Editing Delta modulation (section)

=== Slope overload ===
In delta modulation, there is no limit to the number of pulses of the same sign that may occur, so it is capable of tracking signals of any amplitude without [[Clipping (audio)|clipping]] provided that the signal doesn't change too rapidly.<ref name=":1">{{Cite web |last=Kester |first=Walt |date=2008 |title=ADC Architectures II: Sigma-Delta ADC Basics |url=https://www.analog.com/media/en/training-seminars/tutorials/MT-022.pdf |url-status=live |archive-url=https://web.archive.org/web/20230818131208/https://www.analog.com/media/en/training-seminars/tutorials/MT-022.pdf |archive-date=2023-08-18 |access-date=2023-08-20 |website=[[Analog Devices]]}}</ref> However, if an input signal <math>m(t)</math> has a [[derivative]] <math>\dot{m}(t)</math> larger than<blockquote><math>|\dot{m}(t)|_{max} = \sigma f_s</math>,</blockquote>where <math>f_s</math> is the sampling frequency and <math>\sigma</math> is the quantization step size, then the signal changes too fast, causing slope overload. For example, if the input signal is a cosine wave with frequency <math>\omega</math> and amplitude <math>A</math>,

:<math>m(t)={A\cos (\omega t)}</math>,

then its derivative,

:<math>\dot{m}(t) = -\omega A \sin(\omega t)</math>,

can be as large as

:<math>|\dot{m}(t)|_{max}=\omega A</math>.

Thus, slope overload won't occur for a sinusoidal input if

:<math>\omega A < \sigma f_s</math>.

Consequently, a sinusoidal signal can be transmitted without slope overload if its amplitude is not bigger than

:<math>A_{max}={\sigma f_s \over \omega}</math>.

A real input signal may be more complex than a single sinusoid, but this example illustrates how a transmitted signal may be attenuated depending on the sampling frequency, step size, and the input signal's frequency.

While slope overload (also referred to as slope clipping) can be avoided by increasing the quantum step size or sampling rate, very high sampling rates, typically 20 times the highest frequency of interest, are required to achieve the same quality as [[pulse-code modulation]] (PCM).<ref name=":1" />{{Clarification needed|reason=Citation says "same quality as classical PCM" but it is not clear what the specific bitdepth is meant by "classical PCM".|date=January 2025}}