Digital Processing:

In a digital circuit, the guitar's signal is sampled at a rate of 44,100 (or sometimes 48,000) times per second, and these samples are converted into ones and zeros. Basically what this means is that every 22.7 microseconds a circuit (ADC) measures the voltage level of the incoming signal and converts it into a binary number represented by a certain number of bits. Most pedals use 16 or 24 bits for each number. 16 bits of binary can represent any number between 0 and 65,535. So for a 16 bit pedal, every voltage measurement has 65,536 possible values.

As the signal is sampled, it is being read into a temporary buffer that stores the information so that it can be manipulated. At this point, an effects algorithm can be applied to the signal. An effects algorithm is just mathematical processing of the numbers stored in the buffer. There are almost infinite possibilities to what can be done. The math behind it is very complicated and represents an entire field of graduate level engineering called Digital Signal Processing (DSP). An example of a simple operation would be an amplifier, which is just multiplication. Take those numbers in the buffer and multiply them all by 2, and you have double the signal level. Beyond that, it can get pretty complex, so I'll stop there. The important thing to know is that all of the analog building blocks I will be discussing in a moment have mathematical equivalents that can be done in DSP. The difference is that analog effects have a lot of imperfections in the way they manipulate the signal. Replicating every one of these small imperfections that contribute to the sound of an analog effect can be a monumental task in DSP and take a lot of processing power, but the algorithms keep getting better and better.

To convert the signal back to analog, the numbers in the buffer are read back out one by one and converted to voltage levels again (DAC). An analog filter then smooths out the voltage changes between each sample, and you get the original signal back, plus whatever mathematical process that was done on it with DSP. Cool stuff.

Examples of pedals which use digital processing would be: most Line 6 stuff, most Strymon stuff, almost all reverb pedals, all digital delays, all digital multi-effects pedals, tuners, pitch shifters, etc.

Analog Processing:

Before the 1980s, digital signal processing was still too expensive to put into pedals, so most early guitar effects were all analog. A lot of people still prefer the sound of those early circuits. Analog effects use electrical circuits to directly modify the electrical signal coming from the guitar. The easiest way to explain analog effects is to break the circuits down into a few fundamental building blocks. Most guitar pedals use a combination of these blocks to create an effect: