ABSTRACT
In order to understand the effect of a system on a stochastic process, this chapter introduces the Fourier transform of the autocorrelation function. The Fourier transform of the autocorelation function is called the power spectral density function. A very important property for stochastic processes is stationarity. Wide-sense stationary means that the first- and second-order statistics are invariant over time. The power spectral density function is defined as the Fourier transform of the autocorrelation function. One of the best ways of understanding the power spectral density function is by considering the effect on the power spectral density function of band pass filtering a stochastic process. The signal to noise ratio is usually defined as the ratio of the average power in the signal to the average power in the noise. In nuclear magnetic resonance imaging, signal to noise ratio is commonly used by engineers to describe the free induction decay signal.
