Chapter 2Discrete-Time Signals and Systems in the Time-Domain.ppt

Chapter 2Discrete-Time Signals and Systems in the Time-Domain
Three Concepts:
Analog signal: continuous in time, continuous in amplitude.
Discrete time signal: discrete in time, continuous in amplitude.
Digital signal: discrete in time, quantization in amplitude.
Discrete-Time Signals
How to get a Discrete-Time Signal?
The signal is defined at equally spaced discrete values of time, with the signal amplitude at these discrete times being continuous.
The signal that is got by periodic sampling the continuous signal.
Main contents:
Representation: a sequences of numbers.
Operation: time-shift, time-reversal, adder, product(modulator), differential, time-scaling, convolution,
mon sequences: δ[n] ,u[n], cos[ωn], exp[jωn]…
Time-Domain Representation
We use sequences to represent discrete-time signals.
There are two ways to represent a sequence:
(1) Descriptive way:
(2) Graphic way:
Example: look at books P42~43.
The Classifications of the Discrete-Time Signals
Class standard:
Based on sequence length
Based on symmetry
Based on periodicity
Based on energy and power
Other types of classification
Sequence Length(P44)
Left-sided sequence. .
(a left-sided sequence is called an anticausal sequence.)
Finite-length Sequence:
InFinite-length Sequence:
Right-sided sequence. .
(a right-sided sequence is called a causal sequence.)
Finite-length Sequence
A finite-length discrete-time can be represented as a finite-length sequence in a transform-domain.
If we denote the vector of time-domain samples of length N defined for 0 ≤ n ≤ N-1 as x = [x[0] x[1] … x[N-1]]t, the vector of the transform-domain samples of length N defined for 0 ≤ k ≤ N-1, X = [X[0] X[1] … X[N-1]]t, is obtained by multiplying by an N×N invertible matrix D: X=Dx.
Symmetry(P52)
Conjugate-symmetric sequence:
A real conjugate-symmetric sequence is called an even sequence.
Conjugate-antisymmetric sequence:
A real conjugate-antisymmetric sequence is called an odd sequence.