How to get argument of complex exponential?

Dear all,

I feel a bit ashamed to ask such question but I am quite upset by the outcome of , where z is a chosen complex, which does not give what I expect.

Let's be more precise:

% axis parameters
dt      = 6.25e-3*1e-9;          % [s]    sampling time
Nsamp   = 1024*16;              % []     number of samples
t       = 0:dt:(Nsamp-1)*dt;    % [s]    array of time values

% signal construction
nu      = 193.41e12;            % [Hz]   frequency
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]  

p = 1×2

1.0e+11 * -1.8850 0.0000

2*pi*nu

ans = 1.2152e+15

But it does not give the pulsation I used to construct my signal.

What did I miss?

Does anyone have an idea?

Thanks a lot,

Best,

louis

Answer 1

[Voss]

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"

p0 = 1.2152e+15

fs = 2.01*nu; % sufficient sampling rate
p1 = get_pulsation(nu,fs) % matches target

p1 = 1.2152e+15

fs = 1/(6.25e-3*1e-9); % original sampling rate
p2 = get_pulsation(nu,fs) % does not match

p2 = -1.8850e+11

fs = 1.99*nu; % *nearly* sufficient sampling rate
p3 = get_pulsation(nu,fs) % does not match

p3 = -1.2031e+15

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

[Louis Tomczyk]

Dear @_,

I did not even think about the sampling issue which is totally obvious finally.

This is a perfect example of how coding is useless if we don't know a bit of maths ^_^

Many thanks :)

Best,

louis