The Math Basics

Digital data is essentially binary numbers.

Signal processing is done by arithmetical calculations on the binary numbers instead of by discrete, hardwired analog audio circuits, such as:

You wish to mix two signals? You simply sum the voltage values of each signal for each time increment;
You wish to turn up the level by 6 dB? You simply multiply each voltage value by 2.
You wish to delay a signal by 1 millisecond? You simply divert it into a shift register (a data storage cell) and shift the values through enough such registers to use up the millisecond and then have the signal reenter the data stream.
You wish to filter the signal? You just delay the signal, multiply its value by the appropriate coefficient, and subtract it from the next value in the number stream (which is the same as negative feedback in the analog realm). Please note that the digital flow shown here is drastically simplified to accommodate my limited graphics skills.
The point about all this is that digital signal processing is essentially arithmetical calculations and if you get the arithmetic right you can generate any audio effect you wish, without building a discrete circuit. This is the basis of multi-effect devices, and it is one of the most attractive aspects of digital audio.

Also keep in mind that the arithmetic I’ve suggested here is drastically simplified and that actual useful algorithms, especially for filtering, are extremely complex and not for timid math-phobes such as myself. Also, the little digital function boxes I’ve shown, such as the shift register, adder and multiplier, are essentially general purpose logical switch sets that can be easily thought of as “just more arithmetic.”

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