In the context of
digital signal processing
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are ...
(DSP), a digital signal is a
discrete time,
quantized amplitude signal. In other words, it is a sampled signal consisting of samples that take on values from a
discrete set (a
countable set that can be
mapped one-to-one to a subset of
integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...
s). If that discrete set is finite, the discrete values can be represented with
digital words of a finite
width
Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Interna ...
. Most commonly, these discrete values are represented as
fixed-point words (either
proportional to the waveform values or
companded) or
floating-point words.
The process of
analog-to-digital conversion produces a digital signal.
The conversion process can be thought of as occurring in two steps:
#
sampling, which produces a continuous-valued discrete-time signal, and
#
quantization, which replaces each sample value with an approximation selected from a given discrete set (for example, by truncating or rounding).
It can be shown that an analog signal can be reconstructed after conversion to digital (down to the precision afforded by the quantization used), provided that the signal has negligible power in frequencies above the
Nyquist limit and does not
saturate the quantizer.
Common practical digital signals are represented as
8-bit (256 levels),
16-bit
16-bit microcomputers are microcomputers that use 16-bit microprocessors.
A 16-bit register can store 216 different values. The range of integer values that can be stored in 16 bits depends on the integer representation used. With the two ...
(65,536 levels),
24-bit (16.8 million levels), and
32-bit (4.3 billion levels) using
pulse-code modulation
Pulse-code modulation (PCM) is a method used to digitally represent sampled analog signals. It is the standard form of digital audio in computers, compact discs, digital telephony and other digital audio applications. In a PCM stream, the ...
where the number of quantization levels is not necessarily limited to
powers of two
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer as the exponent.
In a context where only integers are considered, is restricted to non-negati ...
. A
floating point
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can ...
representation is used in many DSP applications.
References
{{Digital electronics
Digital signal processing