[PDF] Design and analysis of FIR digital filter based on matlab

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Degree Project of Bachelor thesis

Design and analysis of FIR filters based on

Matlab

Author:

Su Peng

Date: 2013-05-28

Subject: Electrical Engineering

Level: Bachelor Level

Course code: 2ED14E

2 Design and analysis of FIR digital filter based on Matlab This thesis will deal with the effect of a digital filter based on Matlab. I will use window function, frequency sampling, and convex optimization method to design FIR filter, and also map out the figure of the characteristics of a filter. By using the filter, I will compare the time domain waveform and frequency spectrum before and after filtering sum of sinusoidal functions. 3

Acknowledgements

I have to thank for so many person who helped me with my thesis. Here, I want to thank my advisor Sven Nordebo, who is a very kind and patient teacher. He gives me some useful suggestions before I start to write my thesis. Next, I want to thank Tamim Sakhavat, a good vise advisor, he helped me a lot with the Matlab CVX code, and he is always ready to meet me and give me some easy-understanding lectures about CVX. Besides, I also want to thank my roommate Yiwen Yang, and she encouraged me a lot when I felt frustrated or blocked in some point during the process of my project. Of course, there are so many other friends giving me a hand in the period of writing my thesis, I have to thank all of them help me through this rough time. 4

Abstract

In digital control system, interference, which is mixed in the input signal, has a great influence on the performance of the system. Therefore, processing of input signal has to be done to get useful signal. Finite impulse response (FIR) filter plays an important role in the processing of digital signal. Designing the FIR filter by Matlab can simplify the complicated computation in simulation and improve the performance. By using the methods of window function, frequency sampling and convex optimization techniques, the design of FIR filter has been processed by Matlab. In the view of the designed program of Matlab and I can get the amplitude-frequency characterization. By using the FIR digital filters which have been designed to process the input signal based on the Matlab function, the filtering amplitude-frequency diagrams which have been generated. The experimental results show that the FIR filters designed in this paper are effective. Key words: FIR filter, Matlab, window function, frequency sampling, optimization, amplitude-frequency characterization. 5

1 The digital filter .......................................................................................................... 6

1.1 Introduction of digital filter .................................................................................. 6

1.2 FIR filter ............................................................................................................... 6

1.3 IIR filter ................................................................................................................ 7

1.4 Comparison of FIR and IIR .................................................................................. 7

2 Simulation of electronic communication system ........................................................ 8

2.1 The concept of telecommunications and electronic systems simulation .............. 8

2.2 Steps of computer simulation ............................................................................... 8

3 Brief introduction to Matlab ....................................................................................... 9

3.1 Matlab ................................................................................................................... 9

3.2 Advantages of Matlab .......................................................................................... 9

3.3 CVX ...................................................................................................................... 9

4 Design of FIR filter ................................................................................................... 10

4.1 Window function ................................................................................................ 11

4.2 Frequency sampling ........................................................................................... 12

4.3 Optimization ....................................................................................................... 12

5 The FIR filter design based on Matlab ..................................................................... 14

5.1 The realization of window function method by Matlab ..................................... 14

5.2 The realization of frequency sampling method by Matlab ................................. 20

5.3 The realization of Optimized Equiripple Method by Matlab ............................. 24

5.4 FIR filter with CVX ........................................................................................... 31

Reference ..................................................................................................................... 33

Appendix Matlab code for designing FIR filters ......................................................... 34

App. 1 Window function method ............................................................................. 34

App. 2 Frequency sampling method ......................................................................... 37

App. 3 optimized euiripple method .......................................................................... 39

App. 4 FIR filter with CVX ...................................................................................... 43

1 The digital filter

1.1 Introduction of digital filter

The digital filter is a discrete system, and it can do a series of mathematic processing to the input signal, and therefore obtain the desired information from the input signal. The transfer function for a linear, time-invariant, digital filter is usually expressed as

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