Weak KAM Theorem in Lagrangian Dynamics
Weak KAM Theorem in Lagrangian Dynamics
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发表时间：
2001
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影响因子：
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通讯作者：
A. Fathi
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文献类型：
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作者：
A. Fathi
The circuits described herein are particularly applicable to organs using multiple pitch divider type note generators that are implemented in LS1 form, since one of the aims of the improvements is to reduce the pin count of the LSI chips required in these organs. One such circuit is a synchronizing system used to phase corresponding notes generated in different chips over a single multiplexed buss. Another multiplexed buss is used to identify the lowest octave in use for each note of the chromatic scale. A new touch response circuit employs a digital to analog converter to eliminate the need for capacitors used in previously described fully analog type circuits thereby eliminating many pins. This circuit furthermore enables a superior relation of key velocity to signal level to be obtained which makes practical a wider dynamic gradation of sound. A new digital mechanization of the debounce filters used to overcome chatter of the keyboard contacts eliminates the need for filter capacitors previously employed, thereby saving many pin connections. A new keyer circuit synthesizes sine waves with fewer high value resistors, eliminates the need for filter capacitors to prevent cross modulation, and enables both sine waves and saw tooth waves to be synthesized with a common set of logic elements. Lastly, an improved envelope generator changes the effective envelope time constants inversely with the pitch of the selected note by means of variable duty cycle charging circuits.
