Introduction To Spectral Analysis

Historically, spectral analysis began with the search for “hidden periodicities” in time series data. Chapter 3 discussed fitting cosine trends at various known frequencies to series with strong cyclical trends. In addition, the random cosine wave example in Chapter 2 on page 18, showed that it is possible for a stationary process to look very much like a deterministic cosine wave. We hinted in Chapter 3 that by using enough different frequencies with enough different amplitudes (and phases) we might be able to model nearly any stationary series.^† This chapter pursues those ideas further with an introduction to spectral analysis. Previous to this chapter, we concentrated on analyzing the correlation properties of time series. Such analysis is often called time domain analysis. When we analyze frequency properties of time series, we say that we are working in the frequency domain. Frequency domain analysis or spectral analysis has been found to be especially useful in acoustics, communications engineering, geophysical science, and biomedical science, for example.