I/Q and its conjugates

Kadhiem Ayob December 3, 2011 Coded in Matlab

A complex signal has 8 possible pair formations(let us call them conjugates, though not strictly correct) which all convey the same information but they can differ in frequency polarity and relative phase. The following code models 6 of them:

[I,Q];[I,-Q];[-I,Q];[Q,I];[Q,-I];[-Q,I] ...........ignoring -I,-Q and -Q,-I which obviously  only imply 180 degrees relative phase shift

The code compares all six. For simplicity, the signal chosen is a single complex frequency. Its value and phase can be changed.

 

clear all; close all;

fc = .019;  % frequency relative to Fs of 1(-.5 ~ +.5)
phase = 0;  % degrees

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
shift = floor(phase*1/(fc*360));
x1 = exp(j*2*pi*(0+shift:2^16-1+shift)*fc);   % I,Q
x2 = complex(real(x1),-imag(x1));             % I,-Q
x3 = complex(-real(x1),imag(x1));             %-I,Q
x4 = complex(imag(x1),real(x1));              % Q,I
x5 = complex(imag(x1),-real(x1));             % Q,-I
x6 = complex(-imag(x1),real(x1));             %-Q,I

f1 = fftshift(fft(x1,2^16));
f2 = fftshift(fft(x2,2^16));
f3 = fftshift(fft(x3,2^16));
f4 = fftshift(fft(x4,2^16));
f5 = fftshift(fft(x5,2^16));
f6 = fftshift(fft(x6,2^16));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
f = linspace(-.5,.5,2^16);
figure(1);
subplot(4,1,1);hold;
plot(f,20*log10(abs(f1)),'.-');
plot(f,20*log10(abs(f2)),'r-');
plot(f,20*log10(abs(f3)),'g--');
legend('I,Q','I,-Q','-I,Q')
ylabel('dB')

subplot(4,1,2);hold
plot(f,angle(f1),'.-');
plot(f,angle(f2),'r--');
plot(f,angle(f3),'g--');
legend('I,Q','I,-Q','-I,Q')
ylabel('rad')

subplot(4,1,3);hold;
plot(f,20*log10(abs(f4)));
plot(f,20*log10(abs(f5)),'r-');
plot(f,20*log10(abs(f6)),'g--');
legend('Q,I','Q,-I','-Q,I')
ylabel('dB')

subplot(4,1,4);hold
plot(f,angle(f4));
plot(f,angle(f5),'r--');
plot(f,angle(f6),'g--');
legend('Q,I','Q,-I','-Q,I')
ylabel('rad')

z = 1:ceil(1/abs(fc));
figure(2)
subplot(6,1,1);hold
plot(real(x1(z)),'.-');
plot(imag(x1(z)),'r.-');
legend('I','Q');

subplot(6,1,2);hold
plot(real(x2(z)),'.-');
plot(imag(x2(z)),'r.-');
legend('I','-Q');

subplot(6,1,3);hold
plot(real(x3(z)),'.-');
plot(imag(x3(z)),'r.-');
legend('-I','Q');

subplot(6,1,4);hold
plot(real(x4(z)),'.-');
plot(imag(x4(z)),'r.-');
legend('Q','I');

subplot(6,1,5);hold
plot(real(x5(z)),'.-');
plot(imag(x5(z)),'r.-');
legend('Q','-I');

subplot(6,1,6);hold
plot(real(x6(z)),'.-');
plot(imag(x6(z)),'r.-');
legend('-Q','I');

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