorporating the DNSQ, the modulator can achieve 4th-order noise shaping with only a 2nd-order loop filter. The proposed modulator is fabricated in a 0.13- $\mu \text{m}$ CMOS process with an active area of 0.17 mm2. It operates at 640 MHz and achieves a peak SNDR of 80.4 dB in a 15-MHz bandwidth while consuming 11.4 mW from a 1.2-V power supply.

An oscillatory noise‐shaped quantizer for time‐based continuous‐time sigma‐delta modulators

SummaryIn this paper, a new type of an oscillatory noise‐shaped quantizer (NSQ) for time‐based continuous‐time sigma‐delta modulators is presented. The proposed NSQ is composed of an oscillatory voltage‐to‐time converter and a polyphase sampler. Using Tustin's transformation method and through the approximation of the comparator gain, a linearized model of the NSQ is introduced. This way, a novel realization of the first‐ and second‐order NSQ is presented. Its implementation is based on fully passive continuous‐time filters without needing any amplifier or power consuming element. The ploy‐phase sampler inside the NSQ is based on the combination of a time‐to‐digital and a digital‐to‐time converter. The layout of the proposed NSQ is provided in Taiwan Semiconductor Manufacturing Company 0.18 μm complementary metal‐oxide‐semiconductor 1P6M technology. The verification of the proposed NSQ is done via investigating both the system level and postlayout simulation results. Leveraging the proposed NSQ in an Lth‐order time‐based continuous‐time sigma‐delta modulator enhances the noise‐shaping order up to L + 2, confirming its superior effectiveness. This makes it possible to design high performance and wideband continuous‐time SDMs with low power consumption and relaxed design complexity.

High-performance time-based continuous-time sigma-delta modulators using single-opamp resonator and noise-shaped quantizer

In this paper, a new methodology to improve the performance of continuous-time sigma-delta modulators is presented. The proposed structure notated as the time-based continuous-time sigma-delta modulator (TCSDM) utilizes the time encoding approach. Time-based encoding is known as a promising alternative to overcome the resolution problems of analog-to-digital converters (ADCs) in low-voltage circuits. The proposed TCSDM incorporates a novel time-based noise-shaped quantizer (NSQ) to significantly enhance its performance at a very low cost. Using the proposed NSQ, the modulator's noise-shaping order is improved by two without increasing the loop filter order. Furthermore, the implementation of the proposed TCSDM is alleviated using a new single-opamp resonator (SOR) to realize the loop filter. This significantly reduces the power consumption and saves more area. The concept is elaborated for a second-order TCSDM. The analytical calculations and the system-level simulation results are presented to verify the performance. To further confirm the effectiveness of the presented structure, the circuit-level implementation of the modulator is provided in TSMC 90nm CMOS technology. The results show that the proposed modulator achieves a dynamic range of 82dB over a 30MHz bandwidth while consuming less than 18.2mW power from a single 1V power supply. With the proposed NSQ and SOR, both the order and bandwidth requirements of the loop filter are relaxed, and as a result, the analog complexity of the modulator is significantly reduced.

Distributed Noise-Shaping Quantization: I. Beta Duals of Finite Frames and Near-Optimal Quantization of Random Measurements

This paper introduces a new algorithm for the so-called "Analysis Problem" in quantization of finite frame representations which provides a near-optimal solution in the case of random measurements. The main contributions include the development of a general quantization framework called distributed noise-shaping, and in particular, beta duals of frames, as well as the performance analysis of beta duals in both deterministic and probabilistic settings. It is shown that for random frames, using beta duals results in near-optimally accurate reconstructions with respect to both the frame redundancy and the number of levels that the frame coefficients are quantized at. More specifically, for any frame $E$ of $m$ vectors in $\mathbb{R}^k$ except possibly from a subset of Gaussian measure exponentially small in $m$ and for any number $L \geq 2$ of quantization levels per measurement to be used to encode the unit ball in $\mathbb{R}^k$, there is an algorithmic quantization scheme and a dual frame together which guarantee a reconstruction error of at most $\sqrt{k}L^{-(1-\eta)m/k}$, where $\eta$ can be arbitrarily small for sufficiently large problems. Additional features of the proposed algorithm include low computational cost and parallel implementability.

Low-OSR Over-Ranging Hybrid ADC Incorporating Noise-Shaped Two-Step Quantizer

A noise-shaped two-step ADC is presented in this paper. This ADC exploits residue feedback and a new capacitor/opamp sharing scheme to achieve high order noise shaping with minimal design complexity. The application of the proposed architecture in low power Delta-Sigma modulators is studied in this paper. A prototype ADC is fabricated in a 0.18 μm CMOS process. With a 1.56 MHz bandwidth (8x OSR), 2.6 mW analog power consumption, and 1.2 V analog supply voltage, the measured dynamic range and SNDR of this prototype IC are 78 dB and 75 dB.

Real-Time Perceptual Moving-Horizon Multiple-Description Audio Coding

A novel scheme for perceptual coding of audio for robust and real-time communication is designed and analyzed. As an alternative to PCM, DPCM, and more general noise-shaping converters, we propose to use psychoacoustically optimized noise-shaping quantizers based on the moving-horizon principle. In moving-horizon quantization, a few samples look-ahead is allowed at the encoder, which makes it possible to better shape the quantization noise and thereby reduce the resulting distortion over what is possible with conventional noise-shaping techniques. It is first shown that significant gains over linear PCM can be obtained without introducing a delay and without requiring postprocessing at the decoder, i.e., the encoded samples can be stored as, e.g., 16-bit linear PCM on CD-ROMs, and played out on standards-compliant CD players. We then show that multiple-description coding can be combined with moving-horizon quantization in order to combat possible erasures on the wireless link without introducing additional delays.

ANALYSIS AND DESIGN OF ONE-BIT NOISE-SHAPING QUANTIZER USING VARIABLE STRUCTURE CONTROL APPROACH

This paper offers a straightforward analysis of a one-bit noise-shaping quantizer based on variable structure control methods. The method uses the concept of equivalent control to access the bound on the state signals when the sliding condition is reached. For a stable loop filter, the global stability can be proved to exist by using the Lyanpunov stability theory. For an unstable loop filter, this paper proposes a state constraint approach to ensure that the sliding condition is achieved. Simulation examples and an experimental circuit constructed using off-the-shelf electronic components are given to demonstrate the correctness of the theoretical analysis.

Comments on "A subjective evaluation of noise-shaping quantization for adaptive intra-/interframe DPCM coding of color television signals" (by B. Girod et al.)

In the above named work by B. Girod et al. (see ibid., vol.36, no.3, p.332-46, 1988), a stability condition for a DPCM (differential pulse code modulation) system with additional quantization error noise shaping has been proposed. In the present work, a correction of this stability condition is derived. >

A subjective evaluation of noise-shaping quantization for adaptive intra-/interframe DPCM coding of color television signals

Nonuniform quantizers for just-not-visible reconstruction errors in an adaptive intra-/interframe DPCM (digital pulse-code modulation) scheme for component-coded color television signals are presented, both for conventional and for noise-shaping DPCM. Noise feedback filters that minimize the visibility of reconstruction errors by spectral shaping are designed for Y, R-Y, and B-Y. A closed-form description of the masking function is derived which leads to a one-parameter b-quantizer characteristic. Subjective tests that were carried out to determine visibility thresholds for reconstruction errors for conventional DPCM and for noise shaping DPCM show significant gains by noise shaping. For a transmission rate of around 30 Mb/s, reconstruction errors are almost always below the visibility threshold if variable length encoding of the prediction error is combined with noise shaping within a 3:1:1 system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>