1. 5.Linear Time-Invariant System
5.1 The Frequency Response of LTI systems
5.2 System Functions for Systems Characterized by Linear
Constant-Coefficient Difference
5.3 Frequency Response for Rational System Functions
5.4 Relationship between Magnitude and Phase
5.5 All-Pass Systems
5.6 Minimum-Phase Systems
5.7 Linear Systems with Generalized Linear Phase
5.8 Summary
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2. 5.1 Frequency Response (e.q) Frequency selective filter - ideal
( : delay,centerpoint of sync function)
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3. Group dalay
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4. 5.2 System Functions for Constant Coefficient Systems
Stable if
Causal if Roc includes
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5. Inverse system, stable if all poles and zeros, inside the uc
minimum-phase system
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6. -FIR vs IIR
FIR part
IIR part
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7. 5.3 Frequency Response of Rational System Functions
(note) arg : continuous phase
ARG : its principal value in
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8. Check how they change as r and vary.
(example)
Check how they change as r and vary.
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9. 5.4 Relationship between Magnitude and PhaseF F
(complex cepstrum of x[n])
from Eqs. (11.28) and (11.29) (pp. 781)
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10. ※Relationship between real part and imaginary part of complex sequence (single-side band)
single-side band sequence
(complex sequence) F or
Hilbert Transform
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11. Illustration of decomposition of a one-sided Fourier transform
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12. Inverse Hilbert transform
xr[n]
xr[n]
x[n]
Hilbert transformer
xi[n]
impulse response of an ideal Hilbert transformer
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13. 5.5 Allpass System
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14. - 2nd order allpass function
- Nth order allpass function ( real-coeff)
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15. 5.6 Minimum phase System
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17. Sequences all having the same frequency response magnitude
( zeros are at all combinations of 0.9ej0.6 and 0.8ej0.8 and their reciprocals)
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18. since
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19. - Frequency response Compensation
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20. 5.7 Generalized Linear Phase System
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27. H.W. of Chapter 5 Ref : [1] Project 4.1 Transfer Function Analysis
Text : [2] 5.10    [3] 5.21   [4] 5.38   [5] 5.45
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