The root mean square of sin is 1 / 2 , so the variance of A k sin ⁡ ⁡ ( 2 π π ν ν k t + ϕ ϕ k ) is 1 2 A k 2 . Hence, the contribution to the average power of x ( t ) coming from the component with frequency ν ν k is 1 2 A k 2 . All these contributions add up to the average power of x ( t ) .