The "sampling time" is not small enough. It must be less than 1/(2*nu) - i.e., sampling rate greater than 2*nu - to avoid aliasing.
nu = 193.41e12; % [Hz] frequency
p0 = 2*pi*nu % target "pulsation"
fs = 2.01*nu; % sufficient sampling rate
p1 = get_pulsation(nu,fs) % matches target
fs = 1/(6.25e-3*1e-9); % original sampling rate
p2 = get_pulsation(nu,fs) % does not match
fs = 1.99*nu; % *nearly* sufficient sampling rate
p3 = get_pulsation(nu,fs) % does not match
function out = get_pulsation(nu,fs)
% signal construction
dt = 1/fs; % [s] sampling time
Nsamp = 1024*16; % [] number of samples
t = 0:dt:(Nsamp-1)*dt; % [s] array of time values
CFO = exp(1i*2*pi*nu.*t); % [] Carrier Frequency Offset signal, so "my z"
% getting the angle
ARG = unwrap(angle(CFO)); % [] it should give an ARRAY of size (1;16,384): 2*pi*nu*t
p = polyfit(t,ARG,1); % [rad/s]it should return [2*pi*nu,0]
out = p(1);
end
