Review of linearity proofs, causality proofs, and time (shift)-invariance proofs.
Quick review of complex numbers and phasor notation.
Review of DTFT properties, in particular, the periodicity property and how this is different from continuous Fourier Transforms.
Discrete Time Fourier Transform (cont.)
Symmetry Properties for the DTFT.
Matched Filtering Segment
Use of matched filters to detect an a-priori known sequence in a noisy input signal.
Review of the relationship of cross-correlation to convolution and how this relates to the design of the matched filter.
Know the limiting relationship : The cross-correlation of two uncorrelated signals tends toward 0 as the signal length tends toward infinity.
Know the predicted value of the output at the sample index where the noisy signal of interest is (approximately) equal to coefficients of the matched filter.
Use of matched filters to estimate the period of a periodic input signal with unknown period.
Statistical detection methods to determine the sample indices of the known sequence within the input signal.
Statistical methods to estimate the unknown period from the extracted sample indices.
Week 5 : DTFT and Matched Filtering
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