Spectral Estimation Functions and Toolkits

MatDeck provides several functions for spectral analysis and to determine the frequency content of a signal. The following functions are fft-based non-parametric tools: periodogram(), powspectwelch(), and spectrogram().

In signal processing, a periodogram is used to estimate the power spectral density of a signal. The periodogram is a standard component in more complex methods for spectral estimation, such as Welch's method for spectral estimation. Periodograms are calculated as a Fourier transform of the auto-correlation function that is FT{x(t)*x(-t)}=X(f)*X*(f)=abs(X(f))2. MatDeck contains the function called periodogram().

Welch's method for estimating power spectra is carried out by dividing the time signal into successive blocks, forming the periodogram for each block, and averaging. MatDeck contains a function, powspectwelch(), for this purpose.

A spectrogram is a visual representation of the spectrum of a signal, showing frequency components as they vary with time. MatDeck contains a function spectrogram() which shows results in a 3D graph.

The templates are the most effective use of spectral estimation functions; they can be found in Insert – Select Templates – DSP functions.

Signal operations such as convolution, measurements, windowing, down-sampling, and up-sampling

Convolution, correlation, and covariance are very common operations in DSP. Convolution is used to determine the output of a linear time-invariant system defined by its impulse response. It can also be used to multiply polynomials given by the vector of polynomial coefficients. Correlation is used to test the measure of similarity between signals. In probability theory and statistics, covariance is a measure of the joint variability of the two signals.