Editing Group delay and phase delay (section)

=== Negative group delay ===
<gallery mode="packed" perrow="1" caption="Figure 2: Negative group delay filter circuit">
File:Ltspice-negative-1ms-group-delay.png|[[Electronic circuit|Circuit]] with ''negative'' group delay of <math>\displaystyle \tau_g</math> = {{Nowrap|−RC}} = {{Nowrap|1=−1 ms}} for frequencies much lower than {{Fraction|1|RC}} = {{Nowrap|1 kHz}}.
File:Negative-1ms-group-delay.png|[[LTspice]] [[Alternating current|AC]] simulation of <math>\displaystyle \tau_g</math> from {{Nowrap|1 Hz}} {{Nowrap|(<math>\displaystyle \tau_g</math> ≅ −1 ms}}) to {{Nowrap|10 kHz}} (<math>\displaystyle \tau_g</math> ≅ {{Nowrap|0 ms}}).
File:100Hz-negative-group-delay-wave-1Ghz-bandwidth-opamp.png|[[Transient response|Transient]] simulation of an input (green) wave whose output (red) is ahead by {{Nowrap|1 ms}}, but with instability when the input turns on and off.
</gallery>
Filters will have ''negative'' group delay over frequency ranges where its phase response is positively-sloped. If a signal is [[band-limited]] within some maximum frequency B, then it is predictable to a small degree (within time periods smaller than {{Fraction|1|B}}). A filter whose group delay is negative over that signal's entire frequency range is able to use the signal's predictability to provide an illusion of a non-causal time advance. However, if the signal contains an unpredictable event (such as an abrupt change which makes the signal's spectrum exceed its band-limit), then the illusion breaks down.<ref name="Bariska" /> Circuits with negative group delay (e.g., Figure 2) are possible, though [[causality]] is not violated.<ref name="NakanishiSugiyamaKitan2002" />

Negative group delay filters can be made in both digital and analog domains. Applications include compensating for the inherent delay of low-pass filters, to create ''zero phase'' filters, which can be used to quickly detect changes in the trends of sensor data or stock prices.<ref name="CastorPerry" />