How does spectral analysis work

To perform spectral analysis, we first must transform data from time domain to frequency domain. The technical details of spectral analysis go well beyond the scope of these notes. The classic source is Priestly , but there are plenty of others.

In brief, the covariance of the time series can be represented by a function known as the spectral density. This independence can be improved — as can the visual quality and interpretability of the plot — by smoothing the periodogram using a kernel smoother which is generally some sort of weighted running average.

We can see very clearly that we can recover the periodic signals that we built into our toy time series. Grenfell et al. The series looks extremely regular. We can calculate its power spectrum to determine what frequencies dominate the variance.

The function spectrum is a wrapper for calculating the periodogram i. There are a couple issues that need to keep in mind:. Cazellas et al. Bangkok shows two modes, one yearly and one that is yearly. Sometimes the year period is dominant in Bangkok, but the year period is never dominant in the rest of Thailand. Signal and noise are averaged over the entire panel of traces. As a prerequisite, a stack volume see Adding Data Sets and a polygon see Creating a Polygon must be selected:.

Note: The vertical scale can be configured by right clicking in the view and selecting Configure Track. At Scaling , select Linear, Log or Octave to display the curves in the track in the respective axis space. View in admin portal Edit content on web Edit in desktop. Search term. The Fourier transform of the signal identifies its frequency components.

Use fft to compute the discrete Fourier transform of the signal. Plot the power spectrum as a function of frequency.

While noise disguises a signal's frequency components in time-based space, the Fourier transform reveals them as spikes in power. In many applications, it is more convenient to view the power spectrum centered at 0 frequency because it better represents the signal's periodicity.

Use the fftshift function to perform a circular shift on y , and plot the 0-centered power. You can use the Fourier transform to analyze the frequency spectrum of audio data. The file bluewhale. The file is from the library of animal vocalizations maintained by the Cornell University Bioacoustics Research Program. Because blue whale calls are so low, they are barely audible to humans.

The time scale in the data is compressed by a factor of 10 to raise the pitch and make the call more clearly audible. Read and plot the audio data. You can use the command sound x,fs to listen to the audio. The first sound is a "trill" followed by three "moans". This example analyzes a single moan.