How do I find the phase delay between two signal?

I have two signals. Both of which I have applied the fft function to and now want to find the delay as well as a ratio of the amplitude at a certain frequency. How could I accomplish this?

Answer 1

[Star Strider]

With respect to the delay, see if the finddelay (link) function will do what you want. (I believe it was introduced in R2015b. The documentation does not say specifically.)

To find the amplitudes at a specific frequency, use the fft (link) function, and compare (subtract or divide) the amplitudes at each frequency, or only your frequency-of-interest if you are only interested in one frequency. The signals must be the same length and have the same sampling frequency for this approach to work optimally.

[Mauricio Gomez]

Sounds good thank you! I was wondering if there was a different way to find the delay between the two waves without using the finddelay function?

[Star Strider]

My pleasure.

If you have two signals at the same frequency, in addition to comparing amplitudes using the abs function on each signal, you can use the angle function to get the phase from the real and imaginary components for each signal.

The unwrap function could be helpful, and to put the angles in 0 to 2*pi representation, this utility function works:

Angles2pi = @(a) rem(2*pi+a, 2*pi);                      % For ‘atan2’

for degrees:

Angles360 = @(a) rem(360+a, 360);                        % For ‘atan2d’

These work with the results returned by atan2 and atan2d, respectively. (According to the documentation, the angle function uses atan2.)

[Mauricio Gomez]

Awesome! thank you!

[Star Strider]

As always, my pleasure!

[Mauricio Gomez]

Sorry just a real quick question. What number or variable would I replace "a" with in the "Angles2pi = @(a) rem(2*pi+a, 2*pi);" function?

[Star Strider]

No apology necessary!

The argument ‘a’ is any angle in radian measure that is returned by atan2. It takes angles going from -pi to 0 to pi and produces an angle that goes from 0 to 2*pi.

[Mauricio Gomez]

okay understood. So in this case I would not replace a with a variable that I am graphing correct?

[Star Strider]

Correct.

‘Angles2pi’ is a function that you use just as you would any other function.

Example —

Angles2pi = @(a) rem(2*pi+a, 2*pi);                      % For ‘atan2’

x = -pi/2;

Result = Angles2pi(x)

Result =
     4.7124

[Mauricio Gomez]

Gotcha! Thank you!

[Star Strider]

As always, my pleasure!