File:In-phase and quadrature components of angle modulation.gif
Summary
| Description |
English: Graphic example of the formula The phase modulation (φ(t), not shown) is a non-linearly increasing function from 0 to over the interval 0 < t < 16. The two amplitude-modulated components are known as the in-phase component (I, thin blue, decreasing) and the quadrature component (Q, thin red, increasing).
Alternative description: Example of how an angle-modulated sinusoid can be decomposed into or synthesized from two amplitude-modulated sinusoids. The picture shows a modulation by non-linearly increasing the phase angle of the carrier from 0 to over the interval 0 < t < 16. The two AM sinusoids have the same nominal frequency as the carrier and are offset in phase by one-quarter cycle ( radians). They are known as the in-phase component (I, thin blue, decreasing) and the quadrature component (Q, thin red, increasing). In some contexts it is more convenient to refer to just the enveloping factors of the AM-signals (thick red and blue lines) by those component terms. |
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| Date | ||||
| Source | Own work | |||
| Author | Bob K | |||
| Permission (Reusing this file) |
I, the copyright holder of this work, hereby publish it under the following license:
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| GIF development | ||||
| Octave/gnuplot source | click to expand
This graphic was created by the following Octave script: graphics_toolkit gnuplot
N = 500; %length of plot
sams = 0:N;
cycles = 0.25; % 1/4 cycle of phi(t)
cyc_per_sam = cycles/N;
phi = pi/2 * sin(2*pi*cyc_per_sam*sams);
cycles = 4; % 4 cycles of carrier wave
cyc_per_sam = cycles/N;
z = cos(2*pi*cyc_per_sam*sams + phi); %carrier
x = cos(2*pi*cyc_per_sam*sams).*cos(phi); %in-phase
y = cos(2*pi*cyc_per_sam*sams + pi/2).*sin(phi); %quadrature
figure
plot(sams,sin(phi),'color','red', 'linewidth', 3) %envelope
ylim([-1.2 1.2]);
box off
hold on
plot(sams,cos(phi),'color','blue', 'linewidth', 3) %envelope
plot(sams,x,'color','blue')
plot(sams,y,'color','red')
plot(sams,z,'color','green', 'linewidth', 2)
set(gca, 'xaxislocation', 'origin')
set(gca, 'yaxislocation', 'origin')
set(gca, 'xgrid', 'on');
set(gca, 'ygrid', 'off');
set(gca, 'ytick', [0]);
cycles_per_tick = 0.25;
sam_per_tick = cycles_per_tick/cyc_per_sam;
set(gca, 'xtick', [0:16]*sam_per_tick);
set(gca,'XTickLabel',[' 0'; ' '; '2'; ' '; '4'; ' '; '6'; ' '; '8'; ' '; ' '; '11'; ' '; '13'; ' '; '15'; ' '])
green = [0 170 0]/256;
text(400, .9, '\uparrow sin(\phi(t))', 'color', 'red')
text(30, .86, '\uparrow cos(\phi(t))', 'color', 'blue')
text(147, .44, '\leftarrow I(t)', 'color', 'blue')
text(165, .30, 'Q(t) \rightarrow', 'color', 'red')
text(121, 1, '\leftarrow cos(2\pift + \phi(t)) \rightarrow', 'color', green)
text(146, .87, '= I(t)+Q(t)', 'color', green)
title('In-phase and quadrature components (example)','fontsize', 12);
xlabel('\leftarrow time (t) \rightarrow','fontsize', 12)
ylabel('amplitude','fontsize', 10)
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