A novel delta-sigma modulator that employs a non-uniform quantizer whose spacing is adjusted by reference to the statistical properties of the input signal is proposed. The proposed delta-sigma modulator has less quantization noise compared to the one that uses a uniform quantizer with the same number of output values. With respect to the quantizer on its own, Lloyd proposed a non-uniform quantizer that is best for minimizing the average quantization noise power. The applicable condition of the method is that the statistical properties of the input signal, the probability density, are given. However, the procedure cannot be directly applied to the quantizer in the delta-sigma modulator because it jeopardizes the modulator's stability. In this paper, a procedure is proposed that determine the spacing of the quantizer with avoiding instability. Simulation results show that the proposed method reduces quantization noise by up to 3.8 dB and 2.8 dB with the input signal having a PAPR of 16 dB and 12 dB, respectively, compared to the one employing a uniform quantizer. Two alternative types of probability density function (PDF) are used in the proposed method for the calculation of the output values. One is the PDF of the input signal to the delta-sigma modulator and the other is an approximated PDF of the input signal to the quantizer inside the delta-sigma modulator. Both approaches are evaluated to find that the latter gives lower quantization noise.

This paper demonstrates a pulse width controlled PLL without using an LPF. A pulse width controlled oscillator accepts the PFD output where its pulse width controls the oscillation frequency. In the pulse width controlled oscillator, the input pulse width is converted into soft thermometer code through a time to soft thermometer code converter and the code controls the ring oscillator frequency. By using this scheme, our PLL realizes LPF-less as well as quantization noise free operation. The prototype chip achieves 60 µm 20 µm layout area using 65 nm CMOS technology along with 1.73 ps rms jitter while consuming 2.81 mW under a 1.2 V supply with 3.125 GHz output frequency.

Quantization is an important operation in digital communications systems. It not only introduces quantization noise but also changes the statistical properties of the quantized signal. Furthermore, quantization noise cannot be always considered as an additive source of Gaussian noise as it depends on the input signal probability density function. In orthogonal-frequency-division-multiplexing transmission the signal undergoes different operations which change its statistical properties. In this paper we analyze the statistical transformations of the signal from the transmitter to the receiver and determine how these effect the quantization. The discussed process considers the transceiver parameters and the channel properties to model the quantization noise. Simulation results show that the model agrees well with the simulated transmissions. The effect of system and channel properties on the quantization noise and its effect on bit-error-rate are shown. This enables the design of a quantizer with an optimal resolution for the required performance metrics.

This paper analytically formulates both the optimal quantization noise allocation ratio and the coding gain of the two-dimensional morphological Haar wavelet transform. The two-dimensional morphological Haar wavelet transform has been proposed as a nonlinear wavelet transform. It has been anticipated for application to nonlinear transform coding. To utilize a transformation to transform coding, both the optimal quantization noise allocation ratio and the coding gain of the transformation should be derived beforehand regardless of whether the transformation is linear or nonlinear. The derivation is crucial for progress of nonlinear transform image coding with nonlinear wavelet because the two-dimensional morphological Haar wavelet is the most basic nonlinear wavelet. We derive both the optimal quantization noise allocation ratio and the coding gain of the two-dimensional morphological Haar wavelet transform by introducing appropriate approximations to handle the cumbersome nonlinear operator included in the transformation. Numerical experiments confirmed the validity of formulations.

By modelling the quantization error as additive white noise in the transform domain, Wiener filter is used to reduce quantization noise for DCT coded images in DCT domain. Instead of deriving the spectrum of the transform coefficient, a DPCM loop is used to whiten the quantized DCT coefficients. The DPCM loop predicts the mean for each coefficient. By subtracting the mean, the quantized DCT coefficient is converted into the sum of prediction error and quantization noise. After the DPCM loop, the prediction error can be assumed uncorrelated to make the design of the subsequent Wiener filter easy. The Wiener filter is applied to remove the quantization noise to restore the prediction error. The original coefficient is reconstructed by adding the DPCM predicted mean with the restored prediction error. To increase the prediction accuracy, the decimated DCT coefficients in each subband are interpolated from the overlapped blocks.

A novel delta-sigma modulator that utilizes a resonant-tunneling diode (RTD) quantizer is proposed and its operation is investigated by HSPICE simulations. In order to eliminate the signal-to-noise-and-distortion ratio (SINAD) degradation caused from the poor isolation of a single-stage quantizer (1SQ), a three-stage quantizer (3SQ), which consists of three cascoded RTD quantizers, is introduced. At a sample rate of 10 Gsps (samples per a second) and a signal bandwidth of 40 MHz (oversampling ratio of 128), the modulator demonstrates a SINAD of 56 dB, which corresponds to the effective number of bits of 9.3.