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Introduction
Published in Wen-Long Chin, Principles of Verilog Digital Design, 2022
A digital system represents the discrete-time digital signal as a stream of quantized discrete values sampled from the continuous-time analog signal at discrete points in time, as shown in Figure 1.2. Each sample represents an approximation to the analog signal at a given time instant. According to the sampling theorem, a band-limited continuous-time analog signal can be completely reconstructed by the discrete-time samples if the minimum-sampling rate has been satisfied. However, the quantization process will introduce a quantization error or noise. Despite this, the quantization error can be reduced by increasing the number of bits used to represent the discrete-time samples.
The Dawn of the SAR Mosaics Era
Published in Gianfranco (Frank) De Grandi, Elsa Carla De Grandi, Spatial Analysis for Radar Remote Sensing of Tropical Forests, 2021
Gianfranco (Frank) De Grandi, Elsa Carla De Grandi
The quantization error is defined as the difference between the true signal value and the quantization level assigned to that value. The mean-squared quantization error is given by: ϵ2=∫ϵ2fϵdϵ=∑i∫aiai+aν−ai2pνdν Where p(ν) is the PDF of the signal, f(ε)is the PDF of the quantization error, ai is the ith quantization level, and a is the level spacing.
Vector Quantization
Published in J.-P. Barthelemy, G. Cohen, A. Lobstein, Catherine Fritsch-Mignotte, Maurice Mignotte, Algorithmic Complexity and communication problems, 2020
J.-P. Barthelemy, G. Cohen, A. Lobstein
The general purpose of quantization is as follows: vectors from a source S (generally of a continuous nature) are matched with words chosen from a dictionary of finite size, in order to store them economically or transmit them on a discrete channel. In this chapter, S is assumed to be discrete. The first section contains a survey of the fundamental results of source coding: the minimal space needed to represent a discrete source. The analogy between this correspondence (emitted vector → dictionary word) and the decoding of error-correcting codes is given in §2. In the following section, we consider the case of an approximate reproduction of the source: what is the minimal space needed to represent S with a given average distortion! The fourth section aims to give the link with error-correcting codes when S is equal to Fn, and when the measure of distortion is the Hamming distance. The last section shows that the quantization problem is NP-complete.
A Low-distortion Hardware Efficient MASH
Published in Smart Science, 2018
Rijo Sebastian, Babita Roslind Jose, T. K. Shahana, Jimson Mathew
The demand for high-performance and low power electronic systems often required in next generation wideband applications has intensified the research attention toward developing new efficient wideband analog to digital converter (ADC) architectures. ADC act as a key element in many communication systems. Compared to other kind of ADCs, sigma delta ADC ( ADC) is well suited for medium to high resolution wideband applications. ADC achieves high resolution through oversampling and noise shaping techniques [1]. The ADCs used in higher bandwidth applications are often designed at low oversampling ratio (OSR) due to CMOS technology scaling constraints. A low value of OSR will obviously decrease the achievable signal to noise ratio (SNR). The techniques to improve the resolution in the case of low OSR include increasing the order of loop filter and employing a multi-bit quantizer. The cascaded or multi-stage noise shaping (MASH) modulator architecture eliminates the loop filter instability problems associated with the single-loop higher order modulator structures and became appropriate for the broadband applications. In MASH architecture, the quantization noise of the first-stage modulator is extracted and provided to the next stage as input. An appropriate digital signal processing logic cancels the quantization noise of all except the last stage. The last stage quantization noise is shaped by a noise transfer function (NTF) of order equal to the sum of all the orders.
A re-configurable MASH 2-2 bandpass DQEFM for multi-standard applications
Published in International Journal of Electronics, 2019
Rijo Sebastian, Jos Prakash A. V, Babita R. Jose, Shahana TK, Jimson Mathew
The first and second order bandpass DQEFM architectures are shown in Figure 2(a,b) (Jos Prakash et al., 2018; Rijo et al., 2018). The error associated with the quantization process, i.e. quantization error is obtained by performing analog subtraction between the input and the output of the quantizer. The quantization error is delayed for two clock cycles before it is being fed back to the input of the modulator. The conventional architecture utilises integrator/resonator functions in the loop filter implementation, whereas DQEFMs use differential quantizer in order to generate the noise shaping transfer function (Jos Prakash et al., 2018).
Optimal multi-threshold quantization scheme for bioinformatics inspired cooperative spectrum sensing in cognitive radio networks
Published in International Journal of Electronics, 2018
The energy received according to Equation (4) at a mini-slot is quantized into already defined quantization zones which represent the level of energy received. The M-level quantizer of input variable is represented by a set of quantization levels and a set of quantization thresholds. The quantization thresholds determine the accuracy to which the quantization levels can represent the actual signal. Equation (5) gives the M-level quantization and also the set of quantization thresholds as,