MATLAB CODE FOR FOURIER SERIES OF RECTANGULAR WAVE

MATLAB CODE:

%Fourier series of  rectangular wave

clc;

close all;

clear all;

j=1;

T=4;    %Time period of square wave

tau=1;  %2tau= On time of the square wave

w0=2*pi/T;

N=50;

j=1;

for k=-N:1:N

    if(k==0)

        c(j)=2*tau/T;   % fourier series coefficients of rectangular pulse

    else

        c(j)=2*sin(k*w0*tau)/(k*w0*T);

    end

   j=j+1;

end

k=-N:1:N;

subplot(2,1,1);

stem(k,c);      %plot fourier series coefficients

grid on;

xlabel('k');

ylabel('fourier series coefficient of rectangular pulse');

%%----------------------------------------------------

l=1;

time=10;

for t=-time:0.01:time

    sum=0;

    j=1;

    for k=-N:1:N

        sum=sum+c(j)*exp(i*k*w0*t); %synthesis equation

        j=j+1;

    end

    s(l)=sum;

    l=l+1;

end

t=-time:0.01:time

subplot(2,1,2);

plot(t,s);          % plot rectangular pulse

grid on;

xlabel('time');

ylabel('rectangular pulse');

OUTPUT: 

FOR MORE DETAILS CLICK HERE

 

What is signal processing ?

        Signal processing is the action of changing one or more features (parameters) of a signal according to a predetermined requirement. The parameters that is to be changed may be , amplitude, frequency, phase etc... of the signal . The signal which undergoes such a process is known as input signal. And the entity which performs this processing is known as "Signal processing system" or simply system. ie; the input signal is fed to the system and the appropriately processed signal is coming out of the system. This signal is known as the "Output signal". 

 

Fig:Signal processing 

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MATLAB CODE FOR SAMPLING THEOREM

SAMPLING THEOREM: 
              In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous-time signals (often called "analog signals") and discrete-time signals (often called "digital signals").
To understand sampling theorem the following matlab code is useful.

MATLAB CODE:

%Program for sampling theorem

f1=1/128;

f2=5/128;

n=0:255;

fc=50/128;

x=cos(2*pi*f1*n)+cos(2*pi*f2*n);

xa=cos(2*pi*fc*n);

xamp=x.*xa;

subplot(2,2,1);

plot(n,x);

title('x(n)');

xlabel('Sn-->');

ylabel('Amplitude');

subplot(2,2,2);

plot(n,xa);

title('xa(n)');

xlabel('n-->');

ylabel('Amplitude');

subplot(2,2,3);

plot(n,xamp);

xlabel('n-->');

ylabel('Amplitude');

OUTPUT:

 For MORE DETAILS CLICK HERE

MIMO Systems With Quantized Covariance Feedback

MIMO:
A unified approach is developed for the study of multi-input, multi-output (MIMO) systems under fast fading with quantized covariance feedback. In such systems, the receiver computes, using perfect channel state information (CSI), the covariance matrices to be adopted by the transmitter corresponding to the current channel realization, and feeds back a quantized version of this information to the transmitter using finite, say , bits per channel realization.

                               Fig    :MIMO
        we analyze under a general quantized covariance framework, the capacity achieving strategy as well as the strategy that is rate-optimal under the STPC and their rank reduced versions by mapping these problems into one that involves quantization of positive semi-definite matrices with appropriate rank and trace equality and inequality constraints. The ergodic capacity is analyzed and the achievable rates under finite rate feedback is bounded relative to the ideal CSIT limits



FOR MORE DETAILS:
                              MIMO Systems With Quantized Covariance Feedback

Rank-Two Beamformed Secure Multicasting for Wireless Information and Power Transfer

SECURE MULTICASTING:

                       We investigate secure multicasting for simultaneous wireless information and power transfer (SWIPT) in the presence of multiple energy receivers who have potential to eavesdrop on the messages of information receivers.
Under both, signal-interference-noise ratio (SINR) and harvested energy constraints, we propose a novel secure multicast design to minimize the total power by using the techniques of rank-two beam formed Alamouti coding and semi definite relaxation (SDR).
 

                                              Fig: System and receiver model

The sufficient conditions are derived under which the proposed secure multicast design is optimal. We also present the corresponding rank-two Gaussian randomization procedure to obtain a suboptimal solution when SDR is not tight. Simulation results are then provided to demonstrate the efficacy of the proposed design in power saving.
  FOR MORE DETAILS Rank-Two Beamformed Secure Multicasting for Wireless Information and Power Transfer