Overview of Communication Topics Sinusoidal amplitude modulation - PowerPoint PPT Presentation

Overview of Communication Topics • Sinusoidal amplitude modulation • Amplitude demodulation (synchronous and asynchronous) • Double- and single-sideband AM modulation • Pulse-amplitude modulation • Pulse code modulation • Frequency-division multiplexing • Time-division multiplexing • Narrowband frequency modulation J. McNames Portland State University ECE 223 Communications Ver. 1.11 1

Handy Trigonometry Identities cos( a + b ) = cos( a ) cos( b ) − sin( a ) sin( b ) sin( a + b ) = sin( a ) cos( b ) + cos( a ) sin( b ) 1 2 cos( a − b ) + 1 cos( a ) cos( b ) = 2 cos( a + b ) 2 cos( a − b ) − 1 1 sin( a ) sin( b ) = 2 cos( a + b ) 1 2 sin( a − b ) + 1 sin( a ) cos( b ) = 2 sin( a + b ) J. McNames Portland State University ECE 223 Communications Ver. 1.11 2

Introduction to Communication Systems • Communications is a very active and large area of electrical engineering • Experienced a lot of growth through the nineties with the advent of wireless cell phones and the internet • Still an active area of research • Fundamentals of signals and systems are essential to grasping communications concepts • The next two lectures will merely introduce some of the fundamental concepts • Will primarily focus on modulation and demodulation in continuous-time • Analogous concepts apply in discrete-time J. McNames Portland State University ECE 223 Communications Ver. 1.11 3

Introduction to Amplitude Modulation x ( t ) y ( t ) × c ( t ) y ( t ) = x ( t ) · c ( t ) c ( t ) = cos( ω c t + θ c ) • Modulation : the process of embedding an information-bearing signal into a second signal • Demodulation : extracting the information-bearing signal from the second signal • Sinusoidal Amplitude modulation : a sinusoidal carrier c ( t ) has its amplitude modified by the information-bearing signal x ( t ) J. McNames Portland State University ECE 223 Communications Ver. 1.11 4

Fourier Analysis of Sinusoidal Amplitude Modulation For convenience, we will assume θ c = 0 . c ( t ) = cos( ω c t ) C ( jω ) = π [ δ ( ω − ω c ) + δ ( ω + ω c )] y ( t ) = x ( t ) · c ( t ) 1 Y ( jω ) = 2 π [ X ( jω ) ∗ C ( jω )] X ( jω ) ∗ δ ( ω − ω c ) = X ( j ( ω − ω c )) 1 2 X ( j ( ω − ω c )) + 1 Y ( jω ) = 2 X ( j ( ω + ω c )) • Thus, sinusoidal AM shifts the baseband signal x ( t ) so that it is centered at ± ω c • Thus, x ( t ) can be recovered only if ω c > ω x so that the replicated spectra don’t overlap J. McNames Portland State University ECE 223 Communications Ver. 1.11 5

Fourier Analysis of Sinusoidal Amplitude Modulation X ( jω ) 1 ω ω x − ω x 0 C ( jω ) π ω - ω c ω c 0 Y ( jω ) 1 2 ω - ω c - ω x - ω c ω c - ω x ω c - ω c + ω x 0 ω c + ω x J. McNames Portland State University ECE 223 Communications Ver. 1.11 6

Example 1: Sinusoidal AM of a Random Signal Example of Sinusoidal Amplitude Modulation 0.2 x(t) 0 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 1 −3 x 10 c(t) 0 −1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 −3 0.2 x 10 y(t) 0 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (s) −3 x 10 J. McNames Portland State University ECE 223 Communications Ver. 1.11 7

Example 1: MATLAB Code function [] = AMTimeDomain(); close all; N = 2000; % No. samples fc = 50e3; % Carrier frequency fs = 1e6; % Sample rate k = 1:N; t = (k-1)/fs; xh = randn(1,N); % Random high-frequency signal [n,wn] = ellipord(0.01,0.02,0.5,60); [b,a] = ellip(n,0.5,60,wn); x = filter(b,a,xh); % Lowpass filter to create baseband signal c = cos(2*pi*fc*t); y = x.*c; figure; FigureSet(1,’LTX’); subplot(3,1,1); h = plot(t,x,’b’); set(h,’LineWidth’,0.2); xlim([0 max(t)]); ylim([-0.3 0.3]); ylabel(’x(t)’); title(’Example of Sinusoidal Amplitude Modulation’); box off; AxisLines; subplot(3,1,2); h = plot(t,c,’b’); set(h,’LineWidth’,0.2); xlim([0 max(t)]); ylim([-1.1 1.1]); J. McNames Portland State University ECE 223 Communications Ver. 1.11 8

ylabel(’c(t)’); box off; AxisLines; subplot(3,1,3); h = plot(t,y,’b’,t,x,’g’,t,-x,’r’); set(h,’LineWidth’,0.2); xlim([0 max(t)]); ylim([-0.3 0.3]); xlabel(’Time (s)’); ylabel(’y(t)’); box off; AxisLines; AxisSet(6); print -depsc AMTimeDomain; J. McNames Portland State University ECE 223 Communications Ver. 1.11 9

Synchronous Sinusoidal Amplitude Demodulation Transmitter Receiver y ( t ) y ( t ) w ( t ) Channel H ( s ) x ( t ) x ( t ) ˆ × × c ( t ) c ( t ) y ( t ) = x ( t ) cos( ω c t ) w ( t ) = y ( t ) cos( ω c t ) x ( t ) cos 2 ( ω c t ) = � 1 2 + 1 � = x ( t ) 2 cos(2 ω c t ) 1 2 x ( t ) + 1 = 2 x ( t ) cos(2 ω c t ) • Synchronous demodulation assumptions – The carrier c ( t ) is known exactly – ω c > ω x • The x ( t ) can be extracted by multiplying y ( t ) by the same carrier and lowpass filtering the signal J. McNames Portland State University ECE 223 Communications Ver. 1.11 10

Fourier Analysis of Sinusoidal AM Demodulation Y ( jω ) 1 2 ω ω c − ω c 0 C ( jω ) π ω ω c − ω c 0 W ( jω ) 1 2 ω − 2 ω c 2 ω c 0 H ( jω ) 2 ω 0 R ( jω ) 1 ω J. McNames Portland State University ECE 223 Communications Ver. 1.11 11

Synchronous AM Demodulation Observations Transmitter Receiver y ( t ) y ( t ) w ( t ) Channel H ( s ) x ( t ) x ( t ) ˆ × × c ( t ) c ( t ) • The lowpass filter H ( s ) should have a passband gain of 2 • The transition band is very wide so the filter does not need to be close to ideal (e.g. it can be low order) • We learned how to design this type of filter in ECE 222 • We assumed the signal spectrum X ( jω ) was real • The same ideas hold if X ( jω ) is complex • Called synchronous demodulation because we assumed the transmitter and receiver carrier signals c ( t ) were in phase J. McNames Portland State University ECE 223 Communications Ver. 1.11 12

Synchronous AM Demodulation Carrier Phase Analysis Suppose the transmitter and receiver carrier signals differ by a phase shift: c T ( t ) = cos( ω c t + θ ) c R ( t ) = cos( ω c t + φ ) w ( t ) = y ( t ) c R ( t ) = x ( t ) c T ( t ) c R ( t ) = x ( t ) cos( ω c t + θ ) cos( ω c t + φ ) � 1 2 cos( θ − φ ) + 1 � = x ( t ) 2 cos(2 ω c t + θ + φ ) 1 2 x ( t ) cos( θ − φ ) + 1 = 2 x ( t ) cos(2 ω c t + θ + φ ) J. McNames Portland State University ECE 223 Communications Ver. 1.11 13

Synchronous AM Demodulation Carrier Phase Comments w ( t ) = 1 2 x ( t ) cos( θ − φ ) + 1 2 x ( t ) cos(2 ω c t + θ + φ ) • If θ = φ then we have the same case as before and we recover x ( t ) exactly after a lowpass filter with a passband gain of 2 • If | θ − φ | = π 2 , we lose the signal completely • Otherwise, the received signal is attenuated • The phase relationship of the oscillators must be maintained over time • This type of careful synchronization is difficult to maintain • Phase-locked loops (PLL) can be used to solve this problem • In ECE 323 you will design and build PLL’s • The carrier frequency ω c of the transmitter and receiver must also be the same and remain so over time J. McNames Portland State University ECE 223 Communications Ver. 1.11 14

Introduction to Asynchronous AM Demodulation • Asynchronous modulation does not require the carrier signal c ( t ) be available in the receiver • Thus, there is no need for synchronization • Asynchronous Modulation Assumptions: ω c ≫ ω x x ( t ) > 0 for all t • However, it does require that the baseband signal x ( t ) be positive • In this case, the envelope of the modulated signal y ( t ) is approximately the same as the baseband signal x ( t ) • Thus, we can recover a good approximation of x ( t ) with an envelope detector J. McNames Portland State University ECE 223 Communications Ver. 1.11 15

Example 2: Asynchronous Amplitude Modulation Example of Asynchronous Sinusoidal AM Modulation 0.4 0.2 x(t) 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 1 −3 x 10 c(t) 0 −1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 −3 x 10 0.2 y(t) 0 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (s) −3 x 10 J. McNames Portland State University ECE 223 Communications Ver. 1.11 16

Example 2: MATLAB Code function [] = AAMTimeDomain(); close all; N = 2000; % No. samples fc = 50e3; % Carrier frequency fs = 1e6; % Sample rate k = 1:N; t = (k-1)/fs; xh = rand(1,N)-0.5; % Random high-frequency signal limited to [-0.5 0.5] [n,wn] = ellipord(0.02,0.03,0.5,60); [b,a] = ellip(n,0.5,60,wn); x = filter(b,a,xh); % Lowpass filter to create baseband signal x = x + 0.2; % Convert to positive signal c = cos(2*pi*fc*t); y = x.*c; figure; FigureSet(1,’LTX’); subplot(3,1,1); h = plot(t,x,’b’); set(h,’LineWidth’,0.2); xlim([0 max(t)]); ylim([-0.1 0.4]); ylabel(’x(t)’); title(’Example of Asynchronous Sinusoidal AM Modulation’); box off; AxisLines; subplot(3,1,2); h = plot(t,c,’r’); set(h,’LineWidth’,0.2); xlim([0 max(t)]); J. McNames Portland State University ECE 223 Communications Ver. 1.11 17