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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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- Spring '08