Digital Signal Processing is a science all of its own today. In the old days, there was only analog processing, done by tubes and solid-state (transistors) devices.
If you wanted an effect, such as distortion, you would design one amplifier stage to overdrive another stage to get the desired effect. Reverb was often accomplished by converting the signal into an actual sound wave and transferring it to a metal plate, and then converting it back to an electrical signal again.
This is how plate reverb is accomplished. The Tom Shultz Bass Rockman unit is a completely analog type of processor. It has a stereo chorus, distortion, preset EQ, compression, mixer, headphone out, and line-out jacks. Pretty impressive for analog technology.
Below are some examples of both analog signal processors and digital signal processing.
The top two units are both analog-type processing units: Aphex Aural Exciter, and Numark Stereo Equalizer. The bottom unit is an Alesis Midiverb II, digital unit.
Today, all effects can be emulated by digital signal processing, or DSP for short. This process takes the analog signal and converts it to digital bits and bytes. Today, these bits and bytes are 16-bit, 24 bit and 32-bit numbers. This conversion factor is the resolution of each sample.
When the analog signal is converted to digital, there are often, 44,100 samples taken per second. (This is the standard audio rate in the industry for Compact Discs.) This is known as the sampling rate. It needs to be a least twice the rate of the highest frequency being converted.
Once these samples are taken, they are then processed. The resulting bits and bytes are then converted back to an analog signal, which is then fed into your amplifier and speakers. This entire process occurs very fast and is usually done by a dedicated computer processor or some computer program.
The advantage of this process, while it is complex, is that it is controlled by software and therefore it can be changed easily. This allows you to control several parameters for several different effects.
The other benefit is that multiple effects can be processed on the input signal, with the only limitation being your electronic hardware and processor for the task. They do have limits. Almost all recording today is done in the digital domain. For more information about digital recording check out easy-home-recording.com.
For example, you could take your bass sound and feed it into your laptop. With the right software, you could change the sound of your bass in real-time, and feed the output back into your bass amp.