JPH03154921A - Nonlinear function generator and musical tone synthesizer using the same - Google Patents

Abstract

PURPOSE:To generate a satisfactory hysteresis by using the input signals as the variables to produce a hysteresis function and a non-hysteresis function and synthesizing these functions. CONSTITUTION:A hysteresis function generating means 1 is provided to produce a hysteresis function with an input signal used as a variable together with a non-hysteresis function generating means 2 which produces a non-hysteresis function with an input signal used as a variable, and a synthetic arithmetic means 3 which synthesizes the functions outputted from both means 1 and 2. In other words, a nonlinear function is decomposed into a hysteresis function component and a non-hysteresis function component. These function components are outputted from both means 1 and 2 with the input signals used as variables and then synthesized together by the means 3 like a multiplier, etc. Thus, the satisfactory hysteresis is generated.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a nonlinear function generating device that generates a nonlinear function having hysteresis characteristics, and a musical tone synthesis device using this nonlinear function generating device.

[Prior Art] Conventionally, as a so-called digital sound source used in electronic musical instruments, etc., initial waveform data,
Synthesizes musical tones by introducing data such as impulse signal data and nonlinear signal data and performing regression calculation processing.
A musical tone synthesizer using a so-called delayed feedback type attenuated tone synthesis algorithm is known (for example, Japanese Patent Laid-Open No. 6
3-40199).

This musical tone synthesis device physically approximates the mechanical vibration system of natural musical instruments, such as the pipe of a wind instrument or the string of a stringed instrument, using an electrical circuit, and the closed loop is connected to the reed of a wind instrument, the Ampsure-1, or the bow of a bowed stringed instrument. By inputting a nonlinear signal that corresponds to the heartbeat of the point of contact with the string, it is possible to synthesize the sounds of wind instruments and bowed string instruments naturally and faithfully, including changes due to their dynamics.

FIG. 6 shows the relationship between the external force applied to the string by the bow of a bowed string instrument and the displacement speed applied to the string thereby. When the external force is around O, the contribution of static friction between the bow and the string is dominant, so the displacement speed is proportional to the external force, but when a certain amount of external force is applied, dynamic friction becomes dominant and the displacement speed remains constant or changes to the external force. be inversely proportional. When this transition from static friction to dynamic friction occurs, the degree of contribution of external force to the string displacement speed changes suddenly, so the external force vs. displacement speed characteristic becomes a nonlinear curve as shown in FIG. 6. Furthermore, when the external force decreases, the displacement speed changes nonlinearly when transitioning from dynamic friction to static friction.

A synthesis algorithm for a bowed string instrument requires a nonlinear signal with hysteresis as shown in FIG. Preferably, this nonlinear signal can be finely controlled according to bow pressure, bow speed, and the like.

As a signal source of such a nonlinear signal having hysteresis, the present inventor switches the characteristic function based on static friction and the characteristic function based on dynamic friction according to an input value such as an external force, and sets the threshold level for this switching to a human power value. (Japanese Patent Application No. 1-192708). However, this method has the disadvantage that the hardware and software required for implementation are complicated.

The present inventor has also previously proposed a method of providing hysteresis by including a nonlinear signal generating circuit in a feedback loop (Japanese Patent Application No. 194544/1999). Although this method has a simple configuration, it has other disadvantages as described below.

FIG. 7 shows a nonlinear signal generation circuit for a bowstring algorithm in which hysteresis is caused by feedback. In the figure, a nonlinear table 71 generates a nonlinear function as shown in FIG. This nonlinear function forms a substantially straight line with a negative slope α near the origin, and the portions on both sides of this straight line form curves with positive slopes. Further, the feedback circuit 72 in FIG. 7 has a positive gain β.

If we divide the input/output transfer function of such a nonlinear system into a positive slope part and a negative slope part, in the positive slope part, hysteresis occurs due to positive feedback β. In the part of the negative slope α, the feedback functions as negative feedback (NFB), so the total gain (transfer function) G+<ra is as follows.

In bowed strings, the gain in the nonlinear straight section is a constant (usually −
1 or about 12), so G in the previous equation
For example, if NPB is set to 1, then 0=β-1. Also, considering the stability of the system under the condition that α is negative and β is positive, in the NFB system, parasitic oscillation often occurs if the loop gain αβ is too large, so in the end α = −1, 1, It settles down to about β-0.09. However, with this amount of feedback, positive feedback (P
FB) When the system is constructed, the amount of PFB is insufficient and sufficient hysteresis cannot be generated. In other words, in the configuration shown in FIG. 7, it is necessary to increase the amount of feedback in the PFB system to generate sufficient hysteresis, and it is necessary to decrease the amount of feedback for stable NFB. However, it has been almost impossible to achieve both sufficient hysteresis and system stability.

[Problems to be Solved by the Invention] This invention has been made in view of the problems in the conventional example described above, and is a nonlinear function generator that has a simple configuration, can generate sufficient hysteresis, and has stable operation. The purpose is to provide equipment.

[Means for Solving the Problems] In order to achieve the above object, the nonlinear function generator of the present invention includes a hysteresis function generating means for generating a hysteresis function using an input signal as a variable, and a non-hysteresis function generator using the input signal as a variable. It is characterized by comprising a non-hysteresis function generating means for generating a function, and a composition operation means for synthesizing the functions output from the hysteresis function generating means and the non-hysteresis function generating means.

In one aspect of the present invention, the hysteresis function generation means includes step function generation means for generating a non-hysteresis step function, and positive feedback of an output of the step function generation means to an input terminal of the step function generation means to input the step function. and feedback means for combining the signal with the signal and providing it as a variable to the step function generating means.

[Operation] According to the above configuration, the nonlinear function is decomposed into a hysteresis function component and a non-hysteresis function component, and after being outputted from the hysteresis function generation means and the non-hysteresis function generation means, respectively, using the input signal as a variable, The signals are synthesized by a synthesis calculation means such as a multiplier.

The hysteresis function generating means is, for example, a PFB circuit including a step function generating means, and provides hysteresis to the step function.

(Effects) As described above, according to the present invention, the hysteresis function and the non-hysteresis function are generated separately and combined to obtain a nonlinear function, thereby simplifying the configuration.

Furthermore, even when using a hysteresis function generating means that applies hysteresis by feedback, it is sufficient for the hysteresis function generating means to generate only the hysteresis function component, so it is necessary to make sure that the original non-hysteresis function does not have a negative slope. Alternatively, even if there is a positive slope, it can be set so that it is extremely small. Therefore, the feedback system of this hysteresis function generating means is essentially only the PFB system, and the instability caused by the configuration of the NFB system is eliminated. Therefore, it is possible to set a large feedback gain that takes only hysteresis into consideration.

[Example] Hereinafter, this invention will be explained in detail based on examples.

FIG. 1 shows the configuration of a nonlinear function generator according to an embodiment of the present invention.

The apparatus shown in the figure converts the nonlinear function C shown in FIG. 2C into the nonlinear function C shown in FIG.
The nonlinear function A shown in Figure 2B is decomposed into the product of the nonlinear function B shown in Figure 2B, and hysteresis is given to the nonlinear function A using a feedback method to obtain the hysteresis function shown in Figure 3A. By multiplying by the nonlinear function B, a nonlinear function E with hysteresis as shown in FIG. 3B is generated.
The present invention includes a non-hysteresis function generating circuit 2 that generates a hysteresis function, and a multiplication circuit 3 that multiplies the interval number B by the interval number B.

The hysteresis function generation circuit 1 includes a step function generation circuit 11 that generates a nonlinear function (step function) A consisting of a trapezoidal curve as shown in FIG.
It is provided with a feedback circuit 12 and an adder 13 for feeding back the output of the circuit to the input side. Here, the number of steps A is
As shown in Figure 2A, in the region where human power is negative, the slope is positive;
In the positive region, it has a negative slope. Therefore, if the feedback constant β of the feedback circuit 12 is positive, a negative feedback system will be formed in the region where the input is positive, making it impossible to obtain the desired hysteresis.

Therefore, it is necessary to control the feedback system so that it always becomes a positive feedback system. For this purpose, it is preferable to invert the sign of β depending on the positive/negative and nonlinear characteristics of the input. The β sign control circuit 14 and multiplier 15 included in the hysteresis function generating circuit 1 of FIG. 1 are for controlling the sign of β so that it is opposite to the sign of human input.

4A to 4C respectively represent the β code control circuit 14 of FIG.
A specific example is shown below.

In FIG. 4A, the positive/negative determining circuit 14a determines the sign of β, that is, the positive/negative, and the selector 14b operates the positive/negative determining circuit 14.
Depending on the output of a, one of +β and -β is selected and sent to the multiplier 15.

When the input signal is in two's complement format, the sign of the signal can be determined by the MSB (most significant bit), which is a sign bit indicating the sign of the signal.

In FIG. 4B, an inverter that inverts the MSB of the signal is used as the positive/negative judgment circuit 14a, and if the signal is positive, the judgment output is
If it is negative, a determination output of "0" is generated. Feedback constants +β and -β set according to musical tone parameters are supplied to the selector 14b, and -β, which is supplied to the A input terminal according to the judgment output "1", changes to the judgment output "0". Accordingly, +β supplied to the B input terminal is selected and sent to the multiplier 15.

FIG. 4C shows an example in which a polarity inverting circuit 14c is used in place of the selector 14b in FIG. 4B, and the polarity of β is simply changed depending on the sign of the signal.

1 FIG. 5 shows the configuration of a musical tone synthesizer to which the nonlinear function generator of the present invention is applied. In the same figure, the first
Parts common to those in the figures are given the same reference numerals.

The device shown in the figure synthesizes the performance sound of a stringed instrument such as a violin by digital data calculation processing, and includes delay circuits 51a and 51b, and a low-pass filter (LPF) 52a.
, 52b, multiplier 53a.

53b, 54, 55, adders 56a, 56b.

57.58. It also includes a nonlinear function generator 60, which is a feature of the present invention.

Delay circuits 51a, 51b% LPF 52a, 52b1 multipliers 53a, 53b and adder 56a.

The closed loop consisting of 56b corresponds to the string being bowed, and the delay time of the closed loop corresponds to the resonant frequency of that string.

Delay time of delay circuits 51a, 51b and LPF 52a
, 52b are determined by the performance information generation circuit 61 and musical tone parameter supply circuit 62 provided within the instrument body.
2 based on the performance information.

The multipliers 53a and 53b multiply the input signal by "-1" and output the result, and are used as phase inverters. Note that this multiplier can also be used as an attenuator by multiplying by a constant whose absolute value is smaller than 1.

The adders 56a and 56b correspond to the string rubbing points, and the closed loop includes delay circuits 5 corresponding to both sides of the string rubbing point.
1a, a first signal path consisting of an LPF 52a and a multiplier 53a, a delay circuit 51b, an LPF 52b and a multiplier 5
Adders 56a and 5
They are separated with 6b in between.

The nonlinear function generator 60 is similar to that shown in FIG. 1, and includes a step function generator 11, an adder 13, a β code control circuit 14, a multiplier 15, and a non-hysteresis function generator, which constitute a hysteresis function generator. 2 and a multiplication circuit 3. Note that here, the feedback constant β is set to 1, and the feedback circuit 12 is only a connecting line, so it is not particularly represented as a block.

This nonlinear function generator 60 generates a signal obtained by combining the output of the first signal path and the output of the second signal path by the adder 57.
An adder 58 adds a signal representing the bow speed vb, and a multiplier 54 receives a signal multiplied by a signal representing the reciprocal of the bow pressure 1/Fb. A nonlinear function with input/output characteristics as shown in Figure B is output.

This nonlinear function output signal is sent to the adder 56a.

56b, it is added to the outputs of the second and first signal paths 18, respectively, and then manually input to the first and second signal paths.

The human output characteristics shown in FIG. 3B represent the friction characteristics between the bow and the string, and have nonlinear characteristics and hysteresis characteristics due to the transition from static friction to dynamic friction.

Furthermore, since static friction increases as the bow pressure increases, this hysteresis characteristic changes depending on the bow pressure Fb.

The device shown in Figure 5 is a so-called physical model in which the mechanical vibration system of the strings of a bowed string instrument and the drive system between the bow and the strings are physically approximated by electric circuits. , it is possible to accurately reproduce the sound of an actual musical instrument.

[Brief explanation of the drawing]

FIG. 1 is a block circuit diagram showing the configuration of a nonlinear function generator according to an embodiment of the present invention, and FIGS. 2 and 3 show nonlinear functions for explaining the operating principle of the device shown in FIG. The graphs shown in FIGS. 4A to 4C are block circuit diagrams showing specific circuit examples of the β code control circuit in FIG.
Fig. 5 is a block circuit diagram showing the configuration of a musical tone synthesizer to which the present invention is applied; Fig. 6 is a graph showing the nonlinear function required for the bowed string algorithm; Fig. 7 is a conventional feedback FIG. 8 is a graph showing the nonlinear functions stored in the nonlinear function table in FIG. 7. 6 1: Hysteresis function generation circuit 11 Two-step function generation circuit 12; Feedback circuit 13; Adder 14: β code control circuit 15: Multiplier 2: Non-hysteresis function generation circuit 3: Multiplier circuit

Claims (3)

[Claims] (1) Hysteresis function generation means for generating a hysteresis function using an input signal as a variable; non-hysteresis function generation means for generating a non-hysteresis function using the input signal as a variable; and these hysteresis function generation means and non-hysteresis function generation means. 1. A nonlinear function generator, comprising a composition calculation means for synthesizing functions output from the nonlinear function generator. (2) the hysteresis function generation means includes step function generation means for generating a non-hysteresis step function;
2. The nonlinear function generating device according to claim 1, further comprising feedback means for positively feeding back the output of said step function generating means to the input side of said step function generating means, combining said signal with said input signal, and providing said signal as a variable to said step function generating means. . (3) A musical tone synthesis device comprising a closed loop means including a delay means, and a nonlinear function generating means that uses a performance operation signal and a signal taken out from the closed loop means as variables to generate a nonlinear signal and supply it to the closed loop means, the nonlinear A musical tone synthesis device characterized in that the nonlinear function generating device according to claim 1 or 2 is used as a function generating means.