Geometrically modulated waves

A system for generating a waveform represented by one of the following equations:

• R ⁡ ( θ ) = 1 - θ 4 4 ! + θ 8 8 ! - θ 12 12 ! + θ 16 16 ! - θ 20 20 ! + θ 24 24 ! ⁢ ∑ T = 0 ⁢ ( - 1 ) T ⁢ θ 4 ⁢ T ( 4 ⁢ T ) ! , C ⁡ ( θ ) = θ 3 3 ! - θ 7 7 ! + θ 11 11 ! - θ 15 15 ! + θ 19 19 ! - θ 23 23 ! + θ 27 27 ! ⁢ ∑ T = 0 ⁢ ( - 1 ) T ⁢ θ 4 ⁢ T + 3 ( 4 ⁢ T + 3 ) ! , I ⁡ ( θ ) = θ 2 2 ! - θ 6 6 ! + θ 10 10 ! - θ 14 14 ! + θ 18 18 ! - θ 22 22 ! + θ 26 26 ! ⁢ ∑ T = 0 ⁢ ( - 1 ) T ⁢ θ 4 ⁢ T + 2 ( 4 ⁢ T + 2 ) ! , S ⁡ ( θ ) = θ 1 ! - θ 5 5 ! + θ 9 9 ! - θ 13 13 ! + θ 17 17 ! - θ 21 21 ! + θ 25 25 ! ⁢ ∑ T = 0 ⁢ ( - 1 ) T ⁢ θ 4 ⁢ T + 1 ( 4 ⁢ T + 1 ) ! ,
• wherein θ is the angle in radians of the waveform;
• T is an integer from 1 to ∞ representing the truncation point of the formula;
• and R(θ) represents an amplitude of the waveform, the system comprising:
• an oscillator that receives an input and generates a binary coded decimal output;
• a binary counter that receives the binary coded decimal output and generates a binary signal;
• an EPROM that receives the binary signal at an address and generates an output corresponding to a number contained at the address;
• a digital-to-analog converter that converts the number into a voltage value;
• and
• a signaling power supply that receives the voltage value and generates the waveform.