This experiment deals with the analysis of analog filter, the design of digital filter, and the frequency analysis.
Students implement the programs of convolution, spectrum analysis, and sampling, and apply them to practical digital signals for enhancing the understanding of these subjects. Next, the Gibbs phenomenon and the effect of window function are observed. FIR and IIR filters are designed and applied to some signals such as acoustic signals to confirm the effect of those digital filters. The transfer function of an analog filter is analyzed and a digital filter is designed according to the analyzed transfer function. Finally, through programming of the multirate signal processing, students will learn the examples of its applications.
The aim of this experiment is to achieve deeper understanding of digital signal processing through programming the algorithm and implementing some application examples by using MATLAB.
Discrete signal, linear system, convolution, Fourier transform, DFT, FFT, window function, FIR filter, IIR filter, bilinear transform method, impulse invariant method, downsampling and upsampling
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
Through MATLAB programming on the subjects from Part 1 to 5, and applying the programs to artificial and acoustic data, students acquire deeper understanding by considering the meaning of the results. While it is assumed that students concurrently attend ICT.S210 Digital Signal Processing, the experiment will be carried out independently upon the lecture. If there are any questions, consult either the instructor or TA to solve them. It is recommended to read the reference book for better comprehension of the experiment.
|Course schedule||Required learning|
|Class 1||Part 1 Introduction of signal processing (1) Representation of signal and system||Plot discrete-time signals.|
|Class 2||Part 1 Introduction of signal processing (2) Convolution and Fourier transform||Observe the results of the convolution of two signals.|
|Class 3||Part 1 Introduction of signal processing (3) Spectrum analysis of discrete time signal||Observe the plots of amplitude, phase, and power spectrum of a signal.|
|Class 4||Part 1 Introduction of signal processing (4) Sampling of signal and reconstruction||Generate the simulated continuous-time signal and apply sampling. Observe the aliasing effect in frequency domain.|
|Class 5||Part 2 Mastering FFT (1) Spectrum analysis using DFT||With correct understanding of the meaning of frequency, show the graphs of the DFT results.|
|Class 6||Part 2 Mastering FFT (2) Implementation of convolution using FFT||Implement convolution using FFT. Discuss the method to obtain the same results as linear convolution.|
|Class 7||Part 3 FIR filter (1) Examining the linear phase characteristics||Construct FIR filter from given parameters, and show the filtering results. Observe the graph of frequency response of the filter.|
|Class 8||Part 3 FIR filter (2) Ideal low-pass filter||Design and apply an FIR LPF. Observe the Gibbs phenomenon.|
|Class 9||Part 3 FIR filter (3) FIR filter design by window function method||Design LPF using a Hamming window function.|
|Class 10||Part 4 IIR filter (1) Analysis of analog filter||Design the Butterworth filter with given specifications.|
|Class 11||Part 4 IIR filter (2) IIR filter design, frequency conversion, and BIBO stability||Design an IIR filter by bilinear transform method and impulse invariant method. Design various LPF, BPF, and HPF using the frequency conversion method.|
|Class 12||Part 5 Multi-dimensional and multi-rate signal processing (1) Image processing||Apply 2D FFT to a 2D signal, and show the result. Implement the Sobel filter and apply it to an image.|
|Class 13||Part 5 Multi-dimensional and multi-rate signal processing (2) Downsampling and upsampling||Design the LPF to eliminate aliasing and imaging that occur when down- and up-sampling a signal.|
|Class 14||Part 5 Multi-dimensional and multi-rate signal processing (3) Conversion of sampling rate||Investigate the relationship between the file size, sound quality and sampling rate in various acoustic signals.|
To enhance effective learning, students are encouraged to spend a certain length of time outside of class on preparation and review (including for assignments), as specified by the Tokyo Institute of Technology Rules on Undergraduate Learning (東京工業大学学修規程) and the Tokyo Institute of Technology Rules on Graduate Learning (東京工業大学大学院学修規程), for each class.
They should do so by referring to textbooks and other course material.
Download the course materials through OCW-i.
Grading will be decided based on the understanding level of the contents from part 1 to 5 by submitted reports.
It is desirable that students concurrently attend ICT.S210 Digital Signal Processing.
Masahiro Yamaguchi, E-mail: yamaguchi.m.aa[at]m.titech.ac.jp
Takahiro Shinozaki, E-mail: shinot[at]ip.titech.ac.jp
Tomoya Nakamura, E-mail: nakamura.t.bj[at]m.titech.ac.jp
Contact by e-mail in advance.