overshoot (signal) - wikipedia, the free encyclopedia

An illustration of overshoot, followedby ringing and settle time.

Overshoot (signal)From Wikipedia, the free encyclopedia

In signal processing, control theory, electronics,and mathematics, overshoot is when a signal orfunction exceeds its target. It arises especially inthe step response of bandlimited systems such aslow-pass filters. It is often followed by ringing,and at times conflated with this latter.

Contents1 Definition2 Control theory3 Electronics4 Mathematics5 Signal processing6 Related concepts7 See also8 References and notes

DefinitionMaximum Overshoot (signal) is defined in Katsuhiko Ogata's Discrete-time controlsystems as "the maximum peak value of the response curve measured from the desiredresponse of the system."[1]

Control theory

In control theory, overshoot refers to an output exceeding its final, steady-state value.[2]

For a step input, the percentage overshoot (PO) is the maximum value minus the stepvalue divided by the step value. In the case of the unit step, the overshoot is just themaximum value of the step response minus one. Also see the definition of overshoot in anelectronics context.

The percentage overshoot is a function of the Damping ratio ζ and is givenby[citation needed]

10/3/2012 Overshoot (signal) - Wikipedia, the free …

en.wikipedia.org/wiki/Overshoot_(signal) 1/5

Overshoot and undershoot in electronic signal.

The damping ratio can also be found by

ElectronicsIn electronics, overshoot refers tothe transitory values of any parameterthat exceeds its final (steady state)value during its transition from onevalue to another. An importantapplication of the term is to theoutput signal of an amplifier.[3]

Usage: Overshoot occurs when thetransitory values exceed final value.When they are lower than the finalvalue, the phenomenon is called"undershoot".

A circuit is designed to minimizerisetime while containing distortion of the signal within acceptable limits.

1. Overshoot represents a distortion of the signal.2. In circuit design, the goals of minimizing overshoot and of decreasing circuit

risetime can conflict.3. The magnitude of overshoot depends on time through a phenomenon called

"damping." See illustration under step response.4. Overshoot often is associated with settling time, how long it takes for the output to

reach steady state; see step response.

Also see the definition of overshoot in a control theory context.

MathematicsMain article: Gibbs phenomenon

In the approximation of functions, overshoot is



The sine integral, demonstratingovershoot.

Overshoot (bottom of image), causedby using unsharp masking to sharpenan image.

The sine integral, which is the step

one term describing quality of approximation.When a function such as a square wave isrepresented by a summation of terms, forexample, a Fourier series or an expansion inorthogonal polynomials, the approximation of thefunction by a truncated number of terms in theseries can exhibit overshoot, undershoot andringing. The more terms retained in the series, theless pronounced the departure of theapproximation from the function it represents.However, though the period of the oscillations decreases, their amplitude does not;[4] thisis known as the Gibbs phenomenon. For the Fourier transform, this can be modeled byapproximating a step function by the integral up to a certain frequency, which yields thesine integral. This can be interpreted as convolution with the sinc function; in signalprocessing terms, this is a low-pass filter.

Signal processingFor more details on this topic, see Ringingartifacts.

In signal processing, overshoot is when the outputof a filter has a higher maximum value than theinput, specifically for the step response, andfrequently yields the related phenomenon ofringing artifacts.

This occurs for instance in using the sinc filter asan ideal (brick-wall) low-pass filter. The stepresponse can be interpreted as the convolutionwith the impulse response, which is a sincfunction.

The overshoot and undershoot can be understoodin this way: kernels are generally normalized tohave integral 1, so they send constant functions toconstant functions – otherwise they have gain.The value of a convolution at a point is a linearcombination of the input signal, with coefficients(weights) the values of the kernel. If a kernel isnon-negative, such as for a Gaussian kernel, thenthe value of the filtered signal will be a convex



The sine integral, which is the stepresponse of an ideal low-pass filter.

The sinc function, which is theimpulse response of an ideal low-passfilter.

combination of the input values (the coefficients(the kernel) integrate to 1, and are non-negative),and will thus fall between the minimum andmaximum of the input signal – it will notundershoot or overshoot. If, on the other hand,the kernel assumes negative values, such as thesinc function, then the value of the filtered signalwill instead be an affine combination of the inputvalues, and may fall outside of the minimum andmaximum of the input signal, resulting inundershoot and overshoot.

Overshoot is often undesirable, particularly if itcauses clipping, but is sometimes desirable inimage sharpening, due to increasing acutance(perceived sharpness).

Related conceptsA closely related phenomenon is ringing, when, following overshoot, a signal then fallsbelow its steady-state value, and then may bounce back above, taking some time to settleclose to its steady-state value; this latter time is called the settle time.

In ecology, overshoot is the analogous concept, where a population exceeds the carryingcapacity of a system.

See alsoStep responseRinging (signal)Settle timeDampingOvermodulationIntegral windup

References and notes1. ^ Ogata, Katsuhiko (1987). Discrete-time control systems. Prentice-Hall. p. 344. ISBN 0-

13-216102-8.2. ^ Kuo, Benjamin C & Golnaraghi M F (2003). Automatic control systems

(http://worldcat.org/isbn/0471134767) (Eighth edition ed.). NY: Wiley. p. §7.3 p. 236–237.ISBN 0-471-13476-7. http://worldcat.org/isbn/0471134767.



3. ^ Phillip E Allen & Holberg D R (2002). CMOS analog circuit design(http://worldcat.org/isbn/0-19-511644-5) (Second edition ed.). NY: Oxford UniversityPress. Appendix C2, p. 771. ISBN 0-19-511644-5. http://worldcat.org/isbn/0-19-511644-5.

4. ^ Gerald B Folland (1992). Fourier analysis and its application(http://worldcat.org/isbn/0-534-17094-3) . Pacific Grove, Calif.: Wadsworth: Brooks/Cole.pp. 60–61. ISBN 0-534-17094-3. http://worldcat.org/isbn/0-534-17094-3.

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