I have an asymmetrical clipped repeating waveform and I want to be able to find the root mean square. The function is as follows, with r and b constants: y(t) = ((exp(sin(t)*b)-exp(-sin(t)*b*r))/(exp(sin(t)*b)+exp(-sin(t)*b)))*(1/b) This is pretty computationally heavy. What are some approaches to use to get to a simpler root mean square? Should I use a Fourier transform?
This simplifies to y=1/b * tanh(bsin(t)). If b is small, tanh is approximately linear and you can expand the function to calculate the rms. Alternately, you can calculate the result numerically for various values of b. Note that you must have |b|<1 for convergence.