# [SciPy-User] frequency components of a signal buried in a noisy time domain signal

Ivo Maljevic ivo.maljevic@gmail....
Sat Feb 27 07:37:27 CST 2010

```> > What makes a signal weak/strong periodic ?
>
> By an exactly periodic signal I mean something like sin(f*t). Such a
> signal produces a very narrow peak of a characteristic shape in an
> FFT, and so can be recognized even in the presence of quite strong
> noise. If your signal is only quasi-periodic - perhaps the frequency
> is a slowly-varying function of time - you'll have a much broader
> peak, which will be much lower for the same input signal amplitude,
> and hence more difficult to distinguish from noise. If your signal is
> only quasi-periodic, or comes and goes in the data, you may want to do
> a series of FFTs on short, overlapping pieces of the data, so you can
> look at time evolution of the signal's spectral properties.
>
>
In my opinion this is not quite so. Periodic signal, as you rightly pointed
out,
is a sinusoidal signal. Quasi-periodic signal behaves like a periodic one,
even though
it does not satisfy the periodic condition x(t) = x (t+To), where To is the
period. Best known
examples are when you add two sinusoidal signals with frequencies that are
not a fractional integer of each other.
For example: sin(2pi f t)+sin(2pi^2 f t). You would still see a "spike" in
the frequency domain, but quasi-periodicity
definitely does not relate to low frequency.

Ivo
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