steve_bank
Diabetic retinopathy and poor eyesight. Typos ...
Eureka!!! WE have been eagerly awaiting a new square wave function.
I have no idea what you are doing. I can tell you the utility of the Heaviside step function, the unit step, has wide mathematical application in electric systems. The unit step is mathematically convoluted with a system transfer function to get the step response which is important for several reasons. An electrical step signal is widely used to test physical systems.
The other two major matmatical stimuli are the sine wave and the unit impulse.
A different approach for you would be to look at it as a digital simulation instead of closed direct mathematics.
A sqare wave becomes an array of ones and zeros. Point by point the digital square wave is input to a digital model of the distribution of primes.
Square waves or more generally rectangular waves usualy in reduce to a form of Fourier series.
Another thing to consider is the dc average of the square wave which may cause problems in your math. The average value of a square wave from 0 to 1 is 0.5. From -1 to 1 the average is 0.
You can try a search on La Place transform pair square wave. You might find a differential equation.
I have no idea what you are doing. I can tell you the utility of the Heaviside step function, the unit step, has wide mathematical application in electric systems. The unit step is mathematically convoluted with a system transfer function to get the step response which is important for several reasons. An electrical step signal is widely used to test physical systems.
The other two major matmatical stimuli are the sine wave and the unit impulse.
A different approach for you would be to look at it as a digital simulation instead of closed direct mathematics.
A sqare wave becomes an array of ones and zeros. Point by point the digital square wave is input to a digital model of the distribution of primes.
Square waves or more generally rectangular waves usualy in reduce to a form of Fourier series.
Another thing to consider is the dc average of the square wave which may cause problems in your math. The average value of a square wave from 0 to 1 is 0.5. From -1 to 1 the average is 0.
You can try a search on La Place transform pair square wave. You might find a differential equation.