Q: How do you find the phase between an input and output signal? These signals are swept-sin (chirp: https://en.wikipedia.org/wiki/File:Linear-chirp.svg) signals for system identification, so i'm looking to find a transfer function.(adsbygoogle = window.adsbygoogle || []).push({});

Background:A frequency-domain Transfer Function's magnitude is found by taking the ratio of the output/input FFTs:

FFTratio = Complex{FFT out} / Complex{FFTin}, ∴ Magnitude = abs(FFTratio).

To find the phase, take the angle between the complex FFTs:

atan2( Imag{FFTratio}, Real{FFTratio} )

As a test, in Matlab's System Identification Tool, with two simple, 140 deg shifted and noisy 10 Hz sinusoids -- NON-swept, just simple sines -- the answer is as expected, and the phase is appr. -140 deg at 10 Hz in the phase plot.

Question:BUT when using two simulated constant-phase-shifted chirps, for system identification (chirp), the phase isn't a constant -140 Hz.

The phase drops dramatically from -140 deg near 1 Hz, and above 10 Hz it goes towards -5000 deg. See the attached images. The chirps are 0.01 Hz sinusoid at t=0, and a 400 Hz sinusoid at t=200s.

A zoomed 20s signal is shown for clarity. yc is output (top), uc is input (bottom).

Why is the phase not a constant -140 deg up until ~400 Hz?Why does the phase drop to -5000 deg? The swept-sin (chirp) peaks continue to remain at a constant phase relative to each other, so it should stay at -140

Attachments:

2x time-signals

1x FFTs of output(top) and input (bottom), called "Periodogram"

1x transfer function estimate, magnitude on top, phase on bottom

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# FFTs, and ratio of FFTs! Phase question

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