I would like to create a digital (square) signal on my sound card. It works great if I generate high frequencies. But, since I can't output DC on a sound card, for lower frequencies the resulting digital bits will all slowly fade to 0.
This is what the soundcards high pass does to my square wave: http://www.electronics-tutorials.ws/filter/fil39.gif
What's the mathematical function of a signal, that, when passed through a high pass will become square?
Ideally, the solution is demonstrated in gnuplot.
The sound card cuts out the low frequencies in the waveform, so you need to boost those by some amount in what you pass to it.
A square wave contains many frequencies (see the section on the Fourier series here). I suspect the easiest method of generating a corrected square wave is to sum a Fourier series, boosting the amplitudes of the low frequency components to compensate for the high-pass filter in the sound card.
In order to work out how much to boost each low frequency component, you will first need to measure the response of the high-pass filter in your soundcard, by outputting sine waves of various frequencies but constant amplitude, and measuring for each frequency the ratio r(f) of the amplitude of the output to the amplitude of the input. Then, an approximation to a square wave output can be generated by multiplying the amplitude of each frequency component f in the square wave fourier series by 1/r(f) (the 'inverse filter').
It's possible that the high-pass filter in the soundcard also adjusts the phase of the signal. In this case, one might be better off modelling the high pass as an RC filter, (which is probably how the soundcard is doing the filtering), and invert both the amplitude and phase response from that.
