Editing Delta modulation (section)

==Principle==
Rather than quantizing the value of the input analog waveform, delta modulation quantizes the difference between the input signal and the integral of all previous quantization steps. This quantized signal effectively represents the [[derivative]] of the input signal,<ref name=":5">{{Cite journal |last=Razavi |first=Behzad |date=2016-06-21 |title=A Circuit for all Seasons: The Delta-Sigma Modulator |url=https://www.seas.ucla.edu/brweb/papers/Journals/BRSpring16DeltaSigma.pdf |url-status=live |journal=IEEE Solid-State Circuits Magazine |volume=8 |issue=2 |pages=10–15 |doi=10.1109/MSSC.2016.2543061 |archive-url=https://web.archive.org/web/20240209051709/https://www.seas.ucla.edu/brweb/papers/Journals/BRSpring16DeltaSigma.pdf |archive-date=2024-02-09 |access-date=2024-03-16}}</ref><ref name=":2">{{Cite journal |last1=Inose |first1=H. |last2=Yasuda |first2=Y. |date=1963-11-01 |title=A unity bit coding method by negative feedback |url=https://ieeexplore.ieee.org/document/1444552 |journal=[[Proceedings of the IEEE]] |volume=51 |issue=11 |pages=1524–1535 |doi=10.1109/PROC.1963.2622 |issn=1558-2256 |via=[[IEEE Xplore]]}}</ref> so the original signal is recovered by integration, as shown in the block diagram in Fig.&nbsp;2:

[[Image:Delta1.svg|thumb|280px|none|Fig.&nbsp;2: Block diagram of a Δ-modulator/demodulator{{Efn|The quantizer is synchronized to some sort of clock in synchronous versions. The original 1947 Deloraine and 1950 Cutler patents and the 1952 Jager paper used some pulse generator to control the quantizer so that the samples were time-quantized. The above asynchronous modulator circuit won't work with ideal elements which have no delay, because the loop would happen instantaneously. But real circuits will unavoidably have some amount of delay or hysteresis, which the above asynchronous modulator circuit would require.}}]]

In its simplest form, the quantizer can be realized with a comparator referenced to 0 (a two-level quantizer), whose output is ''1'' or ''-1'' depending on whether the quantizer's input is positive or negative. The demodulator contains an integrator (just like the one in the feedback loop) whose output rises or falls with each 1 or -1 received. An optional [[low-pass filter]] will remove high frequency zigzags (see the blue output signal of Fig.&nbsp;1), so only frequencies in the band of interest remain, to recover a smooth cleaned version of the original signal.

Because each sample is only 1&nbsp;bit, the transmission [[bit rate]] equals the sampling rate.