1. 2 Linear Time-Invariant Systems --Analysis of Signals and Systems in time-domain
An arbitrary signal can be represented as the supposition of scaled (weighted) and shifted unit impulse functions.
A LTI system can be completely characterized in terms of its unit impulse response.
Solving and analyzing a TLI system using its unit impulse response.

2. 2.1 Discrete-Time Signals and Systems
2.1.1 The representation of Discrete-Time Signals in Terms of Impulses

3. 2.1.1 The representation of Discrete-Time Signals in Terms of Impulses

4. 2.1.2 The Discrete-Time Unit Impulse Response and the Convolution-Sum Representation of LTI Systems
[n]  h [n] : Unit Impulse Response
[n-k]  h [n-k] : Time-Invariant Property
x[k][n-k]  x[k] h [n-k] : Linear Property
x[k][n-k]  x[k] h [n-k] : Linear Property
x[n]  y [n]