How can digital systems approximate continuous analog signals?
Consider a simple telephone conversation: A person (message source) speaks into a telephone receiver (encoder), which converts the sound of the spoken word into an electrical signal. This electrical signal is then transmitted over telephone lines (channel) subject to interference (noise). When the signal reaches the telephone receiver (decoder) at the other end of the line it is converted back into vocal sounds. Finally, the recipient (message receiver) hears the original message.
Digital systems approximate continuous analog signals through a two-step process known as analog-to-digital conversion, which relies on the principles of information theory.
Sampling
The process begins by measuring the amplitude of an analog waveform at discrete, equally spaced time intervals. According to the sampling theorem established by Harry Nyquist, a signal with a bandwidth of can be uniquely represented if it is sampled at a rate of at least samples per second. This interval is known as the Nyquist interval.123
Quantization
Because sampled amplitudes can take on an infinite range of values, they must be mapped to a finite set of discrete levels for digital storage or transmission. This step, called quantization, assigns each sample to the nearest available level.4
- Accuracy: Increasing the number of levels improves fidelity but requires more storage or transmission speed.4
- Nonlinear Quantization: To optimize performance, systems may use more levels in amplitude ranges where the signal is more likely to occur.4
- Companding: This technique compresses the signal range before quantization and expands it afterward, effectively increasing the dynamic range.4