Question

The power in the signal (t) = 8cos (20πt – \(\frac{π}{2}\)) + 4sin (15πt) is equal to ______________

(a) 40

(b) 42

(c) 41

(d) 82

This question was posed to me in homework.

The doubt is from Concept of Convolution topic in chapter Signal Transmission Through Linear Systems of Signals and Systems

Answer 1

Correct answer is (a) 40

The explanation: Power of Signal = limT→ ∞ \(\frac{1}{T} \int_{-T/2}^{T/2} |f(t)|^2 \,dt\)

Signal power P is mean of the signal amplitude squared value of f (t).

Rms value of signal = \(\sqrt{P}\)

Now, (t) = 8cos (20πt – \(\frac{π}{2}\)) + 4sin (15πt)

= 8 sin (20πt) + 4 sin (15πt)

= \(\frac{8^2}{2} +  \frac{4^2}{2}\)

= 32 + 8 = 40.