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 BGL/SNU

5.1 Frequency Response (e.q) Frequency selective filter - ideal ( : delay,centerpoint of sync function) BGL/SNU

Group dalay BGL/SNU

5.2 System Functions for Constant Coefficient Systems Stable if Causal if Roc includes BGL/SNU

Inverse system, stable if all poles and zeros, inside the uc minimum-phase system BGL/SNU

-FIR vs IIR FIR part IIR part BGL/SNU

5.3 Frequency Response of Rational System Functions (note) arg : continuous phase ARG : its principal value in BGL/SNU

Check how they change as r and vary. (example) Check how they change as r and vary. BGL/SNU

5.4 Relationship between Magnitude and Phase F F (complex cepstrum of x[n]) from Eqs. (11.28) and (11.29) (pp. 781) BGL/SNU

※Relationship between real part and imaginary part of complex sequence (single-side band) single-side band sequence (complex sequence) F or Hilbert Transform BGL/SNU

Illustration of decomposition of a one-sided Fourier transform BGL/SNU

Inverse Hilbert transform xr[n] xr[n] x[n] Hilbert transformer xi[n] impulse response of an ideal Hilbert transformer BGL/SNU

5.5 Allpass System BGL/SNU

- 2nd order allpass function - Nth order allpass function ( real-coeff) BGL/SNU

5.6 Minimum phase System BGL/SNU

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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) BGL/SNU

since BGL/SNU

- Frequency response Compensation BGL/SNU

5.7 Generalized Linear Phase System BGL/SNU

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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 BGL/SNU