1
$\begingroup$

I was wandering if someone can help me to understand if there is difference between power spectrum and power spectral density. Looking here I found that there are differences https://www.quora.com/What-is-the-difference-between-power-spectrum-and-power-spectral-density

Wikipedia says that are different name for the same thing "More commonly used is the power spectral density (or simply power spectrum)" https://en.wikipedia.org/wiki/Spectral_density

$\endgroup$
1
$\begingroup$

PSD (power spectral density) : distribution of power (of a WSS random process) along frequency... Power Spectrum is the same thing.

For zero mean discrete-time processes, PSD is defined as the DTFT of the ACS:

$$ \boxed{ S_x(e^{j\omega}) = \sum_{m=-\infty}^{\infty} r_{x}[k] e^{-j \omega m} }$$

Where $r_{x}[m]$ is the ACS (auto-correlation sequence) of the WSS random process $x[n]$. Various authors (or textbooks) prefer different symbols or names for ACS and PSD such as: $\phi_x[m]$ for ACS, or $\Phi_x(\omega)$ for PSD.

Sometimes, the Z-transform approach is used and PSD is defined as

$$ \boxed{ P_x(z) = \sum_{n=-\infty}^{\infty} r_{x}[n] z^{-n} }$$

where the spectrum is obtained in the case when $z = e^{j\omega}$.

$\endgroup$
  • $\begingroup$ Thank you. wikipedia was right :)!! $\endgroup$ – Ashish Bhigah Jul 11 at 12:38

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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