EE 329

Prof. Rich Kozick

Spring, 1997

**Signals in the Time Domain and the Frequency Domain **

The important idea from class on Friday, January 24
is to understand how to interpret the *complex numbers*
that arise in the frequency domain (Fourier transform)
representation of signals.
We looked at four signals, and their representations with
real sines/cosines and complex exponentials:

The complex coefficient *D* on the ``positive frequency''
exponential contains the following information:
(refer to for illustrations)

- The real part is the amplitude of the cosine component.
- The imaginary part is the amplitude of the sine component.
- The magnitude |
*D*| is the amplitude of the sinusoid. - The angle is the phase shift of the sinusoid, relative to a cosine.

Thus the complex value of a frequency component tells you
the *amplitude* and the *phase shift*
of the corresponding sinusoid that composes the time signal.

Sun Jan 26 03:24:44 EST 1997