Application of digital filters for measurement of nonlinear distortions in loudspeakers using Wolf s method

Transcription

1 Application o digital ilters or measrement o nonlinear distortions in lodspeakers sing Wol s method R. Siczek Wroclaw University o Technology, Wybrzeze Wyspianskiego 7, Wroclaw, Poland raal.siczek@pwr.wroc.pl 4659

2 The designing process o digital ilters sed or measrement o nonlinear distortions in lodspeakers by the Wol s method is presented in the paper. The Wol s method has been developed in 95 and originally the analog ilters was applied. This method reqires particlarly steep slopes o both band-elimination ilters (at the transmitting part o the measrement system) and band-pass ilters (at the receiving part). The digital ilters allows or achievement o sch steep slopes with a relatively small cost in comparison with analog ones. The very high attenation in the barrage bands can be achieved. In the very narrow transition band any irreglarities do not appear. The design procedres sing MATLAB package have been described. Then, the digital ilters allow or achievement o a high accracy o measrement. Introdction The problem o digital ilters designing with very steep slope in the rejection band is presented in this paper. These ilter are sed or measrement o nonlinear distortion in lodspeakers. The method has been developed by V.Wol in 95 []. Athor in his original work sed the analog ilters. Next contribtion or this method was given by S. Nikaido in 97 [], bt in his work also analog ilters were applied. The application o digital ilters or measrement o nonlinear distortion in lodspeaker are pblished by Imaka and Ohga []. Method o measrement The metod o measrement o nonlinear distortions sing broad-band signal was proposed by V.Wol in 95. A block diagram o the measring system is shown in Fig. To the inpt o measring system the broadband signal (e.g. white noise) is given. This signal is iltered with the bandelimination ilter (in or case 5/9 octave). This signal ater ampliication excites tested lodspeaker. The acostical signal radiated by the lodspeaker is transdced into the electrical one by the measring microphone. This signal is iltered with the band-pass ilter with the same central reqency as the band-elimination ilter at the inpt, bt with slightly narrower bandwidth (in or case / octave). Becase the lodspeaker is a nonlinear system, in analyzed reqency band a prodct o nonlinearity occrs. However, in this band occrs also the residal signal, cased by inite slope o both ilters. This slope shold be siciently steep, in order to keep residal signal level below the prodct o nonlinear distortion. I, instead o single pair o bandelimination and band-pass ilter, the bank o ilter pairs with dierent central reqencies is sed, we can obtain the dependence o prodct o nonlinear distortion on reqency. Fig. Principle o measrement strctre o actal programs transmitted by lodspeakers. The disadvantage is complication connected with reqired very steep slope o sed ilters. I they are insicient, the residal noise dominates over the prodct o nonlinearity. Digital ilters. Introdction The ideal soltion or measrement o nonlinear distortion sing Wol s method seems to be the application o digital ilters. Nowadays, digital ilters became more poplar in comparison with the analog ones becase o their properties. In relatively easy way the very steep slopes can be obtained. Also the signal attenation in the attenation band is very high. The transition band withot ripples can be obtained. Application o digital ilters in measring system o nonlinear distortion shold provide an increase o the accracy o the measrement. The Btterworth FIR ilters have been chosen. They have lat reqency response in pass band, however the alling down o the reqency response at the end o this band is higher than other ilters (e.g. Chebyshev ilters). Also the steep o slope in the transition band is smaller than or Chebyshev ilters. The ilters have been designed sing Filter Design&Analysis Tool, which is inclded into MATLAB system.. Assmptions The designed ilters are Btterworth FIR ilters. The attenation band in band-elimination ilter is eqal to 5/9 octave, and pass band in band-pass ilter is eqal to / octave. At each end o the analysed band the reserve is eqal to /9 octave. This reserve is necessary in order to provide maximm attenation o residal signal dring the measring process. The slope o both ilters is higher, when this reserve is narrower. The order o both ilters has been calclated in sch a manner that the energy o the residal signal was below 0.% o the inpt signal in analyzed reqency band. The calclated minimal vales o orders o the ilters are 4884 or band-elimination ilter and 44 or band-pass ilter. The advantage o this method o measrement o nonlinear distortions in comparison with classical methods i.e. harmonic or intermodlation distortion is better correlation with sbjective evalation o nonlinear distortion, becase the spectral strctre o broadband signal is similar to the 4660

3 . Calclation o the slopes o designed ilters As an example, the design o both ilters: band-elimination and band-pass with common center reqency 0 =5Hz is presented. The eqations or calclation o -db limiting reqencies or the band-elimination ilter with bandwidth o attenation eqal to 5/9 octave are: = = This yields =60Hz, =8Hz () () Fig.4 Freqency response o the designer band-elimination ilters.5 Design o the band-pass ilter The similar calclation as presented in.4 was done or the band pass-ilter Fig. Band-elimination ilter Similarly, the eqations or calclation o -db limiting reqencies or band-pass ilter with bandwidth eqal to / octave: ' ' = ' ' 0 = This yields =80Hz, =54Hz () (4) Fig.5 Freqency response o the designer band-elimination ilters.6 Veriication o correct operations o the designed ilters The veriication o the correct operations o the designed ilters has been made sing the white noise as the inpt signal. The measring setp is presented at Fig. 6. Fig. Band-pass ilter.4 Design o the band-elimination ilter The reqency response o the ilter with center reqency 0 =5 Hz is presented in Fig. 4. Fig.6 Measring setp or veriication o the correct operations o ilters The inpt signal (white noise) id presented in Fig.7 It is RMS vale is approximately eqal to 0 nits. This signal ater iltering by band-elimination ilter is presented in Fig.8. Becase the eliminated reqency band is relatively narrow the RMS vale did not signiicantly change. The signal iltered by band-pass ilter is presented in Fig.9. The RMS vale is approximately eqal to 0.0 nit, it means that it is 0.% o inpt signal. 466

4 Fig.0 General block diagram o the measring system Fig.7 Inpt measring signal white noise Fig. Block diagram o the measring system Simlink The reslts o simlations are presented below. All nonlinearities was considered as static. They are nonlinearities o third order what is typical or lodspeakers. First three examples are symmetrical nonlinearities weak, medim and strong respectively. The orth example is a medim nonlinearity with asymmetry. Fig.8 Inpt measring signal ater iltering by the bandelimination ilter 4. Example No. Inserted nonlinearity is given by the ollowing eqation: ( ) The otpt signal is presented in Fig. = (5) Fig.9 The residal signal at the otpt o band-pass ilter 4 Simlation o the measrement o nonlinear distortions sing Simlink The simlation o measred process has been done sing SIMULINK sotware. SIMULINK is a tool with own graphic interace, which ses MATLAB or compting process. It is applied or versatile analyses o dynamical systems. The measring block diagram is presented in Figs. 0 and. The inpt signal is iltered by the designed band-stop ilter. The iltered noise is given to the nonlinear block, which simlates lodspeaker nonlinearity. In the next step, the signal is iltered by the designed band-pass ilter. At each step o signal processing, the reslt is observed sing Scope block. As the inpt signal the white noise presented in Fig. 7 has been applied. Fig. The signal at the otpt o band-pass ilter (example No. ) Althogh the nonlinearity is weak, the level o the signal is signiicantly higher than the level o residal signal. The dierence is small, then this weak nonlinearity is lower limit o nonlinearity possible to measrement. 4. Example No. Inserted nonlinearity is given by the ollowing eqation: ( ) = (6) The otpt signal is presented in Fig. 466

5 Fig. The signal at the otpt o band-pass ilter (example No. ) This nonlinearity is easy or measrement. 4. Example No. Inserted nonlinearity is given by the ollowing eqation: ( ) + 00 The otpt signal is presented in Fig.4 = (7) Fig.5 The signal at the otpt o band-pass ilter (example No. 4) Comparing the Figres and 5 it can be observed that asymmetry cases an increase o the nonlinearity prodct. 5 Conclsion The method o measrement o nonlinear distortions in lodspeakers sing digital ilters has been presented. Using MATLAB sotware packet developed by MathWorks it is possible to design necessary ilters as well as to simlate the measring process. Reerences Fig.4 The signal at the otpt o band-pass ilter (example No. ) This nonlinearity is very strong and signal level in the analyzed band is almost the same as the exciting signal. 4.4 Example No. 4 [] V. Wol, Dynamic Method o Nonlinear Distortion Investigation (in Rssian), Radiotechnika. vol. 8, no. pp. 7 7, 95. [] S. Nikado, On Distortion Measrement o Lodspeakers Using Programmed Sond Reports o the 6th International Congress on Acostics, vol. III D, Electroacostics and Architectral Acostics, Tokyo, pp [] K. Imaoka and J. Ohga, A New Digital Measrement or Distortion o Acostical Devices, st AES Convention, October 004, preprint 66. Inserted nonlinearity is given by the ollowing eqation: ( ) The otpt signal is presented in Fig.5 = (8) 466