Ses frekansı bölgesi için dalga analizoru ve distorsiyonmetre

Abstract

Bu çalışmada sayısal İşaret işleme yöntemlerine dayalı olarak gerçekleştirilen, bilgisayar kontrollü sayısal bir harmonik anali zor ünün teorisi ve pratik uygulaması anlatılmıştır. Öncelikle ses frekansı bölgesi için gerçeklenen klasik analiz yöntemleri incelenmiş ve tartışılmıştır. Sayısal işaret işleme yöntemlerine dayalı bir sistemin avantajları vurgulanarak.kuramsal inceleme.örnekleme teorisi ve Ayrık Fourier Dönüşümü üzerinde yapılmıştır. Sözkonusu teoriye dayalı olarak çalışan sistemin donanım ve yazılım özellikleri ortaya k onmuş, cihazın çalıştırılması ile elde edilen sonuçlar tartışılmış ve yeni Öneriler ortaya atılmıştır.

Wave Analyser and Distorsionmeter For Audio Frequencies SUMMARY In many cases to represet a time varying signal with the sum of sinusoidal signals is usefull. This sum is known by the name of Fourier Ser i e and the terms of this sum are the harmonics. In order to ob tain the coeffients or the harmonic components, basic ally two methodes can be used: The first one Cthe most classical!) is a standart wave analyser which uses an averaging tuned filter. Also same other analog instruments which have the derivative configuration of this system are used to measure the total harmonic distortion CTHDDor the harmonic components. The second methode is to sample the signal at a higher than Nyquist-rate, transform the samples into digital form. One of the discrete Fourier or Fast Fourier Transform algoritmes can be used to obtain the coefficients. This methode have the advantage of digital technics: measure the amplitude and phase of the harmonic components or if required to reform the i ni t i nal si gnal. The system proposed in this master thesis »depend on the second methode and measure the harmonic components and THD of an audio frequency si nal. Capprox. 20Hz to 50kHz D To per for me a Discrete Fourier Analysis »firs we must sample the signal: CO 6T CtZ> = Z 6 Ct-nTD CI 3 n=-oo i v <5_ fuction is the pulse train used to performs the sampling. The multiplication of <5_ with xCO in time domain give us xCnO sampled values: xCnt3=öT»xCt3 C2Z) Then Fourier Transformation of a discrete func tion can de defind : XCO> = E xCnD eJ (3D n=- oo In our case xCO function is periodic, then to sample the fonction in a Ctl.... t2D on© periode time interval is sufficient ik Ct5=e ;k=0,±l,,±N C4D In terms of Fourier series : X(t)= S x, e CSD. k kn-N *k *s are the Fourier Series coefficients: 1 T'2 -jko> t x, =-=- / xCtD e ° dt C6D k T -TSZ If the signal is sampled in the time interval CO.NTD then Fourier Series coefficients defined as: 1 NT -J&rt/NT *,. - »t ZxCtD<5 CO e dt C7D k NT T O T is the sampling time interval and N is the number of the samples: N-l / xCtD6 Ct3 dt= T E xCnTD and T rvso x - N-4 Z xCnT) e n=0 -jk2fm/N (8D For k=0,l N-l ve n«0,l N-l t=nT,dt=T the equations 8 and 7 are equivalents. If we define equality : -jEn/N =W N COD For the sampled signal train£x<0), x <1>,......» x (N-l) Î The Discrete Fourier Transformation is: N-4 nk X, = Z xCnDW k N n=0 k=0,l,2,N-1 ClOD For the N equations obtained from the equality 10 we cancreate a matrix type equality : f-I N i- 4- N-I 2 (N-I) N N 2 (N-I) *N (N-I) WN k(0) k(I) s(2) z(N-I) (113 x....x are the complexe harmonic coefficients. O n-l r If we represent one of the harmonic components with x =A+iB then we can obtain the amplitude of each har moni c wi th, X =V A2+ B2 A C12D vi and the phase with the formula, 9? =arccos C A/X D C13D The system, to performe the above operations is formed by two main sections: analog amplifier.sampling, analog-digital converter blocks and digital storage »computer communications »control blocks. Analog amplifier is mainly based on two low di s tor si on operational amplifier. With this block we can obtain amplification coefficients up to 10 and voltage division ratio up to -20db. The voltage comparator sec tion of the analog block is composed by 3 comparators. Two of them are used to indicate input volt age level ;and the last one to form a square wave signal from the input sinusoidal signal. Sampling is made by a special sample and hold amplifier LM398 and sampled input signal is applied to the AM6112DC 12 bit analog to digital converter. The min conversion time of this section is 6us. The converted digital value of each sample is stored in a static RAM C Random Access Memory} ; then transferred to the main computer. All the sampled values of one peri ode of the input signal are applied to the Discrete Fourier Trans form algoritm formed by a GW-BASIC software. To perform the above process we must, know also the frequency of the input signal. Then a 16 bit resolution frequency counter is also implemented in the system. The square wave formed from the input signal is mainly used for this purpose. The frequency of the input signal is first read by the computer and, one peri ode time of the input signal is defined ; the sampling frequency of the system is defined also.Then variable frequancy oscil lator..is programmed.... vii The main functional parts are described above but in the realised system there exist also a intelligent liquid crystal display module CLCD module} for displaying the resul s of the analysis or highligt some information or warnings ; a keyboard for giving the instructions. The system is mounted in a box attached to the main computer Cany IBM compatible personal computer D with a 25 wire cable. In the main computer an add -on- card is placed to the extension slot. The 8 bit data bus, the address up to A9, IOR, IOW, AEN signals are buffered and send to the analyser white this card. INPUT COMPUTER COMMUNICATION BUS AMPLITUDE CONTROL ADDRESS 8US Functional Block Diagram C14D * IBM is the trade mark of the International Business Mac hi nes Cor por a t i on viii Finally the system hardware described above have a unique software written by GW-BASIC.The software is formed by special subroutines and modules to control each different hardware blocks like frequency counting »sampling.reading the content of RAM's »LCD display driving or keyboard-LED driving.