Quantisation-noise analysis of digital filters with controlled quantisation

Two models for quantisation noise in digital filters with controlled quantisation are derived. These models are generalisations of models that have been proposed previously for magnitude truncation quantisation. The use of the models is demonstrated by an example.     

Quantisation error curve: a measure of similarity betweenrequantised images

A new similarity measure between a digital image and its quantised version is presented. By calculating the quantisation error on each of a sequence of subdomains, we can obtain a quantisation error curve as a similarity measure. This measure outperforms the commonly used measure for estimating the similarity between requantised images     

Shape adaptive activity controlled multistage gain shape vector quantisation of images

The performance of a shape adaptive activity controlled multistage gain shape vector quantiser for digital image compression is compared with that of more established full search multistage vector quantisation methods. The advantages of the former approach to the vector quantisation coding of images are clearly demonstrated via computer simulation of the respective coding algorithms.     

Heuristic bounds for the frequency of digital oscillators due to quantisation noise

A deterministic approach is used to evaluate bounds for the frequency of the digital oscillator considering either roundoff or magnitude-truncation quantisation. With a proper choice of the number of significant digits, any degree of approximation for a specified sinusoidal oscillation can be achieved.     

Uniform analogue to digital conversion of a normal random process

A method which minimises the noncompanded quantisation error, associated with the uniform analogue to digital conversion of a normally distributed random variable, is presented. The theoretical derivations are verified experimentally.     

Proposed technique for reduction of contouring in quantised (monochrome) image signals

A technique of detecting the presence of quantisation-induced contours in digital monochrome image signals is presented and an interpolation process is proposed that reduces their visibility. Brief informal subjective tests suggest that the improvement is equivalent to a doubling in the number of quantisation levels.     

Quantisation effects in second-order wave digital filters

A novel quantisation strategy is found for the second-order wave digital filter proposed by Verkroost so that the filter possesses near-optimal noise performance and only exhibits very low amplitude limit cycles under constant input conditions.     

Auditory masking and MPEG-1 audio compression

In high-quality digital audio coding, a great deal of attention is focused on the auditory perception process, as the goal of audio compression is to attain perceptually-transparent compression and reproduction. Consequently models for perceptual masking are used extensively in audio coders, allowing quantisation noise to be allocated in the various frequency subbands according to a masking function. In this way, quantisation noise can be made almost inaudible at the receiver. In this paper, the psychoacoustic phenomenon of auditory masking is described. This is followed by a review of the MPEG-1 (Moving Pictures Experts Group) international standard for audio compression, including an outline of the psychoacoustic models used     

Design of f.i.r. direct-form digital filters with two quantisation steps

The direct-form realisation of f.i.r. linear-phase digital filters is investigated when the coefficients are separated in two groups with different quantisation steps. It is shown in an example that considerable improvement in coefficient word length can be achieved by this technique.     

High-order bandpass sigma-delta modulators for high speed D/Aapplications

A multiplier-free structure for implementing high-order bandpass digital sigma-delta modulators is described. Near-optimum noise suppression in the modulators passband region is attained after coefficient quantisation. High-speed operation is achieved as the critical delay path consists of only two adders in series, independent of the modulator order     

Synthesis and performance of a new class of implementation forhigh-order recursive digital filters

The authors investigate a new class of approaches to the synthesis of high-order recursive digital filters. These are all characterised by partitioning the overall filter into a set of parallel subfilters, each of which is of moderate order. The subfilters may be any of the classical implementations: direct form, parallel, cascade or lattice. The authors investigate cascade and lattice implementation of the subfilters. The investigation includes selection of the number of subfilters to use, how to derive their coefficients and theoretical noise calculations. This is supported by simulation testing of a variety of real and synthetic filters using maximal length binary sequences (MLS) as input as this provides information on both the linear and nonlinear errors involved. It is found that particularly when filter order is 50 or more, the new structures have reduced quantisation noise and improved tolerance to quantisation than their classical counterparts     

Static quantised radix-2 fast Fourier transform (FFT)/inverse FFT processor for constraints analysis

This research work focuses on the design of a high-resolution fast Fourier transform (FFT)/inverse FFT (IFFT) processors for constraints analysis purpose. Amongst the major setbacks associated with such high-resolution FFT processors are the high-power consumption resulting from the structural complexity and computational inefficiency of floating-point calculations. As such, a parallel pipelined architecture was proposed to statically scale the resolution of the processor to suite adequate trade-off constraints. The quantisation was applied to provide an approximation to address the finite word-length constraints of digital signal processing. An optimum operating mode was proposed, based on the signal-to-quantisation-noise ratio (SQNR) as well as the statistical theory of quantisation, to minimise the trade-off issues associated with selecting the most application-efficient floating-point processing capability in contrast to their resolution quality.     

Digital image watermarking technique based on vector quantisation

A digital image watermarking technique based on vector quantisation (VQ) is presented. This technique uses codeword indices to carry the watermark information. The technique is secret and efficient: the watermarked image is robust to VQ compression with the same codebook. The simulation results prove the effectiveness of this technique     

Semi-fragile image watermarking method based on index constrained vector quantisation

A novel semi-fragile digital image watermarking method is presented, based on index constrained vector quantisation, which embeds the watermark information into the compressed bit streams. Simulation results show that the proposed method is robust to JPEG compression and VQ compression with high-performance codebooks but fragile to other image processing operations.     

Autocorrelation function of the quantisation-error process for a sinusoid

This letter investigates the variation in the correlation function of a quantisation-error process with the width of quantisation for a sinusoidal-input process. This process does not comply with the quantisation theorem of Widrow, and, in consequence, the orthogonal expansion procedure of Barrett and Lampard is the adopted analysis technique. The results clearly establish that, for this input, the quantisation-error spectrum is white for practical purposes, even when the quantisation is very coarse.     

Effects of the channel profile on correlation measurements

The effects of quantisation on the measurement of statistical properties of random processes are analysed, and the importance of a suitable choice of the channel profile of the convertor is then outlined in order to avoid quantisation errors.     

Nonlinear methods for frame alignment

The optimal way of searching for a frame alignment word in a frame of data, given quantised, noise-corrupted observations of the constituent symbols is derived. The four level quantisation scheme retains most of the benefits of the optimal unquantised scheme, but is only slightly more complex than the digital correlator. It would be particularly appropriate for high noise environments such as radio links     

In-loop quantisation of reflection coefficients

A method to quantise the reflection coefficients inside the computation loop of an LPC analysis for speech signals is proposed. Whereas traditional methods for LPC analysis quantise the reflection coefficients after a whole set of coefficients have been found, the proposed method takes into consideration the effect of quantisation error during the analysis procedure. For a given set of quantisation tables the proposed method can achieve improvement on quantisation error over other scalar quantisation schemes.<>     

Theory for fast and cost-effective frequency response estimation of systems

Frequency response, and hence transfer function, estimation of systems is of vital importance in several engineering fields such as signal processing, communications, control, system modelling and identification. Any digital frequency response scheme with attractive features such as low cost, high speed, good accuracy and excellent noise and harmonic rejection capabilities will therefore be of great practical benefit to practitioners in the above-mentioned fields. The author reports on a new frequency response estimation theory, based on the concept of non-subtractively dithered quantisation, which endows the classical quadrature correlation-based frequency response estimation scheme with all the above-mentioned attractive features. A theoretical analysis of the estimation (bias and variance) accuracy of this technique is given. The theory is tested on a number of filters and under some stringent conditions characterised by the coarsest possible (1-bit) quantisation scheme and very noisy (low SNR) environments. Simulation results substantiate the proposed theory quite well, thus making the VLSI implementation of the proposed 1-bit estimation scheme on a chip an attractive proposition.