# R04 - ENEE 241 02 READING ASSIGNMENT 4 Thu 02/12 Lecture...

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Unformatted text preview: ENEE 241 02* READING ASSIGNMENT 4 Thu 02/12 Lecture Topic: aliasing; introduction to matrices and vectors Textbook References: sections 1.6, 2.1, 2.2.1, 2.2.2 Key Points: • Two continuous-time sinusoids having different frequencies f and f (Hz) may, when sampled at the same sampling rate f s , produce sample sequences having effectively the same frequency. This phenomenon is known as aliasing, and occurs when f ± f = kf s for some integer k . • If a continuous-time signal consisting of additive sinusoidal components is sampled uniformly, reconstruction of that signal from its samples is impossible if aliasing has occurred between any two components at different frequencies. • If the sinusoidal components of a continuous-time signal span the frequency range 0 to f B (Hz), aliasing is avoided if and only if the sampling rate f s exceeds 2 f B , a figure known as the Nyquist rate. • The matrix-vector product Ax , where A is a m × n matrix and x is a n-dimensional column vector, is computed by taking the dot product of each row of A with x . The result is a m-dimensional column vector. Theory and Examples: 1 . We saw that a continuous-time sinusoid of frequency f = 1 /T (Hz) can be sampled at two different rates f s = 1 /T s and f s = 1 /T s to produce sample sequences having the same effective frequency. This happens whenever T s ± T s = kT for some integer k ....
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R04 - ENEE 241 02 READING ASSIGNMENT 4 Thu 02/12 Lecture...

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