How to extract the unwrapped phase of exp(1i*2*p​i*f_c*delt​a*sin(thet​a)/c)

I just want to obtain 2*pi*f_c*delta*sin(theta)/c from exponential, but the command 'angle' and 'phase' will return the wrap phase.

I have tried 'phase = dsp.PhaseExtractor('TreatFramesIndependently',false)', then ploted three kinds of matlab computation.

The results turns out in the following figure.

It still have an intercept between the phase I want(Red line) and the output of dsp.PhaseExtractor(Blue line).

please give me the suggestion! Thank you!

clear;close all;clc;

f_c=2*10^9;
c=3*10^8;
D=50;
theta_deg=-D/2:D/2;
theta=deg2rad(theta_deg);
dis=zeros(D,1);
delta=6*0.15;   % delta will change

for j=1:D 
    dis(j)=exp(1i*2*pi*f_c*delta*sin(theta(j))/c);
end

phase = dsp.PhaseExtractor('TreatFramesIndependently',false);
ph_ex=phase(dis);

ph_Iwant=2*pi*f_c*delta*sin(theta)/c;      %unwrap phase

ph_ph=angle(dis);

plot(ph_ex,'LineWidth',1)
hold on
plot(ph_Iwant,'LineWidth',1)
plot(ph_ph,'LineWidth',1)
grid;ylabel('angle(rad/s)')
title('delta=',num2str(delta));
legend('extract','I want','wrap phase')

Answer 1

[Nikhilesh]

Please have a look at the unwrap function.

Shift phase angles - MATLAB unwrap (mathworks.com)