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v1_011.m
% v1_011.m
%
% This is a script file to demonstrate the relationship
% between magnitude and phase of sin and cos functions and
% complex number notation.
%**********************************************************************
% Author: Randall J. Allemang
% Date: 18-Apr-94
% Structural Dynamics Research Lab
% University of Cincinnati
% Cincinnati, Ohio 45221-0072
% TEL: 513-556-2725
% FAX: 513-556-3390
% E-MAIL: randy.allemang@uc.edu
%*********************************************************************
%
clg, clear
plt=input('Store plots to file (Yes=1): (0)');if isempty(plt),plt=0;end;
freq=input('Sin/Cos Frequency: (5 Hz)');if isempty(freq), freq=5;end;
time=input('Maximum Time: (1 Sec.)');if isempty(time),time=1;end;
%
t=linspace(0,time,501);
SinAmp=3;
CosAmp=4;
F=CosAmp+j*SinAmp;
H=1+j*2;
AmpF=abs(F);
PhaseF=angle(F);
AmpH=abs(H);
PhaseH=angle(H);
SinAmp, CosAmp, AmpF, PhaseF*180/pi
pause
x=SinAmp.*sin(2.*pi.*freq.*t);
y=CosAmp.*cos(2.*pi.*freq.*t);
z=x+y;
fig1=figure(1);
subplot(211),plot(t,x,'.',t,y,'.',t,z),grid
xlabel('Time (Sec.)'),ylabel('Amplitude'),grid
title('Raw Signals')
pause
Z=(AmpF).*cos(freq.*2.*pi.*t-PhaseF);
subplot(212),plot(t,x,'.',t,y,'.',t,Z),grid
xlabel('Time (Sec.)'),ylabel('Amplitude'),grid
title('Magnitude/Phase Cos Formulation')
pause
fig2=figure(2);
subplot(211),plot(t,x,'.',t,y,'.',t,Z),grid
xlabel('Time (Sec.)'),ylabel('Amplitude'),grid
title('Raw Signals')
pause
ZZ=(AmpF).*exp(j*PhaseF);
ZZZ=real(ZZ).*cos(2.*pi.*freq.*t)+imag(ZZ).*sin(2.*pi.*freq.*t);
subplot(212),plot(t,ZZZ),grid
xlabel('Time (Sec.)'),ylabel('Amplitude'),grid
title('Euler Formulation')
pause
X=H*F;
X1=real(X).*cos(2.*pi.*freq.*t)+imag(X).*sin(2.*pi.*freq.*t);
AmpX=abs(H)*abs(F);
PhaseX=angle(H)+angle(F);
X2=AmpX*cos(2.*pi.*freq.*t-PhaseX);
X3=AmpH.*CosAmp.*cos(2.*pi.*freq.*t-PhaseH);
X3=X3+AmpH.*SinAmp.*sin(2.*pi.*freq.*t-PhaseH);
fig3=figure(3);
plot(t,X1,'*',t,X2,'o',t,X3),grid
xlabel('Time (Sec.)'),ylabel('Amplitude'),grid
title('Euler Formulation')
pause
if plt==1
print -deps -f1 v1_011a.eps
print -deps -f2 v1_011b.eps
print -deps -f3 v1_011c.eps
end
pause