Theory: Pulse code modulation (PCM) converts an analog signal to digital format by three separate processes: sampling, quantizing, and coding. The analog signal is first sampled to obtain an instantaneous value of signal amplitude at regularly spaced intervals; the sample frequency is determined by the Nyquist sampling theorem. Each sampled amplitude is then approximated by the nearest level selected from a discrete set of quantization levels. Procedure:

1. Write the coding to encode an analog message as display in Figure 1. Run the coding, then record and observe the output.

2. Write the coding to decode the message as display in Figure 2. Run the coding, then record and observe the output.

3. Repeat step 1-2 for lower and higher sampling value by changing the value of frequency sampling, fs. Compare the output for encode and decode part with the result in step 1 and 2.

4. Repeat step 1-2 for lower and higher quantization steps by changing the value of quantization level. Compare the output for encode and decode part with the result in step 1 and 2.

1

F = 2; ES = 20; Tg = 1/3; ESS = 1.e4; Tas - 1/fss; It - 0:Ts3:2-Tss; d = Ts/40:19:2+T8/40; - pulstran(t, d, 'tectpuls',1/(fs*40)); msin (2 pi*f*t)+1.1; ms - m.p; cm - quant (ms, 2/16); em - 8 (cm): b = 1: for i=1:length (em) if ((((1>1) 66 (em (1) --em (1-1))) || (1==1)) (em (1) -=0)) x (3) - m (1) -1; 1+1; end Jend z = dec2bin (X, 5); z = z': zz(:): 2 - str2num(z) : s = 2 (')-1; Tb - 2/length(s); Fb - 0.5/Tb; BL - Tb/Tas; y = ones (BL, 1); it - 5*y*s; bit - bit(); bit - bit'; Polar Nez bit stream Figure (1): subplot (2,1,1) plot(t,m,'b',c,m,''); Legend ('Analog Mag', 'Sampled Mag') grid: label('t -->'); ylabel('Amplitude): axis ([0 2 0 2.25]); subplot (2,1,2) plot(t,ms, 'k',,m,'I'); legend (Sampled Msg', 'Quantized Msg') grid; xlabel('t -->'); ylabel ('Amplitude); axis ([0 2 0 2.25]); b = bit(cel (Tb/ (TS)) : (Tb/s): length (bit)); b = (+5)/10; 1 = length(b): for 1 - 1:1/5 4 - rb (51)-4:5*1): num2 str() x1 (1) bin.dec 19): e (1) x1(A)+1; end ee/ yi - ones (1, ceal(Ta/40)/T5)): y2 - zeroak, (18/193)-length (y2)); y3 = [yi y2); y3 = y3': al = y3e: Sampled simal from Encoded Signal mal = ml() Filtering Sampled Signal In, w] = butcoxd(1/783, (+1)/83,.6, 4); [a,b] = butter in, w, 'low'); m = filter (a,b,mal): Im = rm50; Recieved Orignal Signal figure (2): subplot(2,1,1) plot(t, em, 'b') xlabel('t -->'); vlabel ("Amplitude) title('Leveled Me): grid; axis ([0 2-0.5 16.5]): subplot (2,1,2) plot(t,bit,'*') xlabel('t- vlabell'Anpitude"); title('POLAR NRZ ENCODED' ); grid; axis ([0 2 -5.25 5.25]); figure (3): subplot (2,1,1) plot(t,ml, 'b'); title('Recovered sampled Mag) grid; xlabel('t-->') ylabel('mplitude'); axis ([0 2 0 2.251); subplot (2,1,2) plot(t,m,'b'): title('Recovered inolog Mac') grid; xlabel('t -->'); ylabel(Amplitude'); axis ( [0 2 0 2.251); Figure 2 Decode message