Fundamental of Wireless Communications ELCT 332Fall C H A P T E R 6 SAMPLING AND ANALOG-TO-DIGITAL CONVERSION

Fundamental of Wireless Communications ELCT 332Fall Sampling Theorem Nyquist Rate Nyquist Interval

Fundamental of Wireless Communications ELCT 332Fall Signal Reconstruction from Uniform Samples Interpolation: The process of reconstructing a continuous time signal g(t) from its samples

Fundamental of Wireless Communications ELCT 332Fall Practical Signal Reconstruction (Interpolation)

Fundamental of Wireless Communications ELCT 332Fall Simple interpolation

Fundamental of Wireless Communications ELCT 332Fall Practical Issues in Signal Sampling and Reconstruction Realizability of Reconstruction Filters

Fundamental of Wireless Communications ELCT 332Fall Aliasing effect. (a) Spectrum of a practical signal g(t). (b) Spectrum of sampled g(t). (c) Reconstructed signal spectrum. (d) Sampling scheme using antialiasing filter. (e) Sample signal spectrum (dotted) and the reconstructed signal spectrum (solid) when antialiasing filter is used. Practical Issues in Signal Sampling and Reconstruction The Treachery of Aliasing

Fundamental of Wireless Communications ELCT 332Fall (a) Non-band limited signal spectrum and its sampled spectrum G( f ). (b) Equivalent low-pass signal spectrum G a ( f ) constructed from uniform samples of g(t) at sampling rate 2B. Maximum Informaiton Rate A maximum of 2B independent pieces of information per second can be transmitted, error free, over a noiseless channel of bandwidth B Hz

Fundamental of Wireless Communications ELCT 332Fall Nonideal Practical Sampling Analysis

Fundamental of Wireless Communications ELCT 332Fall Pulse Amplitude Modulation (PAM) Applications of Sampling Theorem Pulse Width Modulation (PWM) Pulse Position Modulation (PPM)

Fundamental of Wireless Communications ELCT 332Fall Applications of Sampling Theorem Time Division Multiplexing (TDM)

Fundamental of Wireless Communications ELCT 332Fall Pulse Code Modulation (PCM) Natural binary code (NBC) Binary digit (bit) For a audio signal with a bandwidth about 15kHz, the signal is not affected if all the above 3400 Hz are suppressed. If sampled at a rate of 8000 samples per second, and each sample is finalized quantized into 256 levels, the telephone signal requires how many binary pulses per second?

Fundamental of Wireless Communications ELCT 332Fall Quantizing

Fundamental of Wireless Communications ELCT 332Fall Nonuniform Quantizing uLaw ALaw

Fundamental of Wireless Communications ELCT 332Fall The Compandor The Compressor and expander together are called the compandor

Fundamental of Wireless Communications ELCT 332Fall Examples: Transmission Bandwidth and the Output SNR A signal m(t) band-limited to 3kHz is sampled at a rate % higher than the Nyquist rate. The maximum acceptable error in the sample amplitude (the maximum quantization error) is 0.5% of the peak amplitude m p. The quantized samples are binary coded. Find the minimum bandwidth of a channel required to transmit the encoded binary signal. If 24 such signals are time-division-multiplexed, determine the minimum transmission bandwidth required to transmit the multiplexed signal. Nyquist rate R N =6000Hz Sampling rate R A =8000Hz L=200 N=8, C M =24*64000/2=0.768MHz

Fundamental of Wireless Communications ELCT 332Fall Exponential Increase of the Output SNR A signal m(t) of bandwidth B=4kHz is transmitted using a binary companded PCM with μ=100. Compare the case of L=64 with the case L=256 from the point of view of transmission bandwidth and the output SNR.

Fundamental of Wireless Communications ELCT 332Fall T1 carrier system. Digital Telephony

Fundamental of Wireless Communications ELCT 332Fall T1 system signaling format. Digital Telephony

Fundamental of Wireless Communications ELCT 332Fall Transversal filter (tapped delay line) used as a linear predictor. Differential Pulse Code Modulation (DPCM) By estimating the value of the kth sample m[k] from a knowledge of several previous sample values. We transmit the difference between m[k] and its predicted value. More band efficient, and better SNR Line Predictor

Fundamental of Wireless Communications ELCT 332Fall DPCM system: (a) transmitter; (b) receiver. Differential Pulse Code Modulation (DPCM) SNR Improvement: m p, d p

Fundamental of Wireless Communications ELCT 332Fall ADPCM encoder uses an adaptive quantizer controlled only by the encoder output bits. Adapative Differential Pulse Code Modulation (ADPCM)

Fundamental of Wireless Communications ELCT 332Fall (a) The human speech production mechanism (b) Typical pressure impulses. Vocoders And Video Compression Linear Prediction Coding (LPC)

Fundamental of Wireless Communications ELCT 332Fall Analysis and synthesis of voice signals in an LPC encoder and decoder. LPC Models Video Compression: MPEG NTSC TV in digital form Mbit/s Mbit/s HDTV in digital form 800 Mbit/s Mbit/s