Ch4(1) LTI Discrete-Time Systems in the Transform Domain.pdf

LTI Discrete-Time Systems in LTI Discrete-Time Systems in
the Transform Domain the Transform Domain
• An LTI discrete-time system pletely • Such transform-domain representations
characterized in the time-domain by its provide additional insight into the behavior
impulse response sequence {h[n]} of such systems
• Thus, the transform-domain representation • It is easier to design and implement these
systems in the transform-domain for certain
of a discrete-time signal can also be equally applications
applied to the transform-domain
• We consider now the use of the DTFT and
representation of an LTI discrete-time the z-transform in developing the transform-
system domain representations of an LTI system
1 2
Copyright © 2001, S. K. Mitra Copyright © 2001, S. K. Mitra
Finite-Dimensional LTI Finite-Dimensional LTI
Discrete-Time Systems
Discrete-Time Systems
• Applying the DTFT to the difference
• In this course we shall be concerned with equation and making use of the linearity and
LTI discrete-time systems characterized by the time-invariance properties of Table
linear constant coefficient difference we arrive at the input-output relation in the
equations of the form: transform-domain as
N M N M
­ jw k jw ­ jw k jw
å dk y[n ­ k] = å pk x[n ­ k] ådke Y (e ) = å pke X (e )
k=0 k =0 k=0 k=0
where Y ( e j w ) and X ( e j w ) are the