What are the amplitude and phase spectra of a function?

Question

I am studying Fourier transforms. Several of the exercises ask one to plot the amplitude and phase spectra.

For instance, I have transformed rect(t-5) to obtain sinc(w/2)*e^(-i5w).

I know that a complex number can be written in polar form as follows: a*e^(i*theta) where a is the magnitude and theta is the phase. Does this mean that the amplitude spectrum of my function is sinc(w/2) and the phase spectrum is 5w?

Answer 1

You are correct.

The amplitude can be drawn as sinc(w/2) (y-axis), versus w (x-axis).  Frequency is both positive and negative, so the sinc function will be symmetrical about the y-axis.  The function can also go negative.  You can choose to plot only the positive frequencies.  

The phase will be 5w, which is a straight line with slope 5 and a y-offset of zero (DC phase = 0).