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 analyized and a digital filter is desinged 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 achieve deeper understanding of digital signal processing through programing the algorithm and implementing some application examples by using MATLAB.
Dicrete signal, linear system, convolution, Fourier transform, DFT, FFT, window function, FIR filter, IIR filter, bilinear transform method, impulse imvariant 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.
|Course schedule||Required learning|
|Class 1||Part 1 Introduction of signal processing (1) Representation of signal and system||Generate various digital signals and plot their graphs as discrete time signals.|
|Class 2||Part 1 Introduction of signal processing (2) Convolution and Fourier transform||Observe the results of convolution, Fourier transform of convolution, Fourier transform of two signals.|
|Class 3||Part 1 Introduction of signal processing (3) Spectrum analysis of discrete time signal||Derive the Fourier transforms of various signals and observe the plots of their amplitudes and phases.|
|Class 4||Part 1 Introduction of signal processing (4) Sampling of signal and reconstruction||Generate the simulated continuous time signal and apply sampling. Then reconstruct the original signal from the sampled signal. Observe the aliasing effect in time domain and frequency domain.|
|Class 5||Part 2 Mastering FFT (1) Spectrum analysis using DFT||With correct understanding 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||Apply ideal LPF using FFT. Design and apply an FIR LPF. Observe Gibbs phenomenon.|
|Class 9||Part 3 FIR filter (3) FIR filter design by window function method||Design LPF, BPF and HPF using hamming window function and apply them to real digital signal.|
|Class 10||Part 4 IIR filter (1) Analysis of analog filter||Derive frequency response of an analog filter using Laplace transform. Derive the parameters the Butterworth filter.|
|Class 11||Part 4 IIR filter (2) Bilinear transform method and impulse invariant method||Design 2nd-order Butterworth digital filter and Chebyshev digital filter using bilinear transform and window function methods.|
|Class 12||Part 4 IIR filter (3) Frequency conversion||Design various LPF, BPF, and HPF using frequency conversion method and apply them to various signals.|
|Class 13||Part 4 IIR filter (4) Examining BIBO stability||Verify the stability of IIR filters. Apply various digital filters to acoustic signals and compare the results.|
|Class 14||Part 5 Multirate signal processing (1) Downsampling and upsampling||Confirm the difference of output signals with different interpolation functions in upsampling.|
|Class 15||Part 5 Multirate signal processing (2) Conversion of sampling rate||Investigate the relation between the file size / sound quality and sampling rate in various acoustic signals.|
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 assumed 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
Shunsuke Ono, E-mail: ono[at]isl.titech.ac.jp
Tomoya Nakamura, E-mail: nakamura.t.bj[at]m.titech.ac.jp
Contact by e-mail in advance.