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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).
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 variation in the calculus of variations; the Kronecker delta function [20] the Feigenbaum constants [21] the force of interest in mathematical finance; the Dirac delta function [22] the receptor which enkephalins have the highest affinity for in pharmacology [23] the Skorokhod integral in Malliavin calculus, a subfield of stochastic analysis
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.
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.The function is 1 if the variables are equal, and 0 otherwise: = {, =. or with use of Iverson brackets: = [=] For example, = because , whereas = because =.
The graph of the Dirac comb function is an infinite series of Dirac delta functions spaced at intervals of T. In mathematics, a Dirac comb (also known as sha function, impulse train or sampling function) is a periodic function with the formula := = for some given period . [1]
On the contrary, delta modulation and delta-sigma modulation are random processes [clarification needed] that produces a continuous spectrum without distinct harmonics. While intersective PWM uses a fixed period but a varying duty cycle, the period of delta and delta-sigma modulated PWMs varies in addition to their duty cycle.
Sinc N filters are commonly used with delta-sigma modulation ADCs just prior to downsampling to the desired output data rate (ODR) of . A sinc N filter's frequency response will lie under a –20·N dB per decade envelope, so higher orders have steeper roll off for cutting out more high frequency noise, but will also have a lower -3 dB frequency .