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Digital signal (signal processing)
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<p>In the context of <a href="/facts/Digital_signal_processing/PEG7azr8">digital signal processing</a> (DSP), a digital signal is a <a href="/facts/Discrete_time/RR8wpS9e">discrete time</a>, <a href="/facts/Quantization_(signal_processing)/fddS3BE2">quantized amplitude</a> <a href="/facts/Signal/41YqUJ8c">signal</a>. In other words, it is a sampled signal consisting of samples that take on values from a <a href="/facts/Discrete_set/d3EeWxuD">discrete set</a> (a <a href="/facts/Countable/Wj4DmWPv">countable</a> set that can be <a href="/facts/Injective_function/5ES6tqf5">mapped one-to-one</a> to a subset of <a href="/facts/Integer/PUwwrawx">integers</a>). If that discrete set is finite, the discrete values can be represented with <a href="/facts/Word_(computer_architecture)/2e5umRaj">digital words</a> of a finite <a href="/facts/Word_(computer_architecture)/2e5umRaj">width</a>. Most commonly, these discrete values are represented as <a href="/facts/Fixed-point_arithmetic/pd3RU72P">fixed-point</a> words (either <a href="/facts/Linear_function/Ejvy8CKy">proportional</a> to the waveform values or <a href="/facts/Companded/zsfkwSzp">companded</a>) or <a href="/facts/Floating-point/eIckahxe">floating-point</a> words. </p> <p>The process of <a href="/facts/Analog-to-digital_conversion/8YYNsMFg">analog-to-digital conversion</a> produces a digital signal. The conversion process can be thought of as occurring in two steps: </p> <ol><li><a href="/facts/Sampling_(signal_processing)/xxck7aLN">sampling</a>, which produces a continuous-valued discrete-time signal, and</li> <li><a href="/facts/Quantization_(signal_processing)/fddS3BE2">quantization</a>, which replaces each sample value with an approximation selected from a given discrete set (for example, by truncating or rounding).</li></ol> <p>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 <a href="/facts/Nyquist_limit/zwFUKdVR">Nyquist limit</a> and does not <a href="/facts/Saturation_arithmetic/uwMJ68lP">saturate</a> the quantizer. </p><p>Common practical digital signals are represented as <a href="/facts/8-bit/2CkhLNoH">8-bit</a> (256 levels), <a href="/facts/16-bit/bTGS44Ne">16-bit</a> (65,536 levels), <a href="/facts/24-bit/c7x41A13">24-bit</a> (16.8 million levels), and <a href="/facts/32-bit/TDMVce8s">32-bit</a> (4.3 billion levels) using <a href="/facts/Pulse-code_modulation/5gdfjtH3">pulse-code modulation</a> where the number of quantization levels is not necessarily limited to <a href="/facts/Powers_of_two/MA6WEpTt">powers of two</a>. A <a href="/facts/Floating_point/eIckahxe">floating point</a> representation is used in many DSP applications. </p>