信号与系统奥本海姆原版PPT第六章

6 Time and frequency characterization of S&S
6 Time and frequency characterization of S&S
6 Time and frequency characterization of S&S
Problems: 6.5
6.23
F x(t ) X ( j )
X ( j ) | X ( j ) | e jX ( j )
| X ( j ) | Magnitude Spectrum e jX ( j ) Phase Spectrum
6 Time aБайду номын сангаасd frequency characterization of S&S
6 Time and frequency characterization of S&S
6 Time and frequency characterization of S&S
6.3 Time-Domain Properties of Ideal Frequencyselective Filters Lowpass filter: (1) Continous time:
6 Time and frequency characterization of S&S
6. Time and Frequency Characterization of Signals and Systems 6.1 The Magnitude-phase Representation of the Fourier Transform For signal x(t) :
6 Time and frequency characterization of S&S
6.2.2 Group Delay
d Definition: ( ) H ( j ) d Example: y (t ) x(t t0 )
H ( j ) e jt0 H ( j ) t0
6 Time and frequency characterization of S&S
6.4 Time-Domain and Frequency-domain Aspects of Non-ideal Filters Basic parameter of lowpass filter:
6 Time and frequency characterization of S&S
6 Time and frequency characterization of S&S
6 Time and frequency characterization of S&S
6 Time and frequency characterization of S&S
6 Time and frequency characterization of S&S
Effect: Linear phase means non-distortion of signal transmission.
6 Time and frequency characterization of S&S
( Linear phase )
( Original signal )
( Nonlinear phase )
1, | | c sin c t F H ( j ) h(t ) t 0, | | c
(2) Discrete time:
1, | | c sin c n F H ( j ) h[n] 0 , | | c n
6.2.3 Log-Magnitude and Bod Plots
Magnitude spectrum:
| H ( j ) | ~ 20 log 10 | H ( j ) | ~ log 10 ( Bod plots)
Phase spectrum:
H ( j ) ~ H ( j ) ~ log 10 ( Bod plots)
x(t ) 1 1 2 cos( 2t 1 ) cos( 2t 2 ) cos( 2t 3 ) 2 3
1 2 3 0
1 4, 2 8, 3 12
1 6, 2 2 .7, 3 0.93
1 1.2, 2 4.1, 3 7.2
6.27
( ) t0
( signal delay )
Distortionless system: ( ) is flat.
6 Time and frequency characterization of S&S
6 Time and frequency characterization of S&S
6 Time and frequency characterization of S&S
| P( j1 , j 2 ) |
P( j1 , j 2 )
6 Time and frequency characterization of S&S
Magnitude : | P( j1 , j 2 ) | Phase : 0
H ( j ) | H ( j ) | e jH ( j )
| H ( j ) | Magnitude Response e jH ( j ) Phase Response
6 Time and frequency characterization of S&S
6.2.1 Linear and Nonlinear Phase
Linear phase:
H ( j ) k
Nonlinear phase: H ( j ) Nonlinear function
Example: y (t ) x(t t0 )
H ( j ) e jt0 H ( j ) t0 ( Linear phase)
6.2 The Magnitude-phase Representation of the Frequency Response of LTI System System characterization: Impulse response: Frequency response:
F h(t ) H ( j ) Y ( j ) H ( j ) X ( j )
Magnitude : 1 Phase : P( j1 , j 2 )
6 Time and frequency characterization of S&S
Magnitude : Phase : P( j1 , j 2 )
6 Time and frequency characterization of S&S