Lecture Digital signal processing: Chapter 2 - Nguyen Thanh Tuan

Chapter 2 introduce you to quantization. In this chapter, you will learn to: Quantization process, digital to analog converters (DACs), A/D converters, oversampling noise shaping,...and another contents.
Nội dung trích xuất từ tài liệu:
Lecture Digital signal processing: Chapter 2 - Nguyen Thanh TuanChapter 2Quantization Nguyen Thanh Tuan, Click M.Eng. to edit Master subtitle style Department of Telecommunications (113B3) Ho Chi Minh City University of Technology Email: nttbk97@yahoo.com 1. Quantization process Fig: Analog to digital conversion  The quantized sample xQ(nT) is represented by B bit, which can take 2B possible values.  An A/D is characterized by a full-scale range R which is divided into 2B quantization levels. Typical values of R in practice are between 1-10 volts.Digital Signal Processing 2 Quantization 1. Quantization process Fig: Signal quantization R  Quantizer resolution or quantization width (step) Q  2B R R  A bipolar ADC   xQ (nT )  2 2  A unipolar ADC 0  xQ (nT )  RDigital Signal Processing 3 Quantization 1. Quantization process  Quantization by rounding: replace each value x(nT) by the nearest quantization level.  Quantization by truncation: replace each value x(nT) by its below nearest quantization level.  Quantization error: e(nT )  xQ (nT )  x(nT ) Q Q  Consider rounding quantization:  e 2 2 Fig: Uniform probability density of quantization errorDigital Signal Processing 4 Quantization 1. Quantization process Q /2 Q /2 1  The mean value of quantization error e    Q /2 ep(e)de    Q /2 e Q de 0 Q /2 Q /2 2 1 Q  The mean-square error  q 2  e 2   ( e  e ) 2 p (e)de   e 2 de  Q 12 (power)  Q /2  Q /2 Q  Root-mean-square (rms) error: erms   q  e2  12  R and Q are the ranges of the signal and quantization noise, then the signal to noise ratio (SNR) or dynamic range of the quantizer is defined as   x2  R SNR dB  10log10  2   20log10    20log10 (2 B )  6 B dB   Q  q which is referred to as 6 dB bit rule.Digital Signal Processing 5 Quantization Example 1  In a digital audio application, the signal is sampled at a rate of 44 KHz and each sample quantized using an A/D converter having a full-scale range of 10 volts. Determine the number of bits B if the rms quantization error must be kept below 50 microvolts. Then, determine the actual rms error and the bit rate in bits per second.Digital Signal Processing 6 Quantization 2. Digital to Analog Converters (DACs)  We begin with A/D converters, because they are used as the building blocks of successive approximation ADCs. Fig: B-bit D/A converter  Vector B input bits : b=[b1, b2,…,bB]. Note that bB is the least significant bit (LSB) while b1 is the most significant bit (MSB).  For unipolar signal, xQ є [0, R); f ...