pm e jm x e j 0 d 0 d1e j d n e jn

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Unformatted text preview: Example - Compute the energy of the sequence sin ω n hLP [n] = π nc , − ∞ < n < ∞ • Here ∞ 1π 2 jω 2 ∑ hLP [n] = ∫ H LP (e ) dω 2π − π n = −∞ where 13 ⎧1, 0 ≤ ω ≤ ωc H LP (e jω ) = ⎨ ⎩0, ωc < ω ≤ π • Therefore ∞ 2 ∑ hLP [n] = n = −∞ 1 ωc ωc <∞ ∫ dω = 2π −ωc π • Hence, hLP [n] is a finite-energy lowpass sequence 14 Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra DTFT Computation Using MATLAB • The function freqz can be used to compute the values of the DTFT of a sequence, described as a rational function in in the form of p + p1e − jω + .... + pM e − jωM X ( e jω ) = 0 d 0 + d1e − jω + .... + d N e − jωN 15 DTFT Computation Using MATLAB • For example, the statement H = freqz(num,den,w) returns the frequency response values as a vector H of a DTFT defined in terms of the vectors num and den containing the coefficients { pi } and {di } , respectively at a prescribed set of freque...
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