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
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled.
Discrete time
Discrete time views values of variables as occurring at distinct, separate "po ...
,
quantized amplitude signal
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
. In other words, it is a sampled signal consisting of samples that take on values from a
discrete set
]
In mathematics, a point ''x'' is called an isolated point of a subset ''S'' (in a topological space ''X'') if ''x'' is an element of ''S'' and there exists a neighborhood of ''x'' which does not contain any other points of ''S''. This is equival ...
(a
countable
In mathematics, a set is countable if either it is 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 from it into the natural numbers; ...
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 language ...
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
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 b ...
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 provi ...
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
In signal processing, the Nyquist frequency (or folding frequency), named after Harry Nyquist, is a characteristic of a sampler, which converts a continuous function or signal into a discrete sequence. In units of cycles per second ( Hz), it ...
and does not
saturate
Saturate may refer to:
* ''Saturate'' (Breaking Benjamin album), 2002
* ''Saturate'' (Gojira album), 1999
* ''Saturate'' (Jeff Deyo album), 2002
* " Electronic Battle Weapon 8", a song by The Chemical Brothers, a shorter version of which was re ...
the quantizer.
Common practical digital signals are represented as
8-bit
In computer architecture, 8-bit Integer (computer science), integers or other Data (computing), data units are those that are 8 bits wide (1 octet (computing), octet). Also, 8-bit central processing unit (CPU) and arithmetic logic unit (ALU) arc ...
(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 mos ...
(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 32-bit units. Compared to smaller bit widths, 32-bit computers can perform large calculation ...
(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-negative ...
. 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 be ...
representation is used in many DSP applications.
References
{{Digital electronics
Digital signal processing