# Digital Transmission of Analog Data: PCM and Delta Modulation

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1 Digital Transmission of Analog Data: PCM and Delta Modulation Required reading: Garcia and CSE 323, Fall 200 Instructor: N. Vlajic

2 Digital Transmission of Analog Data 2 Digitization process of converting analog data into digital signal example: telephone system human voice analog data analog signal?! analog signal is sensitive to noise, especially over long distance (cannot be perfectly reconstructed) solution: () digitize the analog signal at the sender (2) transmit digital signal (3) convert digital signal back to analog data at the receiver

3 Digital Transmission of Analog Data (cont.) 3 Example [ PCM procedure ]

4 Digital Transmission of Analog Data (cont.) 4 Digitization Procedure aka Pluse Code Modulation (PCM), consists of 2 steps () sampling obtain signal values at equal intervals (T) (2) quantization approximate samples to certain values analog signal (continuous-time, continuous-amplitude) discrete-time signal (discrete-time, continuous-amplitude) discrete-time signal (discrete-time, continuous-amplitude) digital signal (discrete-time, discrete-amplitude)

5 Sampling 5 Sampling aka Pulse Amplitude Modulation (PAM) digitization in time - sampling process results in signal that is discrete in time but analog in amplitude! choice of sampling interval T is determined by how fast a signal changes, i.e. frequency content of the signal Nyquist Sampling Rate Theorem: To ensure accurate reproduction of an analog signal, the sampling rate must be at least 2*(highest signal freq.). sampling rate = T = 2 max_signal_freq x(t) x(nt) t Sampler t

6 Sampling (cont.) 6 Example [ Recovery of a sampled sine wave for different sampling rates ]

7 Quantization 7 Quantization PAM signal samples have amplitudes of precision direct encoding of such amplitudes would require number of bits (digital pulses) per sample to convert PAM signal to digital signal (that is practical for transmission), each sample has to be rounded up to the nearest of M possible quantization levels M quantization levels m=log 2 (M) bits per level M better precision, more bits per sample M poor precision, fewer bits per sample PAM signal quantized signal

8 Quantization (cont.) 8 Example [ Quantization of PAM Signal ] Assume an analog signal, as shown below, has to be quantized using at most 8-bits per sample. How many different quantization levels are allowed / should be used?

9 Quantization (cont.) 9 Quantization Error by quantizing the PAM signal, the original signal is now only approximated & cannot be 00% recovered effect known as quantizing error or quantizing noise SNR ratio due to quantizing noise can be expressed as SNR [db] 6m +.76 [db] # bits per sample every additional bit used in quantizer will increase SNR by 6 [db] # of quantization levels higher SNR better (received) signal quality signal interpolation

10 Quantization (cont.) 0 Example [ voice signal in telephone system ] Natural human voice occupies the range of 80 3,400 [Hz]. Human ear can tolerate SNR of 40 [db]. Assume we want to transmit human voice in digitized form. What bit rate [bps] should be supported by the channel to enable such transmission? () Sampling rate?! Based on Nyquist Sampling Theorem: max freq. = 4 [khz] sampling rate = 2*4 [khz] = 8000 [samples/sec] (2) # of bits per sample?! Based on SNR formula: 40 [db] = 6*m +.76 # bits per sample = 7 # of levels = 2 7 = 27 Overall data rate R = 8000*7 = [bps] = 56 [kbps] rate = # samples per second * # bits per sample = 56 kbps

11 Example [ PCM ] A t 0 T t t 2 t 3 t 4 t 5 t 6 t

12 Example [ Delta Modulation ] 2 A t t 0 t t 2 t 3 t 4 t 5 t 6

13 Delta Modulation 3 Delta-Modulation most popular alternative to PCM analog signal is approximated by staircase function only a single binary digit is required for each sample!!! at each sampling time (kt), the function moves up or down a constant amount δ (step size) the staircase function attempts to track the original waveform as closely as possible at each sampling time, the analog input is compared to the most recent value of the approximating staircase function binary- is generated if the function goes up, binary-0 otherwise

14 Delta Modulation (cont.) 4 Example [ Delta modulation / demodulation ]

15 Delta Modulation (cont.) 5 Delta Modulation Parameters () step size (δ) should not be too small, nor too large small δ + signal changes rapidly underestimation large δ + signal changes slowly overestimation (2) sampling time (T) smaller T increase overall accuracy but, small T increases output data rate, i.e. # of bps Delta-modulation rule: smaller δ smaller T, T, larger δ larger T..

16 Example [ Delta Modulation: δ step reduced 50%, T remains the same ] 6 A t t 0 t t 2 t 3 t 4 t 5 t 6 t 7 t 8

17 Example [ Delta Modulation: both δ-step and T reduced 50% ] 7 A t 0 t t 2 t 3 t 4 t 5 t 6 t 7 t 8 t 9 t 0 t

18 8

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