Signal Power and Energy

Signal Power and Energy

Two fundamental quantities describe the "strength" of a signal.

Signal Energy

The energy of a discrete signal $x[n]$ over $N$ samples is the sum of squared values:

$E = \sum_{n=0}^{N-1} x[n]^2$

Signal Power

The average power is energy normalized by the number of samples:

$P = \frac{1}{N} \sum_{n=0}^{N-1} x[n]^2$

RMS (Root Mean Square)

The RMS value is the square root of average power — it represents the effective amplitude:

$\text{RMS} = \sqrt{\frac{1}{N} \sum_{n=0}^{N-1} x[n]^2} = \sqrt{P}$

For a pure sinusoid $x[n] = A\sin(\theta)$, the RMS is $A/\sqrt{2} \approx 0.707 A$.

Example

For the signal $[1, -1, 1, -1]$ (alternating $\pm 1$):

• Energy $= 1 + 1 + 1 + 1 = 4$
• Power $= 4/4 = 1.0$
• RMS $= \sqrt{1.0} = 1.0$

For $[0, 1, 0, -1]$:

• Power $= (0+1+0+1)/4 = 0.5$
• RMS $= \sqrt{0.5} \approx 0.7071$

Your Task

Implement:

• signal_power(samples) — returns $\frac{1}{N}\sum x[n]^2$
• signal_energy(samples) — returns $\sum x[n]^2$
• rms(samples) — returns $\sqrt{\text{power}}$

import math

def signal_power(samples):
    return sum(x**2 for x in samples) / len(samples)

def signal_energy(samples):
    return sum(x**2 for x in samples)

def rms(samples):
    return math.sqrt(signal_power(samples))