June 2007 - DSP LOG

Interpreting the output of fft() operation in Matlab

It might be interesting to interpret the output of the fft() function in Matlab. Consider the following simple examples.

fsMHz = 20; % sampling frequency
fcMHz = 1.5625; % signal frequency
N = 128; % fft size
% generating the time domain signal
x1T = exp(j*2*pi*fcMHz*[0:N-1]/fsMHz);
x1F = fft(x1T,N); % 128 pt FFT
figure;
plot([-N/2:N/2-1]*fsMHz/N,fftshift(abs(x1F))) ; % sub-carriers from [-128:127]
xlabel('frequency, MHz')
ylabel('amplitude')
title('frequency response of complex sinusoidal signal');

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First order digital PLL for tracking constant phase offset

Considering a typical scenario where there might exist a small phase offset between local oscillator between the transmitter and receiver.

Figure 1 : Transmitter receiver with constant phase offset

In such cases, it might be desirable to estimate and track the phase offset such that the performance of the receiver does not degrade.

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