Taylor 展開を用いたレコードの再生ひずみ除去方法
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I)Introduction Reproduction of recorded sound on disk records causes tracing distortion. Recently some record makers have published their recording techniques to reduce tracing distortion by means of corrected recording signals. Different methods for obtaining the corrected signals have been proposed by RCA Laboratory and Telefunken Laboratory. A new recording technique was devised by Toshiba Central Research Lab. Several methods have been thought out to obtain the corrected recording signals, for example 1) phase modulation 2) correction terms obtained by Fourier expansion are added to the original recording signals. 3) correction terms are obtained by Taylor expansion of recording signals at the point where a modulated groove wall comes into contact with a reproducing spherical stylus. Method 3) was realized with comparatively simple electronic circuits, which can erovide corrected signals even when other causes of distortion have to be taken into account. II)Method to calculate corrected signals Assume that a spherical repoducing stylus S with a redius of r contacts with a modulated groove wall W(x) rigidly. (Fig. 1)The reproduced signal P(x) can be expressed in the form P(x-Δx)=W(x)-r1-cosθ) (1) In order that P(x-Δx) agrees well with R(x-Δx), W(x) must be in the following relation. W(x)=R(x-Δx)+r1-cosθ) (2) When both x and θ are small, corrected signals which are the sum of the original recording signals and correction terms, can be obtained approximately by Taylor expansion. W(x)=R(x)-rホsec{dR(x)/dx}-1]+(1/2)r^2sin^2{dR(x)/dx}ヤ^2R(x)/dx^2 (8) III)Calculation of harmonic distortion of a sinusoidal wave Let an input signal be denoted by R(x)=Aンin(γx), then corrected recording signals are given in the form W(x)=Aンin(γx)-rホsec{Aγャos(γx)}-1]-(1/2)r^2A^3γ^4cos^2(γx)ンin(γx) (10) Hence, reproduced signals are, P(x-Δx)=Aンin(γx)-rホsec{Aγャos(γx)}-1]-(1/2)r^2A^3γcos^2(γx)ラn(γx)+r/√<1+E^2> where, E=dW(x)/dx, and Δx=γE/√<1+E^2>. Percent harmonic distortion can be obtained by Fourier expansion of these signals. Denoting γA by Θ, and rγ^2A by η, Fig. 3(a)-(f) show the 2nd and 3rd harmonics in Θ-η coordinates. These graphs show a remarkable decrease in harmonics, especially in the 2nd harmonics, compered with signals to which no correction term is applied. In order to express corrected signals by Eq. (8), the following limitations are required; Θ≦1/2, η≦1 and A≦50, where η is the ratio of the radius of a spherical stylus to the minimum radius of curvature of a modulated groove wall. Even harmonics (2nd and 4th) and odd harmonics (3rd and 5th) are given in A-γ coordinates under the new limitations as shown in Fig. 4. Higher frequency or larger amplitude is available than in an uncorrected groove under the same distortion factor. γ is a function of signal frequency f, the radius of a groove R and the number of revolutions of a disk N. Fig. 5 shows the relation between γ, f and R, when N=33/3 rpm. IV)IM distortion Fig. 6 shows the calculated value of intermodulation distortion for harmonic signals of 400 and 4000 cps at a velocity ratio of 4:1 and a maximum velocity of 6. 22 cm/sec. Sidebands are greatly reduced by this method. V)Tracing Distortion Correlator. Fig. 7 shows a blockdiagram of a Tracing Distortion Correlator. This circuit consists of amplifiers, which have a variable amplification factor proportional to 1/R, function generators, differentiators and multipliers. Errors in each block are kept within 1%. Satisfactory results were obtained in hearing tests of disk records produced with this correlator, and the distortion factor of these records were measured to be half that of uncorrected ones. VI)Conclusion This device is useful for the reduction of tracing distortion. A remarkable decrease in secondary distortion is effective especially for stereo disk reproduction. The electronic circuits can be constructed easily.
- 社団法人日本音響学会の論文
- 1967-03-30