- 2072 Kartik · 2+3 marks
Energy or power: u[n] and δ[n]
Short answer
Energy signal has finite energy; power signal has finite nonzero average power. Unit step u[n]: energy infinite, power=½, so power signal. Unit impulse δ[n]: energy=1 (finite), power=0, so energy signal.
Define energy and power signal. Check whether the signals x[n] = u[n] and x[n] = δ[n] are energy or power type.
Definitions
- Energy signal: E = Σ |x[n]|² is finite (0 < E < ∞); then average power P = 0.
- Power signal: E = ∞ but P = lim(N→∞) 1/(2N+1) Σ(n=−N to N) |x[n]|² is finite and non-zero.
Unit step x[n] = u[n]
E = Σ(n=0 to ∞) 1² = ∞, so it is not an energy signal.
P = lim 1/(2N+1) Σ(n=0 to N) 1 = lim (N+1)/(2N+1) = ½
P is finite, so u[n] is a power signal.
Unit impulse x[n] = δ[n]
E = Σ δ²[n] = 1 (only the sample at n = 0 is non-zero). It is finite, so δ[n] is an energy signal.
Check: P = lim 1/(2N+1) · 1 = 0, as expected for an energy signal.
| Signal | Energy | Power | Type |
|---|---|---|---|
| u[n] | ∞ | ½ | Power |
| δ[n] | 1 | 0 | Energy |
✓ Answer checked by Claude Opus 5.5 (high effort)
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