Computing frequency from phase angle. How to remove the frequency spikes?

I want to calculate frequency of a complex signal from its angle deviation. The problem with this is that I am getting large values of difference. See images attached.

How can I remove the large spikes, what method I can use to smooth the data at those samples. Note: The signal or angle deviation can actually be random or varying with time.

ps - the x-axis labeled as time in seconds, which is actually number of time steps or samples.

Answer 1

[David Goodmanson]

Hi Jan,

The angle function is restricted to -pi < angle < pi, so in your first plot the angle has a series of sudden jumps from +pi down to -pi, which is phase wrap. You can use the unwrap function to make a continuous function, and then differentiate that. It looks like your frequency is around .04, so:

f0 = .04   
t = 0:.01:120;
y = exp(2*pi*i*f0*t);
a = angle(y);
a1 = unwrap(a);
figure(1)
plot(t,a1)
ylabel('angle')
f = (diff(a1)./diff(t))/(2*pi);
f1 = min(f)
f2 = max(f)

There is no point in plotting f since for this waveform it equals .04 for all t. Absent the jumps, your f appears to be up around 50, so it appears that something is not quite right there.