ZT Tables_rev2

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

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online