# power spectrum -PSD

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

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 $$z = e^{j\omega}$$.

• Thank you. wikipedia was right :)!! – Ashish Bhigah Jul 11 '19 at 12:38