The signal xt has a duration of 10 seconds and is the sum of

The signal x(t) has a duration of 10 seconds and is the sum of two sinusoidal signals of unit amplitude, one with frequency 100 MHz and the other with frequency 300MHz.

x(t) = cos(2*100t) + cos(2*300t), 0t10

= 0                                             otherwise,

The signal is sampled at a sampling rate of 1000 samples per second. Use MATLAB to find the power content and the power spectral density for this signal.

Solution

Power and energy content of a signal is often calculated in signal processing for communication application. In Matlab NORM is used to calculate power.

T=10; %total evaluation time

Ts=.001; %Sampling Time

Fs=1/Ts; %Sampling Period

t=[0:Ts:T]; %define Simulation Time

%calculate Power

x=cos(2*pi*100*t)+cos(2*pi*300*t);

power=(norm(x)^2)/length(x);

%Calculate Power Spectral Density

psd1=spectrum(x,1024);

specplot(psd1,Fs);

The formula for power spectral density is Welch\'s Spectral Density estimate. In the formula of psd 1024 means...generate 1024 samples of a multichannel signal.