Review of difference equations, IIR filters, FIR filters, cascade and parallel connections of filters.

Review of solving discrete difference equations and how the form of the particular solution for these equations varies in relation to the homogeneous solution, or more specifically, the roots of the difference equation characteristic polynomial.

Review of tabular computation of convolution sums and how to properly locate the sample beginning, end, and zero-index of a convolution sum using this technique.

Review of how to determine the difference equation which corresponds to a specified set of FIR filter coefficients.

Matched Filtering Segment (cont.)

Use of matched filters on noisy periodic input signals for the purpose of estimating the signal to noise ratio (SNR) of the input signal.

What is SNR and why is it important to know (or be able to estimate)?

The definition of SNR.

Definition of some statistical quantities and how to estimate their value from data :

Mean

Covariance

Variance

Standard Deviation

The (auto) correlation coefficient and its role in determining the SNR.

How statistical measures and the correlation coefficient may be used to estimate the SNR of a noisy input signal.

Return the DTFT

DTFT Theorems