Matlab：如何获取正弦信号的幅度和相位

Question

Given two signals:

x1 = A1*exp(j*2*pi*f1*t + Phi1); 
x2 = A1*exp(j*2*pi*f1*t + Phi1) + A2*exp(j*2*pi*f2*t + Phi2);

Matlab should be able to calculate magnitude and phase:

abs(x1) = A1;
angle(x1) = Phi1;

abs(x2) = A1+A2;
angle(x2) = Phi1+Phi2;

Is this correct? I am really not sure about x2. Now, I am given a sinusoidal signal:

x3 = A3*cos(2*pi*f3*t + Phi3); 
x4 = A3*cos(2*pi*f3*t + Phi3) + A4*cos(2*pi*f4*t + Phi4);

What will abs() / angle() of these signals yield?

The complex envelope of x2 is given by:

A1*exp(j*2*pi*(f1-f2)/2 t + Phi1) + A2*exp(j*2*pi*(f2-f1)/2 t + Phi2) 

assuming a carrier frequency that is between f1 and f2. The amplitude and also the phase of the complex envelope should be somewhat equivalent to the original signal. Now I wonder, is it?

Answer 1

EDIT: I am still not sure what exactly you need, but perhaps this identity might me helpful:

cos(a) = [exp(j*a) + exp(-j*a) ] / 2

If you need to estimate (some of) the parameters A, f, Phi, take a look at the Discrete Time Fourier Transform (DTFT). This page for example has the math of least squares sinusoidal parameter estimation .