Will the integral of the PSD of a down-sampled signal still equal the variance in all cases


1 Answer 1


No. The aliased component will interfere with the non-aliased components and the interference can constructive or destructive.

Trivial example:

$$x[n] = \sin\left(\frac\pi2n\right)$$

If you down sample this to $y[n] = x[2n]$, you get all zeros.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.