Discrete Sequences
and
Linear Time-Invariant Systems
Lecture
2
Reading
assignment:
Textbook : 2.0, 2.1, 2.2, 2.3, 2.4
Digital Signal Processing - Fall 2015
1
Motivation
The discrete-time sequences are the basic data sets being
processed by DSP operations.
Linear Constant Coefficient
Difference Equations
Reading assignment:
Textbook 2.5
HW1: 2.23 , 2.25, 2.28, 2.30, 2.31,
Plus GQ: 2.48
Digital Signal Processing - Fall 2015
1
Topics
Inverse System Definition for LTI systems
Linear Constant Coefficient Differ
Z-Transforms
Reading Assignments:
Textbook 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7
1
Complex Functions
Complex function are complex valued and complex arguments .
The domain usually spans over some open regions on complex
plane.
z0
z1
2
Digital Signal Pro
Transform Analysis of
LTI Systems
Motivation
LTI systems have been found to be characterized
by their impulse and frequency responses.
We have also seen how the frequency response
may sometimes be extended to (be realized in) a
complex domain using the z
Discrete-Time Structures
Motivation
Discrete - Time Structures apply to causal LCCDE systems,
which are an important class of LTI's because their recursions
can be implemented with finite digital hardware. The objective
here is to find alternate forms of
Filter Design
University of Rochester Fall 2005, J. Astheimer
1
Filter Specifications (1)
The primary objective is to attain certain Gain characteristics which may be
described by giving an ideal target for the gain GIdeal together with
tolerances that br
Discrete-Time
Fourier Transforms
Reading assignment:
Textbook 2.6, 2.7, 2.8, 2.9
Digital Signal Processing - Fall 2015
Motivation
The behavior of systems are naturally explored by
probing them with a variety of inputs.
For linear time invariant systems t
Continuous & Discrete Signals
Digital Signal Processing - Fall 2015
Motivation
Using discrete sequences to approximate
continuous signals is fundamental to DSP.
It is critically important to understand the
relationship between a continuous signal and its