A periodic signal has a repeating pattern. What are the three different characte

Question

A periodic signal has a repeating pattern. What are the three different characteristics of a periodic signal? Determine there, if you can, for a periodic sinusoidal signal that swings between -110 and 110 volts, completing one cycle in 20 millseconds. If a characteristic cannot be determined from this information, so state.

(I believe these characteristics are referring to phase, frequency, amplitude and period...so if you can find those from that. If it means something else go ahead and do what it actually means)


Will rate lifesaver for a well explained answer, thanks!

Explanation / Answer

Not everything is given. The information that is missing is its location and phase. A sine wave with no shift in phase is zero at the origin, while a cosine wave is one at the origin. The phase shift will determine how late or how early the respective wave is from its normal position. For instance, the sine wave is 90 degrees or -/2 radians off from cosine.

But we are given enough to find the amplitude, and the frequency. One cycle is the period of the function. One cycle means the time it takes a signal to complete its pattern without repeat. frequency is the inverse of period.

f = (1/20*10-3) = 50 s-1. This means that the same wave passes a point in space 50 times a second. The angular frequency would just be 50*2* = 314.16 radians/sec.

The typical anatomy of a signal is thus:

A*cos(t - ). If we were to assume the function cosine, which is common, this is what it would look like.

110 * cos ( 314.16t + )

where phi is the phase shift of the angle. This denotes whether there is a delay or an advancement of the signal from the normal cosine angle which is 1 at the origin or t = 0. Whichever you want to say it.

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