文档介绍：Chapter 1 Continuous-time Signals and Systems
§ Introduction
Any problems about signal analyses and processing may be thought of letting signals trough systems.
h(t)
f(t)
y(t)
From f(t) and h(t),find y(t), Signal processing
From f(t) and y(t) ,find h(t) ,System design
From y(t) and h(t),find f(t) , Signal reconstruction
§ Introduction
There are so many different signals and systems that it is impossible to describe them one by one
The best approach is to represent the signal as bination of some kind of most simplest signals which will pass though the system and produce a response. Combine the responses of all simplest signals, which is the system response of the original signal.
This is the basic method to study the signal analyses and processing.
§ Continue-time Signal
All signals are thought of as a pattern of variations in time and represented as a time function f(t).
In the real-world, any signal has a start. Let the start as t=0 that means
f(t) = 0 t<0
Call the signal causal.
Typical signals and their representation
Unit Step u(t) (in our textbook (t))
u(t)
1
0
t
u(t- t0)
1
0
t
t0
u(t) is basic causal signal, multiply which with any non-causal signal to get causal signal.
Typical signals and their representation
Sinusoidal Asin(ωt+φ)
f(t) = Asin(ωt+φ)= Asin(2πft+φ)
A - Amplitude
f - frequency(Hz)
ω= 2πf angular frequency (radians/sec)
φ– start phase(radians)
Typical signals and their representation
sin/cos signals may be represented plex exponential
Euler’s relation
Typical signals and their representation
Sinusoidal is basic periodic signal which is important both in theory and engineering.
Sinusoidal is non-causal signal. All of periodic signals are non-causal because they have no start and no end.
f (t) = f (t + mT) m=0, ±1, ±2, ···, ±
Typical signals and their representation
Exponential f(t) = eαt
α is real
α<0 decaying
α=0 constant
α0 growing
Typical signals and their representation
Exponential