how to plot x(t) = 0.9^k*cos(pi*k/5)*u(k) with simulink

I tried to plot x(t) = 0.9^k*cos(pi*k/5)*u(k) with simulink.

I used constant, sine wave, Pulse generator and product block in order to express 0.9, cos(pi/5), and u(t). But I couldn't figure out how to express 0.9^k.

Please help...

Answer 1

[Paulo Silva]

Something is wrong with that equation, can you see the error?

here's the MATLAB code, I leave the simulink for you to do, it's easy after knowing the basics.

k=1:100; %samples
u(k)=ones(1,numel(k)); %the input is a discrete step
x(k) = 0.9.^k.*cos(pi*k/5).*u(k);
plot(k,x(k))
hold on
plot(k,u(k),'r')
axis([0 numel(k) -2 2])
legend('x(k)=0.9^k*cos(pi*k/5)*u(k)','u(k)')

I couldn't wait so I just tested it on simulink, never done something similar before so I improvised, the results are similar to those of the script.

First thing you should do is change the configuration parameters.

Start time -> 1 Stop time -> 100 Solver Type -> Fixed step Sample time -> 1

Now the blocks

Clock -> Fcn -> Scope

In the Fcn put the expression -> 0.9^u*cos(pi*u/5)

Do the simulation

PS: Don't blame me if there's something wrong, try it and check if all is correct.

[Samuel]

Is the equation wrong????

I plot this equation with matlab. This is discrete time signals.

[Paulo Silva]

x(t) should be x(k) or something similar

[Samuel]

It was typo. It is x(k).

I plot this eq. with code below

anyway, I will try again..Thanks.

m = 10;

k = -m:m;

x = (0.8).^k.*cos((pi*k)./5).*(k>=0);

subplot(2,1,1);

stem(k,x); grid on;

axis([-m,m,-1,1]);

set(gca,'XTick',-m:m);

set(gca,'XTicklabel',-m:m);

set(gca,'YTick',-1:1);

set(gca,'YTicklabel',-1:1);

title('1i) x(k)=(0.8)^k*cos(pi*k/5)*u(k)');

xlabel('k');

ylabel('x(k)');

Answer 2

[Samuel]

Thank you very much Paulo.

I successed ploting this equation based on your idea. I used ram function instead of clock as input of FCN and producted pulse with output of FCN because it is discrete squence signal.

Thanks again..!