Signals and Linear Systems Flipped Class Notes 16 - Various Responses of Discrete LTI Systems
The Flipped Classroom16 of Signals and Linear Systems
Corresponding textbook: "Signal and Linear System Analysis (Fifth Edition)" Higher Education Press, written by Wu Dazheng
1. Key points
(1, focus) The concept of the unit sequence response (unit response) of the discrete LTI system, and master the use of time domain methods to find the unit sequence response;
(2) Understand the step response and its relationship with the unit sequence response;
(3, focus) The relationship between the zero-state response of the discrete LTI system, the unit sequence response and the system excitation (convolution sum);
(4, focus) calculation of the convolution sum;
(5) properties of the convolution sum;
(6) using convolution and find the zero-state response of the system.
2. Questions and Answers
(*1) What is the unit sequence response h(k) of the discrete LTI system? What is the relationship between discrete system excitation, unit sequence response, and zero-state response? Briefly describe the derivation of this relationship in the textbook (textbook formulas 3.3-1, 3.3-2, 3.3-3), and explain the properties of the system used in the derivation.
(2) Solve Problem 3.10 (a).
(*3) Solve exercises 3.11 (1), (2), (3) and summarize the convolution sum of two finite-length sequences. How to determine the non-zero interval of the convolution sum.
(4) It is known that a certain signal f(k)=(1-0.5^(k-1))ε(k-1), how to express it in the form of (...)ε(k)? (Hint: ε(k-1)=ε(k)-δ(k))
(*5) How to define the step response g(k) of the discrete LTI system? What is the relationship between the step response and the unit sequence response of a discrete system (hint: δ(k)=ε(k)-ε(k-1))? Based on this relationship, solve Exercise 3.15.
(*6) Solving exercise 3.22, summary: a composite discrete LTI system composed of multiple subsystems, the relationship between the unit sequence response of the composite system and the unit sequence response of each subsystem.
1. Excitation, unit response and zero-state response of discrete LTI system
What is the unit sequence response h(k) of a discrete LTI system? What is the relationship between discrete system excitation, unit sequence response, and zero-state response? Briefly describe the derivation of this relationship in the textbook (textbook formulas 3.3-1, 3.3-2, 3.3-3), and explain the properties of the system used in the derivation.
①The unit sequence response refers to the zero-state response of the system when the excitation of the LTI system is the unit sequence △(k).
② Zero-state response = excitation * system unit sequence response
③
Properties: homogeneity of linear systems, shift invariance of time-invariant systems, and zero-state linear properties of systems.
2. Find the system unit response from the system block diagram
Solve Problem 3.10 (a).
3. Finite length sequence convolution sum
Solving exercises 3.11 (1), (2), (3), summarize the convolution sum of two finite length sequences, and how to determine the non-zero interval of the convolution sum.
Summary: If the non-zero intervals of f_1 (k) and f_2 (k) are [a,b],[c,d] respectively, then the non-zero interval of f_1 (k)*f_2 (k) is [a+c,b+ d]
4. Calculation involving ε(k-1)
It is known that a certain signal f(k)=(1-0.5^(k-1))ε(k-1), how to express it in the form of (...)ε(k)? (Hint: ε(k-1)=ε(k)-δ(k))
5. Step response of discrete LTI system
How to define the step response g(k) of the discrete LTI system? What is the relationship between the step response and the unit sequence response of a discrete system (hint: δ(k)=ε(k)-ε(k-1))? Based on this relationship, solve Exercise 3.15.
6. Unit sequence response of composite system
Solving exercise 3.22, summary: a composite discrete LTI system composed of multiple subsystems, the relationship between the unit sequence response of the composite system and the unit sequence response of each subsystem.
3. Reflection and Summary
None yet