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| [[File:High accuracy settling time measurements figure 1.png|thumb|An illustration of overshoot, followed by [[ringing (signal)|ringing]] and [[settle time]].]] | | Ugg Boots are created using traditional wool and sheep sales. When not cleaned properly, not so nice to see and [http://tinyurl.com/nqbkz6z cheap ugg boots] boots need cleaning from time to time. Thomas Sabo OnlineshopThere are some cleaning techniques and methods that are practical and useful for making clean uggs and glitter. Combining these techniques will give you clean ugg boots and a longer life for your uggs.<br><br> |
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| In [[signal processing]], [[control theory]], [[electronics]], and [[mathematics]], '''overshoot''' is when a signal or function exceeds its target. It arises especially in the [[step response]] of [[bandlimited]] systems such as [[low-pass filter]]s. It is often followed by [[ringing (signal)|ringing]], and at times conflated with this latter.
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| ==Definition==
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| Maximum overshoot is defined in Katsuhiko Ogata's ''Discrete-time control systems'' as "the maximum peak value of the response curve measured from the desired response of the system."<ref>{{Cite book| title = Discrete-time control systems | first = Katsuhiko | last = Ogata | publisher = Prentice-Hall | year = 1987 | isbn = 0-13-216102-8 | page = 344}}</ref>
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| ==Control theory==
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| In [[control theory]], '''overshoot''' refers to an output exceeding its final, steady-state value.<ref name=Kuo>
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| {{cite book
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| |author=Kuo, Benjamin C & Golnaraghi M F
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| |title=Automatic control systems
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| |edition=Eighth edition
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| |page=§7.3 p. 236–237
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| |year= 2003
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| |publisher=Wiley
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| |location=NY
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| |isbn=0-471-13476-7
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| |url=http://worldcat.org/isbn/0471134767}}
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| </ref> For a [[step response|step input]], the '''percentage overshoot''' (''PO'') is the maximum value minus the step value divided by the step value. In the case of the unit step, the ''overshoot'' is just the maximum value of the step response minus one. Also see the definition of '''overshoot''' in an [[#Electronics|electronics context]]. <!-- I'll try to remember to generate an image when I'm at work tomorrow, but I might not get back to this for days. Feel free to do as you see fit -->
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| The percentage overshoot is a function of the [[Damping ratio]] ζ and is given by <ref>Modern Control Engineering (3rd Edition), Katsuhiko Ogata, page 153.</ref>
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| :<math> PO = 100\% \cdot e^{\left ({\frac{-\zeta \pi}{\sqrt{1-\zeta^2}}}\right )}</math> | |
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| The damping ratio can also be found by
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| :<math> \zeta = \sqrt{\frac{(\ln \frac{PO}{100%})^2}{\pi^2+(\ln \frac{PO}{100%})^2}} </math>
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| ==Electronics==
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| [[File:clock signal.gif|300 px|thumb|Overshoot and undershoot in [[electronics|electronic]] [[Signal (electrical engineering)|signal]].]]
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| In electronics, '''overshoot''' refers to the transitory values of any parameter that exceeds its final (steady state) value during its transition from one value to another. An important application of the term is to the output signal of an amplifier.<ref name=Allen>
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| {{cite book
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| |author=Phillip E Allen & Holberg D R
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| |title=CMOS analog circuit design
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| |edition=Second edition
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| |page=Appendix C2, p. 771
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| |year= 2002
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| |publisher=Oxford University Press
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| |location=NY
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| |isbn=0-19-511644-5
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| |url=http://worldcat.org/isbn/0-19-511644-5
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| |nopp=true}}
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| </ref>
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| ''Usage'': Overshoot occurs when the transitory values exceed final value. When they are lower than the final value, the phenomenon is called ''"undershoot"''.
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| A [[electrical network|circuit]] is designed to minimize [[risetime]] while containing [[distortion]] of the [[Signalling (telecommunication)|signal]] within acceptable limits.
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| #Overshoot represents a [[distortion]] of the signal.
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| #In circuit design, the goals of minimizing overshoot and of decreasing circuit [[risetime]] can conflict.
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| #The magnitude of overshoot depends on time through a phenomenon called ''"[[damping]]."'' See illustration under [[Step_response#Results|step response]]''.
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| #Overshoot often is associated with [[settling time]], how long it takes for the output to reach steady state; see [[Step_response#Control_of_settling_time|step response]].
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| Also see the definition of '''overshoot''' in a [[#Control theory|control theory context]].
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| ==Mathematics==
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| [[File:Sine integral.svg|thumb|The [[sine integral]], demonstrating overshoot.]]
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| {{main|Gibbs phenomenon}}
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| In the approximation of functions, '''overshoot''' is one term describing quality of approximation. When a function such as a square wave is represented by a summation of terms, for example, a [[Fourier series]] or an expansion in [[orthogonal polynomials]], the approximation of the function by a truncated number of terms in the series can exhibit overshoot, undershoot and [[ringing (signal)|ringing]]. The more terms retained in the series, the less pronounced the departure of the approximation from the function it represents. However, though the period of the oscillations decreases, their amplitude does not;<ref name=Folland>
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| {{cite book
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| |author=Gerald B Folland
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| |title=Fourier analysis and its application
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| |pages=60–61
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| |year= 1992
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| |publisher=Wadsworth: Brooks/Cole
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| |location=Pacific Grove, Calif.
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| |isbn=0-534-17094-3
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| |url=http://worldcat.org/isbn/0-534-17094-3}}
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| </ref> this is known as the [[Gibbs phenomenon]]. For the [[Fourier transform]], this can be modeled by approximating a [[step function]] by the integral up to a certain frequency, which yields the [[sine integral]]. This can be interpreted as convolution with the [[sinc function]]; in [[#Signal processing|signal processing terms]], this is a [[low-pass filter]].
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| ==Signal processing==
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| [[File:Usm-unsharp-mask.png|thumb|Overshoot (bottom of image), caused by using [[unsharp masking]] to sharpen an image.]]
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| [[File:Sine integral.svg|thumb|The [[sine integral]], which is the [[step response]] of an ideal low-pass filter.]]
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| [[File:Sinc function (normalized).svg|thumb|The [[sinc function]], which is the [[impulse response]] of an ideal low-pass filter.]] | |
| {{details|Ringing artifacts}}
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| In [[signal processing]], overshoot is when the output of a [[Filter (signal processing)|filter]] has a higher maximum value than the input, specifically for the [[step response]], and frequently yields the related phenomenon of [[ringing artifacts]].
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| This occurs for instance in using the [[sinc filter]] as an ideal ([[brick-wall filter|brick-wall]]) [[low-pass filter]]. The step response can be interpreted as the [[convolution]] with the [[impulse response]], which is a [[sinc function]].
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| The overshoot and undershoot can be understood in this way: kernels are generally normalized to have integral 1, so they send constant functions to constant functions – otherwise they have [[gain]]. The value of a convolution at a point is a [[linear combination]] of the input signal, with coefficients (weights) the values of the kernel. If a kernel is non-negative, such as for a [[Gaussian kernel]], then the value of the filtered signal will be a [[convex combination]] of the input values (the coefficients (the kernel) integrate to 1, and are non-negative), and will thus fall between the minimum and maximum of the input signal – it will not undershoot or overshoot. If, on the other hand, the kernel assumes negative values, such as the sinc function, then the value of the filtered signal will instead be an [[affine combination]] of the input values, and may fall outside of the minimum and maximum of the input signal, resulting in undershoot and overshoot.
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| Overshoot is often undesirable, particularly if it causes [[Clipping (signal processing)|clipping]], but is sometimes desirable in image sharpening, due to increasing [[acutance]] (perceived sharpness).
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| == Related concepts ==
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| A closely related phenomenon is [[ringing (signal)|ringing]], when, following overshoot, a signal then falls ''below'' its steady-state value, and then may bounce back above, taking some time to settle close to its steady-state value; this latter time is called the [[settle time]].
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| In [[ecology]], [[overshoot (ecology)|overshoot]] is the analogous concept, where a population exceeds the carrying capacity of a system.
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| ==See also==
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| *[[Step response]]
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| *[[Ringing (signal)]]
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| *[[Settle time]]
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| *[[Damping]]
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| *[[Overmodulation]]
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| *[[Integral windup]]
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| ==References and notes==
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| <references/>
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| [[Category:Transient response characteristics]]
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| [[Category:Control theory]]
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