2023 Discrete-Time System

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Academic unit or major
Undergraduate major in Electrical and Electronic Engineering
Kurosawa Minoru 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
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Course description and aims

In discrete time system such as digital signal processing, z-transform is essensial to understand a system behavior and analysis; same as contenious system's Laplace transform. The z-transform is widely apply to the linear time invarient systems. The lecture topics are, discrete time signal and systems, z-transforme and inverse z-transform, z-transforme property, transmission function and frequency response, FIR and IIR filters, s-z transform and system stability.

The aim of this course is to understand z-transform to analize time discrete systems. In linear time invarient systems, time domain and frequency domain basic comprehension will be accomplished.

Student learning outcomes

This course will give students understanding time domain and frequency domain responses of time discrete systems. For analytical method, z-transform is essential and basic mathematics.


differential equation, linear time invarient system, convolution, z-transform, inverse z-transform, transmission function, frequency response, FIR filter, IIR filter, s-z transform, digital filter, digital signal processing, system stability

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills
・Fundamental specialist skills on EEE

Class flow

At the beginning of each class, solutions to exercise problems that were assigned during the previous class are reviewed. Towards the end of class, students are given exercise problems related to the lecture given that day to solve. To prepare for class, students should read the course schedule section and check what topics will be covered. Required learning should be completed outside of the classroom for preparation and review purposes.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Discrete time system - Mathmatical description of discrete time signal and systems. Differential equation for discretetime systems
Class 2 Discrete time signal and response - Impulse response, linear time invarient system and convolusion Linear time invarient system and output signal by convolusion
Class 3 z-transform and invers z-transform - Linear, time shift and convolution in time domain Function of z-transform and invers z-transform
Class 4 Transmission function and frequency response - impulse response,differencial equation and transform function, frequency response Output signal obtained form transmission function and frequency response
Class 5 Transmission function of FIR circuit and IIR circuit - first and second low pass, high pass, band pass and band discrimination Circuit stracture and transmission function
Class 6 Filater circuit and response - FIR filter design and linear phase response FIR filter design
Class 7 s-z transform and filter design - Butterworse response, impulse invariance method, bilinear transform Stability of discrete time system - stable condition, zero poinl and pole IIR filter design using s-z transform stable pole placement in z-plain

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


Ohta, Masaya. Introduction to Digital Signal Processing. Tokyo: Corona Publishing; ISBNISBN978-4-339-00857-9. (Japanese)

Reference books, course materials, etc.

Oishi, Kunio. Introduction to Digital Signal Processing with C Programming Language. Tokyo: Corona Publishing; ISBN978-4-339-00847-0. (Japanese)
Higuchi, Kawamata. Digital Signal Processing (2nd ed.). Tokyo: Morikita Publishing; ISBN978-4-627-79212-8. (Japanese)

Assessment criteria and methods

Students' knowledge of difference equation for discrete time system, z-transform and their ability to apply them to problems will be assessed. Final exams 90%, exercise problems 10% will be standard for evaluation.

Related courses

  • EEE.M211 : Fourier Transform and Laplace Transform
  • EEE.C311 : Advanced Electronic Circuits
  • EEE.C321 : Digital Electronic Circuits

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed Fourie Transform and Laplace Transform (EEE.M211) or have equivalent knowledge.

Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

Minoru Kuribayashi Kurosawa, mkur[at]ee.e.titech.ac.jp, 045-924-5598

Office hours

Contact by e-mail in advance to schedule an appointment.

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