thomas.greenleaf@[EMAIL PROTECTED]
wrote:
> If i generate a signal, using matlab, like this
> t=0:0.001:1;
> y=sin(2*pi*t*17+2);
> then I get a sine wave with frequency 17, amplitude 1 and phase****ft
> 2.
>
> If I then calculate a fast fourier transform
> ft = fft(y);
> and look at the phase for the correct frequency
> phase = angle(ft(18)); //1 is DC component,så index is ****fted by one
> then I get 0.4822 radians or 37.6 degrees
>
> Initially I expected to get 2, which was the ****ft I used, but after a
> little consideration it was obvious that to measure a phase ****ft of
> zero one would need to have a cosine wave with a phase ****ft of 0 and
> to measure 2 it would have to be a cosine wave with a ****ft of 2.
> In other words, I should not generate a sine wave but a cosine wave if
> I want to get the correct phase back.
>
> I am somewhat new to fourier transform så I may be missing something,
> but is my thinking correct about this?
> I can see why it will work with cosine and not sine, but all the
> previous sound generation I have done have been sines.
>
> Perhaps I can be more specific about how I try to look at things.
> For a frequency such as 17 (Hz in my example) you have a basis
> function exp(-2*pi*t*17*i).
> This describes a rotating vector initially the real value 1, but as t
> goes from 0 to 1, it will rotate counter clockwise in the complex
> plane. When t is 0.25 it will point at 0+i and so on.
>
> When you fold the signal f(t) with the basis g(t) you will, for t=0,
> get f(0)*1. For t=1/17/2 (which is half a full wave) you will get f
> (1/17/2)=-1. At that time g is also -1, so you get -1*-1=1, same as
> for f(0).
> Point being... the integral of f(t)*g(t) over t will return a complex
> number which is 1+0i. The angle of that is zero, and the phase ****ft
> of the cosine wave was zero, so it works out. For a sine it would not.
>
> Should I just forget about sinewaves and simply look at the signals as
> cosine waves and then just work with the transform and its inverse by
> considering complex numbers and ignoring the sine/cosine waves it
> represent?
sci.image.processing is an image processing
group. Why are you posting your question
here?
--
Regards,
Martin Leese
E-mail: please@[EMAIL PROTECTED]
http://members.tripod.com/martin_leese/
|
