The behavior of quantization spectra as a function of signal-to-noise ratio

An expression for the spectrum of quantization error in a discrete-time system whose input is a sinusoid plus white Gaussian noise is derived. This quantization spectrum consists of two components: a white-noise floor and spurious harmonics. The dithering effect of the input Gaussian noise in both components of the spectrum is considered. Quantitative results in a discrete Fourier transform (DFT) example show the behavior of spurious harmonics as a function of the signal-to-noise ratio (SNR). These results have strong implications for digital reception and signal analysis systems. At low SNRs, spurious harmonics decay exponentially on a log-log scale, and the resulting spectrum is white. As the SNR increases, the spurious harmonics figure prominently in the output spectrum. A useful expression is given that roughly bounds the magnitude of a spurious harmonic as a function of the SNR

Uniform and non-uniform quantization of Gaussian processes

Quantization of a continuous-value signal into a discrete form (or discretization of amplitude) is a standard task in all analog/digital devices. We consider quantization of a signal (or random process) in a probabilistic framework. The quantization method presented in this paper can be applied to signal coding and storage capacity problems. In order to demonstrate a general approach, both uniform and non-uniform quantization of a Gaussian process are studied in more detail and compared with a conventional piecewise constant approximation. We investigate asymptotic properties of some accuracy characteristics, such as a random quantization rate, in terms of the correlation structure of the original random process when quantization cellwidth tends to zero. Some examples and numerical experiments are presented

A Study of trellis coded quantization for image compression

Trellis coded quantization has recently evolved as a powerful quantization technique in the world of lossy image compression. The aim of this thesis is to investigate the potential of trellis coded quantization in conjunction with two of the most popular image transforms today; the discrete cosine transform and the discrete wavelet trans form. Trellis coded quantization is compared with traditional scalar quantization. The 4-state and the 8-state trellis coded quantizers are compared in an attempt to come up with a quantifiable difference in their performances. The use of pdf-optimized quantizers for trellis coded quantization is also studied. Results for the simulations performed on two gray-scale images at an uncoded bit rate of 0.48 bits/pixel are presented by way of reconstructed images and the respective peak signal-to-noise ratios. It is evident from the results obtained that trellis coded quantization outperforms scalar quantization in both the discrete cosine transform and the discrete wavelet transform domains. The reconstructed images suggest that there does not seem to be any considerable gain in going from a 4-state to a 8-state trellis coded quantizer. Results also suggest that considerable gain can be had by employing pdf-optimized quantizers for trellis coded quantization instead of uniform quantizers

D/A Resolution Impact on a Poly-phase Multipath Transmitter

In recent publications the Poly-phase multipath technique has been shown to produce a clean output spectrum for a power upconverter (PU) architecture. The technique utilizes frequency independent phase shifts before and after a nonlinear element to cancel out the harmonics and sidebands due to the nonlinearity. A major advantage of this technique is that it circumvents the need to use dedicated RF filters which makes it a potential candidate for cognitive radio transmitters. This paper addresses the requirements on the digital and mixed signal part of such a transmitter. An architecture is proposed based on complex multiplication which can be used to generate the digital multiphase signals required by the multipath technique. Due to equal phase difference of all the paths the same digital hardware could be utilized for carrying out all the phase shifts. When the digital signals pass through a D/A converter which doesn’t have a reconstruction filter, the output in this case would be amplitude discrete like that of a zero order hold. The spectrum of this amplitude discrete signal would have distortion components in it. This can be termed as quantization distortion but now in the context of limited D/A resolution. The multipath technique’s effect on harmonic cancellation, in the presence of such a quantization distortion is explored in this paper. It is shown through simulation that when using ideal phase shifts the multipath technique is able to cancel most of the harmonics produced by an amplitude discrete representation of pure sinusoids. When (upconversion) mixers are used for the second set of phase shifts then with multipath the highest quantization spurs go down with roughly 8db/bit for a single tone and around 10db/bit for two tone inputs

Conditional hitting time estimation in a nonlinear filtering model by the Brownian bridge method

The model consists of a signal process $X$ which is a general Brownian diffusion process and an observation process $Y$, also a diffusion process, which is supposed to be correlated to the signal process. We suppose that the process $Y$ is observed from time 0 to $s>0$ at discrete times and aim to estimate, conditionally on these observations, the probability that the non-observed process $X$ crosses a fixed barrier after a given time $t>s$. We formulate this problem as a usual nonlinear filtering problem and use optimal quantization and Monte Carlo simulations techniques to estimate the involved quantities

Sparse representation for audio noise removal using zero-zone quantizers

In zero zone quantization, bins around zero are quantized to a zero value. This kind of quantization can be applied on orthogonal transforms to remove the unwanted or redundant signal. Transforms reveal structures and properties of a signal and hence careful application of a zero zone over the transform coefficients leads to noise removal. In this thesis, such quantizers are applied over Discrete Fourier Transform and Karhunen Loeve Transform coefficients separately, and outputs compared. Further, the localization of the zero zones to certain frequencies leads to better performance in terms of noise removal. PEAQ (Perceptual Evaluation of Audio Quality) scores have been used to measure the objective quality of the denoised signal