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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).
The Whittaker–Shannon interpolation formula is mathematically equivalent to an ideal low-pass filter whose input is a sequence of Dirac delta functions that are modulated (multiplied) by the sample values. When the time interval between adjacent samples is a constant (), the sequence of delta functions is called a Dirac comb.
English: Delta-sigma modulation loop model with quantization noise in the Laplace (s) domain. Integration become 1/s, and the quantization process can be modeled as simply adding noise. Integration become 1/s, and the quantization process can be modeled as simply adding noise.
Noise shaping is commonly implemented with delta-sigma modulation. Using delta-sigma modulation, Direct Stream Digital achieves a theoretical 120 dB SNR at audio frequencies using 1-bit audio with 64× oversampling.
Delta modulation (DM or Δ-modulation) is an analog-to-digital and digital-to-analog signal conversion technique used for transmission of voice information where quality is not of primary importance. DM is the simplest form of differential pulse-code modulation (DPCM) where the difference between successive samples is encoded into n-bit data ...
If the sequence of divide by N and divide by (N + 1) is periodic, spurious signals appear at the VCO output in addition to the desired frequency. Delta-sigma fractional-n dividers overcome this problem by randomizing the selection of N and (N + 1) while maintaining the time-averaged ratios.
This results in a broadband dynamic range of only 7.78 dB, but it is not consistent among frequency bands, and in the lowest frequencies (the audible range) the dynamic range is much greater — over 100 dB. Noise shaping is inherently built into the delta-sigma modulators. The 1-bit converter is the basis of the DSD format by Sony.
Similarly, high-speed pulse-width modulation or delta-sigma modulation produces outputs that only assume two states, but the effective output swings through a continuous range of motion. These complications can be avoided by using a different nonlinear control design method that produces a continuous controller.