# Spectral Analysis vs. Spectral Line Analysis

We usually talk about "spectral analysis" but some resources (this paper or this doc) talk about "spectral line analysis".

Does this make sense to you, i.e. are the 2 fields actually different or the 2 names refer to the same thing?

Spectrum analysis is more general: it involves looking at the entire spectrum of a given signal.

Spectral line analysis assumes that the spectrum contains several peaks (lines) of interest at specific frequencies. The aim then is to find the precise frequency, magnitude, and phase of those peaks (lines).

Just to enrich the previous answer, the line spectrum is defined in Stoica, P., & Moses, R. (2005). Spectral analysis of signals. Prentice Hall. p.144 as associated to signals of the form: $$y(t)=x(t)+e(t)$$ where $x(t)$ is a sinusoidal noise-free signal defined as $x(t)=\sum_{k=1}^{n}\alpha_k e^{i(\omega _k t+\phi _k )}$ and $e(t)$ is circular white noise with power $\sigma^2$.

So a line spectrum equals $\sigma^2$ everywhere except for some specific frequencies, hence the name line spectrum.

See e.g. the following picture from Michael Richmond: UPDATE : an extra reference explaining the different types of spectra is p.142 in Percival, D. B., & Walden, A. T. (1998). Spectral analysis for physical applications.

In this reference, line spectras are called discrete or purely discrete.

• Nice addition!!! – Peter K. Oct 7 '15 at 22:32