Transcript Signal and System - Universitas Udayana

PSD, Signal and System
SIGNAL AND SYSTEM
Sub-topics:
 Signal and System
 Signal Classification
 The Frequency Concept in Continuous-Time and
Discrete-Time Signals
 Introduction to ADC and DAC
1/15
PSD, Signal and System
Signals and System
• Signal: any physical quantity that varies with
time, space, or any other independent variable
or variables
– e.g. ECG, EEG
• System: a physical device that performs an
operation on a signal
• Signal Processing: the processing of the signal
involves filtering the noise and interference from
the desired signal
2/15
PSD, Signal and System
3/15
PSD, Signal and System
Person is resting
Radar Signal
4/15
PSD, Signal and System
Analog
Input
Signal
Analog
Signal
Processor
Analog
Output
Signal
Analysis
Filtering
Extracting
Changing its characteristics
…
5/15
PSD, Signal and System
Digital
output
signal
Digital
Input
signal
Analog
Input
Signal
A/D
Converter
Analog
Signal
Processor
D/A
Converter
Analog
Output
Signal
Programmable computer
Microprocessor
DSP chip
…
6/15
PSD, Signal and System
Classification of Signals
 Multichannel and Multidimensional Signals
 Continuous-Time vs Discrete-Time Signals
 Continuous-Valued vs Discrete-Valued
Signals
 Deterministic vs Random Signals
7/15
PSD, Signal and System
• Multi-channel Signal
• Signals are generated by multiple sources or
multiple sensors
• Multidimensional Signal
• Signal is a function of multiple independent
variables
Earthquake Signals
 s1 ( t )
 s ( t )
 2 
. 
S ( t )  
. 


 . 
 s n ( t )
 I r ( x , y ,t ) 


I ( x , y ,t )   I g ( x , y ,t )
 I ( x , y ,t ) 
 b

8/15
PSD, Signal and System
• Continuous-Time Signal or Analog Signal
• A signal as a function of a continuous variable (time)
• Discrete-Time Signal
• A signal as a function of a discrete variable (time)
9/15
PSD, Signal and System
• Continuous-Valued Signal
• If a signal takes on all possible values on a finite or an infinite
range
• Discrete-Valued Signals
• If the signal takes on values from a finite set of possible
values
• Digital Signal
• A discrete-time signal having a set of discrete-value
10/15
PSD, Signal and System
• Deterministic Signal
• Any signal can be described by an explicit
mathematical expression, a table of data, or a welldefined rule
• To emphasize the fact that all past, present, and
future values of the signal are known precisely
– E.g. Sinusoidal signal
• Random Signal
• Signals that either cannot be described to any
reasonable degree of accuracy by explicit
mathematical formulas
• Signals evolve in time in an unpredictable manner
– E.g. seismic signals, speech signals, etc.
11/15
PSD, Signal and System
The Frequency Concept in Signals
•
•
•
•
Continuous-Time Sinusoidal Signals
Discrete-Time Sinusoidal Signals
Continuous-Time Exponential Signals
Discrete-Time Exponential Signals
12/15
PSD, Signal and System
• Continuous-Time Sinusoidal Signals
• Xa(t)=A cos(Ωt + θ); -∞<t<∞
– A=amplitude
– Ω=frequency (rad/s), θ = phasa (rad)
• Relationship between F (frequency Hz) and Ω (frequency
rad/s) is Ω = 2 πF
• The analog sinusoidal signal is characterized by
the following properties:
• For every fixed value of the frequency F, xa(t) is periodic
xa(t + Tp) = xa(t); Tp = 1/F is the fundamental period of the
sinusoidal signal
• Continuous-time sinusoidal signals which distinct freq. are
themselves distinct
• Increasing the freq. F results in an increase in the rate of
oscillation of the signal, in the sense that more periods are
included in a given time interval
13/15
PSD, Signal and System
• Discrete-Time Sinusoidal Signals
• x(n)=A cos(n + θ); -∞<n<∞
•  = 2f
–
–
–
–
–
n=integer variable
A=amplitude of the sinusoid
=frequency (rad/sample)
θ=phasa (radian)
f=frequency (Cycle/sample or Hz)
• x(n)=A cos(2fn + θ); -∞<n<∞
• The properties:
• A discrete-time sinusoid is periodic only if its freq. f is a
rational number
• Discrete-time sinusoids whose freq. are separated by an
integer multiple of 2 are identical
• The Highest rate of oscillation in a discrete-time sinusoid is
attained when  =  (or  = -) or equivalently, f = ½ (or f = 14/15
½)
PSD, Signal and System
• Continuous-Time Exponentials
• sk(t) = ejkΩ0t = ej2πkF0t; k = 0, ±1, ±2
• Discrete-Time Exponentials
• Sk+N(n) = ej2πn(k+N)/N = ej2πnsk(n) = sk(n)
15/15