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# Analog to-digital conversion

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### Analog to-digital conversion

1. 1. Muhammad Uzair Rasheed ROLL# 2009-CPE-03 UCE&T BZU MULTAN
2. 2. PAM(Pulse Amplitude Modulation)PCM(Pulse Code Modulation)
3. 3. 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.
4. 4.  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
5. 5.  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
6. 6. 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
7. 7.  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)
8. 8. Uniform quantizer Error signalsWaveform of signals PCM signal PCM word
9. 9.  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.
10. 10. 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
11. 11. 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
12. 12.  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
13. 13.  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)
14. 14. Quantizer n bits Bandwidth SQNR| dB_PKLevel, M M=2 n >nB 4.8+6n2 1 2B 10.84 2 4B 16.88 3 6B 22.816 4 8B 28.932 5 10B 34.964 6 12B 40.9128 7 14B 46.9256 8 16B 52.9512 9 18B 59.01024 10 20B 65.02048 11 22B 71.04096 12 24B 77.08192 13 26B 83.016384 14 28B 89.132768 15 30B 95.165536 16 32B 101.1
15. 15.  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
16. 16. THANKS