How do Analog-to-Digital Converters Work?
In order to convert an analog signal into a digital signal it is essential to include an Analog-to-digital converter somewhere along the signal path. What does it mean to convert an analog signal into a digital signal? In the physical world there are many natural phenomena (sound, light, voltage, heat, etc…) which are expressed in the form of wavelengths. It is possible to collect data on these occurrences by analyzing the wavelengths. In nature, these vibrations travel in a contentious, analog way. The process of converting an analog vibration into its digital form involves breaking down the signal into equally spaced intervals of time, and interpolating a value based on the quality of that signal.
Signal Path
The analog input needs to be prepared before it can be converted to a digital signal.
Multiplexer
A multiplexer (MUX) is a device that selects signals from multiple inputs and forwards the signal to a single output. This is achieved with a combinational logic circuit that functions much like a rotary switch; transferring data from a multitude of inputs into a unified output signal. Since digital processing usually requires a single source of data, it is necessary to combine multiple inputs into a single output. This is the primary utility of the multiplexer, and is the first step on the signal path of an Analog-to-digital conversion.
Analog Signal Processor
From a mathematical perspective, an analog signal is represented by a continuous function that does not contain any abrupt changes in value.
Convolution is the process through which an input signal can be combined with the system’s function to find the output signal. Through the process of convolution it is possible to amalgamate an analog waveform with the incoming data stream from the multiplexer.
Fourier transform is a mathematical transform that decomposes functions depending on space or time into functions depending on spatial or temporal frequency, such as the expression of a musical chord in terms of the volumes and frequencies of its constituent notes.
Analog-to-Digital Converter
An Analog-to-digital converter changes an analog signal’s continuous time and continuous amplitude into the discrete time and discrete amplitude characteristic of digital signal processing. The conversion process involves subjecting the analog signal to a process of quantization. Quantization works through a sample and hold mechanism in which the signal’s waveform is superimposed on to a grid. The sampling rate determines the bandwidth of the grid. When processing analog signals into digital form, it is inevitable that certain inaccuracies will arise in the fidelity of the digital signal. These artifacts are unfortunate biproduct of the quantization process. The degree to which the signal is accurately represented digitally is called resolution. Resolution is correlated with the bandwidth, or sampling rate.
In order to digitize an analog signal, it is necessary to declare a sample rate at which the signal will be processed. The sample rate corresponds to the bandwidth with which the computer dissects the signal flow to derive digital values. The Nyquist-Shannon sampling theorem suggests a sampling rate should be higher than twice the highest frequency of the signal.
