# I need a good explanation of phase and magnitude spectra

• Jncik

#### Jncik

I understand that having a periodic signal x(t) we can find a signal y(t) which uses harmonically related exponentials in order to construct the x(t) signal

each exponential has a frequency and magnitude, for example

$$3*e^{j 2 \omega}$$ has a frequency of $$\frac{2 \pi}{2 \omega} = \frac{pi}{\omega}$$

and also a magnitude of 3

similarly $$2*e^{j 3 \omega}$$ has a frequency of $$\frac{2 \pi}{3 \omega}$$

and a magnitude of 2

now if we plot the amplitude spectra of y(t) we will get discrete values where for the x coordinate we will be having the frequency, and for the y the amplitude on that frequency

so we will have a discrete value on the frequency(x) $$\frac{\pi}{\omega}$$ with an amplitude(y) of 3 and also a value for the frequency(x) $$\frac{2 \pi}{3 \omega}$$ with an amplitude of 2

I hope that I'm correct

now, the thing is that I don't understand the phase, what will the phase represent? for example suppose we have this graph

[PLAIN]http://img191.imageshack.us/img191/8259/unledpsg.png [Broken]

what does the phase graph represent? what are these lines referring to? if you can please explain the x,y coordinates and what they mean

thanks in advance :)

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The coefficients of Fourier components of a signal are complex numbers, having both magnitude and phase. So they look as Aeejωt. The amplitude spectrum shows A(ω) and the phase spectrum is φ(ω)
If you use real Fourier series instead of complex ones, the components are of the form Asin(ωt+φ). A is the amplitude and φ is the phase of the Fourier component.

ehild