discreteamplitude

Discreteamplitude is a term used to describe a signal situation in which the instantaneous amplitude is limited to a finite, discrete set of values. It arises when a continuous-amplitude signal is processed by a quantizer or when a modulation scheme encodes information in a finite number of amplitude levels. In this sense, discreteamplitude contrasts with signals of continuous amplitude, where the amplitude can take any real value.

Mathematically, for a real-valued discrete-time signal x[n], a discreteamplitude version a[n] is produced by a quantizer Q that maps the real line to a finite set A = {a1, a2, ..., aM}. The result is a[n] = Q(x[n]). The difference e[n] = x[n] - a[n] is the quantization error. The parameter M, the level spacing, and the choice of A determine the resolution and distortion of the signal.

Applications of discreteamplitude appear in digital communications and signal processing. In digital communications, discrete amplitudes characterize amplitude-shift keying (ASK) and the amplitude components of amplitude-phase modulations such as quadrature amplitude modulation (QAM), where each symbol selects a particular amplitude from a finite constellation. In audio and image processing, quantization to discrete amplitudes is a core step in analog-to-digital conversion.

Properties and design considerations include the introduction of distortion and quantization noise. Uniform quantizers have equally spaced levels, while nonuniform quantizers allocate levels according to input statistics. Dithering can reduce artifacts by randomizing quantization error. Related concepts include quantization, analog-to-digital conversion, and various modulation schemes.