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 a ...
(DSP), a digital signal is a
discrete time,
quantized amplitude signal
A signal is both the process and the result of transmission of data over some media accomplished by embedding some variation. Signals are important in multiple subject fields including signal processing, information theory and biology.
In ...
. In other words, it is a sampled signal consisting of samples that take on values from a
discrete set
In mathematics, a point (topology), point is called an isolated point of a subset (in a topological space ) if is an element of and there exists a Neighborhood (mathematics), neighborhood of that does not contain any other points of . This i ...
(a
countable
In mathematics, a Set (mathematics), set is countable if either it is finite set, finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function fro ...
set that can be
mapped one-to-one to a subset of
integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
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 Intern ...
. Most commonly, these discrete values are represented as
fixed-point words (either
proportional to the waveform values or
companded) or
floating-point
In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a Sign (mathematics), signed sequence of a fixed number of digits in some Radix, base) multiplied by an integer power of that ba ...
words.
The process of
analog-to-digital conversion
In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide ...
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).
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
In computer architecture, 32-bit computing refers to computer systems with a processor, memory, and other major system components that operate on data in a maximum of 32- bit units. Compared to smaller bit widths, 32-bit computers can perform la ...
(4.3 billion levels) using
pulse-code modulation
Pulse-code modulation (PCM) is a method used to digitally represent 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 amplitud ...
where the number of quantization levels is not necessarily limited to
powers of two. A
floating point representation is used in many DSP applications.
References
{{Digital electronics
Digital signal processing