How can I find the fundamental period, frequency and angular frequency of a time signal?

Given this

    xt=sym('2*sin(6*t)*cos(11*t)+6*(cos(5*t))^2');

how can i find its fundamental period, frequency and angular frequency?

Answer 1

[Walter Roberson]

syms w real
f = fourier(xt)

now look at real(f) and imag(f) . For example

3*pi*(dirac(w - 10) + dirac(w + 10)) + 6*pi*dirac(w)

Read off the dirac() terms: they are at w = +10, w = -10, w = 0 . Frequency w = 0 is a term for a constant shift. w = 10 and w = -10 are due to the symmetries of the fourier transform. If you look only at positive frequencies, then the dirac term kicks in at w = 10. That is the fundamental frequency of the real portion.

You get other frequencies for the imaginary term, corresponding to the beat frequencies between sin(6*t) and cos(11*t) . Those are a phase shift.

The overall cycle is not really complete until the least common multiple of all of the real frequencies and the imaginary frequencies.