Multidimensional spectral estimation

Power spectral estimation forms the basis for distinguishing and tracking signals in the presence of noise and extracting information from available data. One dimensional signals are expressed in space and time domain while multidimensional signals are represented in wave vector and frequency spectrum. Therefore spectral estimation in the case of multidimensional signals gets a bit tricky.

Motivation

Multidimensional spectral estimation has gained popularity today because of their application in fields like medicine, aerospace, sonar, radar, bio medicine and geophysics. In the recent past, a number of methods have been suggested to design models with finite parameters to estimate the power spectrum of multidimensional signals. In this article, we will be looking into the basics methods used to estimate the power spectrum of multidimensional signals.

Application

There are many applications of spectral estimation of multi-D signals such as classification of signals as low pass, high pass, pass band and stop band. It is also used in compression and coding of audio and video signals, beam forming and direction finding in radars, Seismic data estimation and processing, array of sensors and antennas and vibrational analysis. In the field of radio astronomy, it is used to synchronize the outputs of an array of telescopes.

Basic Concepts

In a single dimensional case, a signal is characterized by an amplitude and a time scale which makes the detection process pretty simple. The basic concepts involved in spectral estimation include autocorrelation, Fourier transform, mean square error, separable functions and entropy. When it comes to detecting a multidimensional signal, there are two approaches: use a bank of beamformers which is similar to filter banks or estimate the parameters of the random process in order to estimate the power spectrum. We are interested in the latter method and it is classified as follows:-