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Delta-sigma (ΔΣ; or sigma-delta, ΣΔ) modulation is an oversampling method for encoding signals into low bit depth digital signals at a very high sample-frequency as part of the process of delta-sigma analog-to-digital converters (ADCs) and digital-to-analog converters (DACs).
To achieve high signal-to-noise ratio, delta modulation must use oversampling techniques, that is, the analog signal is sampled at a rate several times higher than the Nyquist rate. Derived forms of delta modulation are continuously variable slope delta modulation, delta-sigma modulation, and differential modulation.
It is called the delta function because it is a continuous analogue of the Kronecker delta function, which is usually defined on a discrete domain and takes values 0 and 1. The mathematical rigor of the delta function was disputed until Laurent Schwartz developed the theory of distributions, where it is defined as a linear form acting on functions.
A delta-sigma ADC (also known as a sigma-delta ADC) is based on a negative feedback loop with an analog filter and low resolution (often 1 bit) but high sampling rate ADC and DAC. The feedback loop continuously corrects accumulated quantization errors and performs noise shaping : quantization noise is reduced in the low frequencies of interest ...
Oversampling DACs or interpolating DACs such as those employing delta-sigma modulation, use a pulse density conversion technique with oversampling. Audio delta-sigma DACs are sold with 384 kHz sampling rate and quoted 24-bit resolution, though quality is lower due to inherent noise (see § Figures of merit).
English: Simple circuit performing delta-sigma modulation on an input 20 kHz sine wave s(t). An ideal op amp integrator using s(t) and p(t) produces ε(t), which can be quantized and sampled by an ideal D flip flop to produce a pulse density modulation result p(t), which used as negative feedback.
Continuously variable slope delta modulation (CVSD or CVSDM) is a voice coding method. It is a delta modulation with variable step size (i.e., special case of adaptive delta modulation), first proposed by Greefkes and Riemens in 1970. CVSD encodes at 1 bit per sample, so that audio sampled at 16 kHz is encoded at 16 kbit/s.
Delta-sigma modulation – Another (feedback) method of encoding a continuous range of values in a signal that rapidly switches between two states (i.e., a kind of specialized sliding-mode control) Pulse-density modulation – A generalized form of delta-sigma modulation.