Question

2. Categorise each of the following signals as either an energy or power signal, and find the energy or power of the signal. (12 marks a) *(t) = 5 cos 2nft. - <t <co b) x[n] = 2e/3n c) *(t) = cos(t) + 5cos 2t ,- <t< W d) *(t) = {Acos 2nft - To/2st ST,/2, where To = 1/5 otherwise

Answer 1

Complex exponentials, as well as sine or cosine functions, are power signals. But a finite duration signal is an energy signal. Hence, (a), (b) and (c) are power signals while (d) is an energy signal.

For a sine or cosine function, power = amplitude²$\div$ 2 and for complex exponential, power = amplitude².

So

a) Power = 5²$\div$2 = 12.5 W

b) Power = 2² = 4 W

c) Power = 1²$\div$2 + 5²$\div$2 = 13 W

To get energy of (d) we need to find area under the finite duration of the square of the signal.

To = 1 / 3 ftol Also, energy _To/21 ²-A725 / 2 (1-4ft) at = 4% [ To/ - (- Top Tala da cas taft at C


= ARTE - AP Te Taindafta 't sinaaf To je energy to [-]