This course introduces basic theories of the followings: discrete time signals and system, linear time invariant system and convolution operation, application of Fourier transform to signal processing, sampling theorem, DFT and FFT, Laplace and z transforms, frequency characteristics, digital filters (FIR and IIR). It also enhances students' understanding through exercises for the acquisition of knowledge to understand digital signal processing. It further introduces the application of digital signal processing to show students the relationship between theory and practice explaining how digital signal processing techniques are utilized for real systems in the multimedia field.
【Course Objectives】 At the end of the course, participants are expected to understand signal processing systems that treat audio, image, and other sensor signals as digital data, and to acquire basic concepts of theory for designing the systems.
【Themes】 To understand basic theories of digital signal processing that plays essential roles in today's information processing and multimedia technologies, this course deals with such as handling of discrete time signals and systems in time and frequency domains, the theoretical framework of sampling theorem, and design, construction, and implementation of digital filters. In addition, this course also covers application examples of signal processing techniques for data transmission, audio data, and image data that are components of multimedia.
Discrete time signal, Discrete time system, LTI system, Impulse response, Frequency response, Sampling theorem, Discrete time Fourier transform, DFT, z-transform, Transfer function, Digital filter (FIR, IIR), 2D signal processing
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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The course provides lectures with handouts as well as exercises for deeper understanding.
Course schedule | Required learning | |
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Class 1 | Overview of signal processing | What are the applications of digital signal processing? |
Class 2 | Discrete time signals, discrete time systems | How are discrete time signals and discrete time systems expressed mathematically? Draw the shape of a discrete signal expressed by an equation. |
Class 3 | Fourier series expansion and Fourier transform | Why is Fourier transform important in signal processing? What is the relation between the convolution and Fourier transform? |
Class 4 | Sampling theorem, alias, and reconstruction | What is the condition for sampling signals without aliasing? Explain the method to reconstruct the continuous signal from the sampled discrete signal. What is "oversampling"? |
Class 5 | Discrete time Fourier transform (DTFT), Discrete Fourier Transform (DFT) | Explain the relation between the discrete time convolution and the DTFT. What is the difference between DTFT and DFT? |
Class 6 | Fast Fourier Transform (FFT) | Why is the amount of computation reduced in FFT? Explain how to apply FFT to practical discrete signals. |
Class 7 | Laplace transform and z transform | What are the meanings of poles and zeros? Explain the method for calculating z-transform and inverse z-transform. |
Class 8 | Transfer function and frequency response of linear time-invariant systems | Calculate the transfer function from a difference equation, and draw the shape of the frequency response. |
Class 9 | Stability of linear time-invariant systems | Judge the stability of a system using a difference equation. |
Class 10 | Digital filters (FIR) | Illustrate the block diagram of an FIR filter given by a difference equation. Explain the method to design an FIR digital filter from desired frequency response. |
Class 11 | Digital filters (IIR) | Illustrate the block diagram of an IIR filter given by a difference equation. How do you design an IIR digital filter from a prototype analog filter? |
Class 12 | Change of sampling rate (up-sampling and down-sampling) | Explain the methods for down-sampling and up-sampling. What is "filter bank"? |
Class 13 | Adaptive signal processing | Explain how to estimate the characteristics of an unknown LTI system. In what case is an adaptive filter effective? |
Class 14 | Two-dimensional system (Image signals) | What is "spatial frequency"? Explain the meaning of 2D frequency domain obtained by 2D Fourier transform. Describe a method to enhance edges in an image using 2D digital filtering. |
Class 15 | Orthogonal transformation and image compression | What are the differences between the discrete cosine transform and DFT? Explain the schematic structure of JPEG image compression. |
"Basics of digital signal processing systems" by Eiji Watanabe, MORIKITA PUBLISHING CO., Ltd, written in Japanese.
"Well understandable signal processing" by Nozomu Hamada, Ohmsha Ltd, written in Japanese.
"Basics of digital signal processing" edited by IEICE, editorial supervised by Shigeo Tsujii, written in Japanese.
The levels of attainment of student learning outcomes are evaluated by exercises and a mid-term exam (20%) and a final exam (80%).
It is recommended for students to have completed ICT.S206 "Signal and System Analysis" or have equivalent knowledge.
Masahiro Yamaguchi, E-mail: yamaguchi.m.aa[at]m.titech.ac.jp
Natsue Yoshimura, E-mail: yoshimura[at]pi.titech.ac.jp
Masahiro Yamaguchi, Natsue Yoshimura: Contact by e-mail in advance.