[PDF] Design of FIR Low-pass Filter Based on MATLAB





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Use MATLAB to create three magnitude Bode plots for the high pass filter For the first and second plots use the transfer function of the circuit with the nominal and measured values from Table F respectively and a frequency range of 10? rad/s ? ? ? 20000? rad/s For the third plot use the empirical data generated by the Bode plot VI

What is a low-pass filter in MATLAB?

  • Low-Pass Filter Design low-pass filters using MATLAB A low-pass filter is a filter that allows signals below a cutoff frequency (known as the passband) and attenuates signals above the cutoff frequency (known as the stopband).

What is a high-pass filter?

  • High-pass filter? ?? ???? ??? ????, ??? ???? ?? ???? ????, ??? ????? ???? ??? ??? ???? ????, ??? ????? ???? ??? ?????? ???? ??? ???? ? ?????. ?? ??? high-pass filtering.

How to design a filter in MATLAB?

  • In practical life, we use LRC circuits to design these filters. In MATLAB, we can design them in different ways. We can see the response of any filter by designing an LRC circuit in MATLAB Simulink, or we can just give a signal to a built-in filter in Simulink and use the scope to see it.

How do I know if a signal is filtered in MATLAB?

  • The waveforms show the filtration clearly but we can also listen to the music to get the difference. To listen to the music in Matlab, we execute the sound command sound (xn, fs) for the noisy signal in the command window. We also do the same for the filtered signal sound (y, Fs).

Design of FIR Low-pass Filter Based on MATLAB

Weiwei Tian

a, Zixuan Ni b, *

Lanzhou University, Lanzhou 730107, China;

a weiweitian96@163.com, bnzx18069832761@163.com

Corresponding author: Zixuan Ni

Keywords: MATLAB, FIR, low-pass filter, audio processing. Abstract. With the rapid development of the global electronic market, the filter has been greatly promoted. And the development of digital technology also create a good technical foundation for the

filter. This paper introduces the basic concepts of digital filters, the brief introduction of MATLAB

Software, and the design method of FIR low-pass filter. Taking MATLAB as working platform and

development tools, the design and simulation of FIR low-pass filter are realized by MATLAB

program. And the practicability of low-pass filter for audio processing is proved by tests.

1. Introduction

Digital signal processing technology has entered the mature stage at present. In the process of

digital signal processing, digital filtering is a very important part. The digital filtering converts the

digital signal through some arithmetic logic, and eliminates some frequencies or improves the relative

occupancy ratio of some frequencies at the same time, so as to eliminate the interference frequency [1].

Compared with traditional filtering, digital filter has great advantages both in stability and flexibility.

Therefore, the comprehensive analysis of digital filters is of great significance for the promotion and

application of digital signal technology. In this paper, FIR low-pass filter designed by MATLAB

software is used to realize low-pass filtering of audio files and the high frequency is filtered to get the

bass part finally.

2. Overview of Digital Filter

Digital filter is an algorithm or device made up of digital multiplier, adder and delay unit. The

function of digital filter is to handle digital code of the discrete signal input, in order to change the

signal spectrum. There are many kinds of filters. Functionally, filters can be divided into low pass,

high pass, band stop, and band pass. In terms of the unit impulse response, the digital filter can be

divided into finite impulse response filter and infinite impulse response filter. In the process of using

the filter, it is necessary to make a comprehensive analysis of the two filters before deciding what kind

of filters to use. In general, the FIR filter achieves the goal of filtering through the superposition

algorithm, so there is no ready-made formula for it to use in the design process. And the IIR filter can

complete the design work only through the analog filter design parameters, but in the flexibility, the

IIR filter has the obvious inferiority compared with the FIR filter.

3. Brief Introduction of MATLAB Software

MATLAB language is an engineering application software which can integrate scientific computing, data visualization and program design. It has become the essential basic software for the

subject of computer to have aided engineering analysis, design, simulation as well as teaching, which

is composed of MATLAB main package, simulink module and toolbox with various functions [2]. MATLAB has efficient numerical computation and symbolic computation function which can relieve users from mathematical analysis in complex. And it has a complete graphics processing function

which can realize the visualization results and programming. Its rich function (such as signal 2nd International Conference on Computer Engineering, Information Science & Application Technology (ICCIA 2017)Copyright © 2017, the Authors. Published by Atlantis Press.

This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Advances in Computer Science Research, volume 74460

processing toolbox, communication toolbox, etc.), provides a number of convenient and practical tools

for users.

4. Design of The FIR low-pass Filter

4.1 The Design Method of FIR Low-pass Filter

Usually MATLAB is used to design and simulate the FIR filter coefficients, the usual way is optimization design, FDA TOOL design and window function design [3]. For the method of optimization design, Park-Mc-Clellan algorithm can be used to design linear phase FIR filter which makes the maximal error between actual frequency response and the expected response frequency

minimum, but this design method cannot directly set the filter resistance band attenuation parameter.

FDA Tool (filter design & analysis tool) is a tool specifically for the design and analysis of filter in the

MATLAB toolbox which provides an interactive design environment for the entire process. Users design almost all types of filters by setting amplitudes and zeros and poles, including type, order, frequency and other parameters. The window function method is to set the unit impulse response sequence h(n) by adding a window according to the given frequency response feature. The window functions commonly used in the project include rectangular Windows, hanning Windows, hamming Windows, cassett Windows, blackman Windows and bartlett Windows and so on. The function commands based on fir1 and fir2 can easily get the filter coefficients.

4.2 Design and analysis of FIR low-pass filter based on MATLAB

The fast algorithm of FFT discrete Fourier transform in MATLAB can transform a signal into the frequency domain. After FFT, N sample points can get the FFT results of N points. In order to

facilitate FFT operations, N usually takes integer power of 2. Assuming that the sampling frequency is

sF, the signal frequency F and the sampling point is N, so the result of FFT is a complex number of

N points. Each point corresponds to a frequency point. The module value of this point is the amplitude

characteristic of the frequency. For example, the frequency of a point n is: NFnFs n)1(. If the sampling frequency is 1024Hz, the sampling point is 1024, then it can be identified by 1Hz. In other words, sampling the signal for a second time and conducting FFT, the result can be analyzed to 1Hz

and if the sample is sampled for two seconds and the conducting FFT, the result can be analyzed to 0.5

Hz. If you want to increase the frequency resolution, you have to increase the number of samples, which is the sampling time. Frequency resolution and sampling time are reciprocal. The most common FIR implementation architecture is called the direct-form FIR [4]. Low-pass filter is to take low-frequency component out and abandon the high frequency part of the

digital signal, and the band-pass filter is take digital signal in a certain range of frequencies. So the

band-pass filter after the translation is a low-pass filter. The structure of the low-pass filter is shown in

figure 1.

Figure. 1 Structure of the low-pass filter

Its function expression is: )()()(0ccffUffUfh (1)

And the low-pass filter is shifted by the band-pass filter. Its function expression is: )()()()()(1111fffUfffUfffUfffUfhcccc (2)

Advances in Computer Science Research, volume 74461 The Discrete Fourier Transform of the input digital signal is:

NnnfjenxfX2)()( (3)

The Fourier transform of the output signal is:

NnccccnfjfffUfffUfffUfffUenxfHfXfY)]()()()([)()()()(11112 (4) Take the inverse Fourier Transform and we can get output signal: Nnc ntfntfntnxny)())(2cos())(2sin()(2)(1 (5)

This is the output of the pass-through filter.

4.3 The filtering effect of audio signal

Because

cf and

1f are normalized, the period of frequency is 1, so when the frequency is greater

than 0.5, it is a high frequency component, whereas less than 0.5 is the low frequency part. For a low-pass filter, the sum of cf and

1f is less than 0.5. Taking a signal, the sample frequency of which

is 11400hz. First, the spectrum and digital signal of the experiment audio are obtained which were shown in figure 2.

Figure. 2 The digital signal and its spectrum

Then obtained the following results after pass the designed low-pass filter in figure 3 and figure 4.

The analysis of the audio shows that the lower part of the audio is retained and higher part is removed

through the low-pass filter. cf is 1109/88200Hz, 1f is 1091/88200Hz) Figure. 3 Audio data Figure. 4 Spectrum And then obtained the following results after pass the designed band-pass filter in figure 5 and

figure 6. The analysis of the audio shows that the audio becomes thinner and deeper than before, as the

audio through the band-pass filter loses a portion of the frequency. cf is 1109/88200Hz, 1f is 10091/88200Hz) Advances in Computer Science Research, volume 74462 Figure. 5 Audio data Figure. 6 Spectrum

5. Conclusion

MATLAB is a large and powerful software that is suitable for multi-disciplinary, multi-working

platform. It has many functions include mathematical statistics, digital signal processing, time series

analysis, dynamic system simulation and so on. In this paper, the low-pass filter designed by

MATLAB can be used for signal selection. It can be used to select the signal according to the frequency, to avoid interference of high-frequency signals, and it also can be used in instruments, acoustics, signal processing and other circuits.

References

[1]. Xuran LI. Design of FIR Low Pass Filter Based on Matlab. Computer Knowledge and

Technology. Vol. 10 (2014) No. 36, p. 8806-8807.

[2]. Sul Seung Ki, Kim.Jang Hwan, Choi. Jong Woo. Novel Rotor-Flux observer using observer characteristic function in Complex vector space for field-oriented induction motor drives. IEEE

Trans I. A. vol.38(2002), pp.1334-1343.

[3]. ZHANG Bo, PEI Dongxing. Design of FIR Low- pass Filter Based on DSP Technology. Audio

Engineering. Vol. 38 (2014) No. 9, p. 33-35.

[4]. Fred J. Taylor.Digital Filters: Principles And Applications With Matlab.IEEE Press,2011, p.

131-133.

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