How it works
A continuous-time signal x(t) is defined for every value of t on the real line; a discrete-time signal x[n] exists only at integer values of n. Periodic signals satisfy x(t) = x(t + T) for all t and a fundamental period T > 0 — a 50 Hz sinusoid has T = 20 ms. Energy signals have finite total energy E = ∫|x(t)|² dt < ∞ and zero average power; power signals have finite average power P = lim(T→∞) (1/2T)∫|x(t)|² dt but infinite energy. A signal cannot simultaneously be both an energy and a power signal.
Key points to remember
The unit step u(t) is a power signal with P = 0.5 W (normalised to 1Ω load), while a rectangular pulse of finite duration is an energy signal. Deterministic signals are completely specified mathematically; random signals like thermal noise are described by statistical parameters such as mean and variance. Even signals satisfy x(−t) = x(t); odd signals satisfy x(−t) = −x(t). Any signal can be decomposed into even and odd parts: x_e(t) = [x(t) + x(−t)]/2 and x_o(t) = [x(t) − x(−t)]/2. The signum function sgn(t) is a classic odd signal and the cosine is a classic even signal used in exam examples.
Exam tip
The examiner always asks you to classify a given signal as energy or power and compute E or P — set up the integral carefully, apply the correct limits, and state the conclusion explicitly to earn the final mark.