ZT Tables_rev2

ZT Tables_rev2 - Z Transform Table Time Signal[n[n q q = 1...

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Unformatted text preview: Z Transform Table Time Signal [n ] [n - q], q = 1, 2, K Z Transform 1 1 = z -q , q = 1, 2, K q z z z -1 zq - 1 , q = 1, 2, K z q -1 (z - 1) z , a real or complex z-a z (z - 1)2 z2 (z - 1)2 z (z + 1) (z - 1)3 az (z - a )2 az (z + a ) (z - a )3 2az 2 (z - a )3 z 2 - cos(o ) z z 2 - 2 cos(o ) z + 1 sin(o ) z 2 z - 2 cos(o ) z + 1 z 2 - a cos(o ) z z 2 - 2a cos(o ) z + a 2 a sin(o ) z 2 z - 2a cos(o ) z + a 2 u[n ] u[n] - u[n - q], q = 1, 2, K a n u[n ], a real or complex nu[n ] (n + 1)u[n ] n 2u[n ] na n u[n ], a real or complex n 2a n u[n ], a real or complex n ( n + 1)a n u[n ], a real or complex cos(o n )u[n ] sin(o n )u[n ] a n cos(o n)u[n ] a n sin(o n )u[n ] One-Sided Z Transform Properties Property Name Linearity Right Time Shift (Causal Signal) Right Time Shift (Non-Causal Signal) ax[n ] + bv[n ] x[n - q], q > 0 x[n - 1] x[n - 2] x[n - q], q > 0 Property aX ( z ) + bV ( z ) z - q X (z ) z -1 X ( z ) + x[ -1] z -2 X ( z ) + x[ -2] + z -1 x[ -1] z - q X ( z ) + x[ - q ] + z -1 x[ - q + 1] + L L + z - q+1 x[ -1] Multiply by n Multiply by n2 Multiply by Exponential Multiply by Sine Multiply by Cosine Summation (Causal Signal) Convolution in Time Initial-Value Theorem nx[n] n 2 x[n ] -z d X (z ) dz 2 d 2 d z X ( z) + z X ( z) dz dz 2 a n x[n ], a real or complex X ( z / a ), a real or complex sin(o n ) x[n ] cos(o n ) x[n ] x[i ] i =0 n x[n ] * h[n ] x[0] = lim[X ( z )] x[1] = lim[zX ( z ) - zx[0]] z j X (e jo z ) - X (e - jo z ) 2 1 X (e jo z ) + X (e - jo z ) 2 z X ( z) z -1 X ( z)H ( z) [ ] [ z x[ q ] = lim z N X ( z ) - z q x[0] - z q -1 x[1] - L - zx[ q - 1] z [ Final-Value Theorem If X(z) is rational and the poles of (z 1)X(z) are inside unit circle Then lim x[n ] = [( z - 1) X ( z )]z =1 n ...
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This note was uploaded on 02/29/2012 for the course EECE 301 taught by Professor Fowler during the Fall '08 term at Binghamton.

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ZT Tables_rev2 - Z Transform Table Time Signal[n[n q q = 1...

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