Pulse ModulationAnalogue modulated systems are quite widely used, becauseof their simplicity.An alternative to analogue modulated systems is Pulsedsystems.This system is based on digital signals or pulses.The basis of such a system is the use of a digital carriersignal, which is modulated by an analogue signal.There are various ways in which this can be achieved, givingrise different systems.
Definition PCM is essentially analog to digital conversion of a signal type where the information contained in the instantaneous samples of an analog signal is represented by digital words in a serial bit stream Analog signal is first sampled at a rate higher than Nyquist rate, and then samples are quantized Uniform PCM : Equal quantization interval Nonuniform PCM : Unequal quantization interval
Based on the sampling theorem Each analog sample is assigned a binary code Analog samples are referred to as pulse amplitude modulation (PAM) samples The digital signal consists of block of n bits, where each n-bit number is the amplitude of a PCM pulse
Pulse Code ModulationPCM is the most commonly used technique in digitalcommunicationsUsed in many applications: Telephone systems Digital audio recording CD laser disks voice mail digital video etc.They are a primary building block for advancedcommunication systems
PCM requires much wider bandwidth But, Inexpensive digital circuitry PCM signal from analog sources(audio, video, etc.) may be merged with data signals(from digital computer) and transmitted over a common high-speed digital communication system (This is TDM)
Uniform quantizer Error signalsWaveform of signals PCM signal PCM word
Is the process of converting the sampled signal to a binary value Each voltage level will correspond to a different binary number The magnitude of the minimum step size is called the resolution.
Analog LPF Analog signal Samplersignal BW=B & Hold Quantizer Encoder PCM Quantized No. of levels=M signal PAM signal Channel, Telephone lines with regenerative repeater Reconstruction Decoder PCM LPF Quantized signal PAM signal Analog Signal output
Uniform distribution Let M=2n is large enough Xmax ∆=2Xmax/M x ) xi Distortion ∆2 Di = 12 M M ∆2 D = ∑ Di = i =1 12 -Xmax x -∆/2 ∆/2 x ) xi
Distortion 2 xmax 2 ( ) ∆ 2 2 xmax 2 xmax 2 xmax D= = M = = = 12 12 3M 2 3(2n ) 2 3(4n ) SQNR Let normalized input : E[ X 2 ] X = xmax E[ X 2 ] 3M 2 E[ X 2 ] 3(4 n ) E[ X 2 ] SQNR = = = = 3(4 n ) X 2 D xmax xmax SQNR dB = 10 log10 SQNR ≈ 4.77 + 6.02n + 10 log10 X 2 SQNR dB _ pk ≈ 4.77 + 6.02n
Hard to analyze because PCM is nonlinear Bandwidth of PCM If sinc function is used to generate PCM R = , nf s 1 1 where R is bit rate BPCM ≥ 2 2 If rectangular pulse is used , first BPCM = R = nf s null bandwidth If fs=2B (Nyquist sampling rate)
Telephone communication Voice frequency : 300 ~ 3400Hz Minimum sampling frequency = 2 x 3.4KHz = 6.8KHz In US, fs = 8KHz is standard Encoding with 7 information bits + 1 parity bit Bit rate of PCM : R = fs x n = 8K x 8 = 64 Kbits/s Required Bandwidth of PCM If sinc function is used: B > R/2 = 32KHz If rectangular is used: B = R = 64KHz SQNR|dB_PK = 46.9 dB (M = 27) Parity does not affect quantizing noise but decrease errors caused by channels