Modeling and Simulation of Digital Filter Jie Zhao

Transcription

1 4th National Conference on Electrical, Electronic and Comuter Engineering (NCEECE 05) Modeling and Simulation of Digital Filter Jie Zhao School of Electronic Information and Electrical Engineering, Shangluo Univerity, Shangluo, 76000, China Keyword: Digital Signal Proceing; Digital Filter, Simulation. Abtract. Digital filter i a baic algorithm to eech, image roceing, attern recognition, ectrum analyi and o on. It lay a very imortant role in digital ignal roceing. At reent, many deigner ue oftware tool uch a Matlab to model and imulate the digital filter. Thi aer decribed the deign and imulating roce of a FIR low a filter. The Equivalent rile aroximation algorithm i ued for the deign. Intead of uing code in command or m-file, the FDA tool and Simulink are adoted to comlete the tet ytem. Filtering roceing for teted ignal how that the deign method i convenient for engineering and education. Introduction Digital filter i now becoming an imort engineering and education ubject. Digital filter are a very imortant art of digital ignal roceing []. In fact, their extraordinary erformance i one of the main reaon that DSP ha become o oular. Digital filter are ued for two general uroe: earation of ignal that have been combined, and retoration of ignal that have been ditorted in ome way. Analog filter can be ued for the ame uroe; however, digital filter can achieve far uerior reult. The digital filter are uually divided into two tye: IIR and FIR []. The FIR filter i widely ued ince it ha the advantage of enure linear hae, and i eaily to imlement [3]. Preently, the cloe aroximation to ideal frequency reone characteritic i what mot method trive for. The common deign method of FIR digital filter i mainly baed on the window function, the frequency amling and Equivalent rile aroximation (Remez exchange algorithm). Thee method can be imlemented by virtue of Matlab. The traditional method wa uing the inut command in the command window of Matlab [4]. In the coure of digital ignal roceing, the theory and concluion are motly derived from the mathematical derivation, the more abtract and difficult to undertand. In the coure of digital ignal roceing, the theory and concluion are motly derived from the mathematical derivation, the more abtract and difficult to undertand. The exerimental teaching i commonly ued the MATLAB oftware. The roceing rocedure can take advantage of the FDA Tool and Simulink of Matlab. Thi method i more direct and convenient and i effectively for teaching and engineering. The DSP Builder comonent i convenient to realize the traditional imulation, and it alo can generate HDL code [5]. It ha been ued in the coure teaching. Equivalent Rile Aroximation According to the window function and the frequency amling method, the aroximation error in the whole frequency ditribution i not uniform. If the deign index i jut achieved at the band with the mot error, the index at the band with the leat error will be far better than the deign command. And then the reource will be wated. However, The Equivalent rile aroximation (Remez exchange algorithm) ha minimized the maximum, and the aroximation error in the whole frequency ditribution i uniform. Thi deign method make the filter order minimum with the ame index; or make the mot aroximation minimum with the ame order [6]. 06. The author - Publihed by Atlanti Pre 333

2 If H d (ω) i ued to denote the amlitude characteritic wihed to aroximate, and i ued to denote the amlitude characteritic of the ractical deigned FIR filter, the weighted error function i that: E( ω) = W ( ω)[ H d ( ω) H ( ω)] () g Where W (ω) i the weighted function, and it i ued to control the aroximation reciion of different frequency band. The baic idea of Remez exchange algorithm can be ummarized a: calculate the filter coefficient by the rincile which minimize the mot aroximation error of E (ω). The olution of thi algorithm i comlicated. Fortunately, it can be imlified with the hel of Matlab tool. Filter Deign The coefficient of Remez exchange algorithm are given a: Cut-off frequency of a band: ω Maximum attenuation of a band: α Cut-off frequency of to band: ω Minimum attenuation of to band: α Generally, the rile amlitude δ and δ are alo acquired. They can be obtained by then δ + δ α = 0lg = 0lg, + δ δ + δ 0 = 0 α / 0 α / 0 + δ, δ 0 α and α : δ α = 0lg 0lgδ () α / 0 = (3) The low a FIR filter i deigned for intance. The deign coefficient were given a: ω =00Hz, ω =400Hz, α =3dB, α =0dB. Then the ocillation rile amlitude coefficient were calculated a: δ =0.7, δ =0.36. The amlitude and hae frequency characteritic of thi low a filter i hown in figure. Fig.. The frequency characteritic of the low a filter 334

3 The traditional deign method i ued m-file or command window with the hel of code. The FDA tool i interactive grahic ignal roceing in Matlab, and it i convenient to imlement the filter deign and reone analyi. Sinulink i another owerful tool. The whole tet circuit can be contructed and imulated in Simulink environment. The ame low a filter deigned by FDA tool and Simulink follow thee main te: () Set the reone tye, deign method, filter order and filter coefficient. () Run deign filter, the reone of thi deigned filter can be obtained. Fig.. The deigned reult interface (3) Exort the deigned filter by FDA tool to Simulink model, and comlete the whole tet circuit model. The wee ine wa et a original inut ignal. The model wa hown in figure 3. Fig.3. The whole tet circuit (4) Run the imulation and obtain the tet reult, and the reult wa hown in figure 4. Fig.4. The imulation reult 335

4 The above roce i till far from the hardware imlementation. The digital filter by FPGA i uually achieved by code. Thi i difficult for the beginner, and the teacher alo feel more laboriou. The DSP Builder tool can imlify the roce without HDL code. Figure 5 reented the three order FIR filter contructed by DSP Builder comonent. Fig.5. Three order filter Then two above filter contructed the even order filter. It wa hown in Figure 6. Fig.6. Seven order filter The whole tet model wa hown in Figure 7, and the tet reult wa hown in Figure 8. Fig.7. The whole tet model 336

5 Fig.8. The tet reult The uer half art of Figure 8 how the wee ignal, and the lower half how the roceed ignal through the digital filter. Thi reult wa ame a the Figure 4. Thi mean the filter model contructed by DSP Builder comonent achieve the ame effect. Then the model can generate HDL code and the Quartu II roject. It alo can be imulated in Modelim by virtue of DSP Builder. The Modelim imulation reult wa hown in Figure 9. Concluion Fig.9. The Modelim tet reult Thi aer ha decribed the imlementation of digital filter deign and imulation of a toolkit which i caable of converting a code baed deign attern into a grahic and model tool. The commonly ued low a filter i deigned by FDA tool and the whole imulation ytem i teted by Simulink. The traditional deigned attern i uing code in command or m-file. The deign and tet method baed on FDA tool and Simulink become more and more oular in engineering and education at college and univeritie. In addition, the deign can be develoed to the hardware by the Simulink and DSP Builder. Thi roceing rocedure avoid the code writing, and contact everal coure. Acknowledgement Suorted by the Reearch and Reform of Education and Teaching Foundation Project of Shangluo Univerity (Grant NO. 3jyjx39) 337

6 Reference [] Liu Huiheng, Tian Ling. Reform and ractice of teaching method to Digital Signal Proceing [J]. Reearch in Teaching, 008, 3(3): [] Liang Yingbo,Zhang Lihong. Simulation and imlementation of FIR digital filter uing window function [J]. Journal of Zhoukou Normal Univerity, 03, 30(5): [3] Guo Sumin, Guo Sufan, Wu Bo. Exloration on the Teaching Reform and Imlementation of Digital Signal Proceing Coure [J]. Reearch in Teaching, 006, 9(5): [4] Xie Liming, Zheng Rui. Matlab-baed Deign of IIR Digital Filter [J]. Machinery & Electronic 0, (): [5] Lu Yizhe, Meng Meihai, Zhang Feng, Zhang Ke. FPGA DDS Deign Baed on DSP Builder [J]. Journal of Detection & Control, 0, 33(6): [6] Chen Minge, Jiao Zhanya, An Xiaogang. A method of deigning of equirile linear-hae FIR filter [J]. Journal of Xi'an Univerity of Science and Technology, 008, 8():