function plotBP_aper(N)
% Plots the complex frequency response and beampattern for 
% an aperature  
% H(j*2*pi*cos(phi)/lambda_0)=N*lambda_0*exp(j*pi*N*cos(phi))*sinc(pi*N*cos(phi)))
% for 10 periods of hz=1/lambda centered around hz = 0
% NOTE: hz=cos(phi)/lambda_0

warning off
figure
cos_phi_limit=1;
cos_phi_step=.001;
cos_phi=-cos_phi_limit:cos_phi_step:cos_phi_limit;    
                                  % cos(phi) vector

% labels
label_x_fr=['{\it{cos(\phi )}}'];
label_title_fr=['Complex Freqency Response of H(\it{j2{\pi} cos(\phi ) /\lambda_0})'];
label_title_bp=['Beampattern \it{BP(\phi )}'];
label_title_pbp=['Polar Beampattern \it{BP(\phi )}'];
label_x_bp=['\it{\phi}'];

% Complex Frequency Response
H_j2pi_cos_phi=N*exp(-j*pi*N*cos_phi).*sinc(N*cos_phi);  
                                  % sinc is a built-in MATLAB function
                                  % sinc(x)=Sin(pi*x)/(pi*x)

% Calculate Magnitude and frequency responses of H(j*2*pi/lambda)                              
mag_H=abs(H_j2pi_cos_phi);
phase_H=angle(H_j2pi_cos_phi);


% Calculate Complex Wavelength Response versus phi of H(j*2*pi*cos(phi)/lambda)
phi=-pi:pi/5000:pi;
H_j2pi_phi=N*exp(-j*pi*N*cos(phi)).*sinc(N*cos(phi));  

% Calculate Magnitude and frequency responses of H(j*2*pi*cos(phi)/lambda)                              
mag_Hcos=abs(H_j2pi_phi);

% Convert H(j*2*pi*cos(phi)/lambda) to Polar
polar_Hcos=mag_Hcos.*exp(j*phi);

% plot results 
subplot(221)
title(label_title_fr)
hold on
axis square
axis([-cos_phi_limit cos_phi_limit 0 N])
plot(cos_phi,mag_H)
xlabel(label_x_fr), ylabel('Magnitude')

subplot(223)
hold on
axis square
axis([-cos_phi_limit cos_phi_limit -1 1])
plot(cos_phi,phase_H/pi)
xlabel(label_x_fr), ylabel('Phase/\pi')

subplot(222)
title(label_title_bp)
hold on
axis square
plot(phi,mag_Hcos)
xlabel(label_x_bp), ylabel('Magnitude')

subplot(224)
title(label_title_pbp)
hold on
axis equal
plot(polar_Hcos)
xlabel(label_x_bp)