# eq_sheet - |x(t)|2 dt E= T /2 1 P= T |x(t)|2 dt T /2 (t) (t...

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E = Z -∞ | x ( t ) | 2 dt P = 1 T T/ 2 Z - T/ 2 | x ( t ) | 2 dt Z -∞ φ ( t ) δ ( t - T ) dt = φ ( T ) rect( t ) = ( 1 | t | ≤ 1 / 2 0 | t | > 1 / 2 r ( t ) = ( t t 0 0 t < 0 s = σ + d N y dt N + a 1 d N - 1 y dt N - 1 + ··· + a N - 1 dy dt + a N y ( t ) = b N - M d M x dt M + b N - M +1 d M - 1 x dt M - 1 + ··· + b N - 1 dx dt + b N x ( t ) Complex roots: y o ( t ) = c 1 e ( α + ) t + c 2 e ( α - ) t c 1 = c 2 e and c 2 = c 2 e - y o ( t ) = ce αt cos( βt + θ ) h ( t ) = b o δ ( t ) + [ P ( D ) y n ( t )] u ( t ) where, y n (0) = ˙ y n (0) = ¨ y n (0) = ··· = y ( N - 2) n (0) = 0 and y ( N - 1) n (0) = 1 x ( t ) * h ( t ) = Z -∞ x ( τ ) h ( t - τ ) if x ( t ) = e st , y ( t ) = h ( t ) * x ( t ) = e st Z -∞ h ( τ ) e - = e st H ( s ) T h = R -∞ h ( t ) dt h ( t o ) E x = X n = -∞ | x [ n ] | 2

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P x = lim N →∞ 1 2 N + 1 N X - N | x [ n ] | 2 y [ n + N ] + a 1 y [ n + N - 1] + ··· + a N - 1 y [ n + 1] + a N y [ n ] = b 0 x [ n + N ] + b 1 x [ n + N - 1] + ··· + b N - 1 x [ n + 1] + b N x [ n ] y [ n ] + a 1 y [ n - 1] + ··· + a N - 1 y [ n - N + 1] + a N y [ n - N ] =
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## This note was uploaded on 12/14/2011 for the course BME 343 taught by Professor Emelianov during the Spring '09 term at University of Texas at Austin.

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eq_sheet - |x(t)|2 dt E= T /2 1 P= T |x(t)|2 dt T /2 (t) (t...

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