Insignal processing,control theory,electronics, andmathematics,overshoot is the occurrence of a signal or function exceeding its target.Undershoot is the same phenomenon in the opposite direction. It arises especially in thestep response ofbandlimited systems such aslow-pass filters. It is often followed byringing, and at times conflated with the latter.

Maximum overshoot is defined in Katsuhiko Ogata'sDiscrete-time control systems as "the maximum peak value of the response curve measured from the desired response of the system."^[1]

Incontrol theory, overshoot refers to an output exceeding its final, steady-state value.^[2] For astep input, thepercentage overshoot (PO) is the maximum value minus the step value divided by the step value. In the case of the unit step, theovershoot is just the maximum value of the step response minus one. Also see the definition ofovershoot in anelectronics context.

For second-order systems, the percentage overshoot is a function of thedamping ratioζ and is given by^[3]

${\displaystyle \mathrm{P}\mathrm{O}=100\exp \left(\frac{-\zeta \pi }{\sqrt{1-{\zeta }^2}}\right)}$

The damping ratio can also be found by

${\displaystyle \zeta =\frac{-\ln \left(\frac{\mathrm{P}\mathrm{O}}{100}\right)}{\sqrt{{\pi }^2+{\ln }^2\left(\frac{\mathrm{P}\mathrm{O}}{100}\right)}}}$

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.^[4]

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

Acircuit is designed to minimizerise time while containingdistortion of thesignal within acceptable limits.

1. Overshoot represents adistortion of the signal.
2. In circuit design, the goals of minimizing overshoot and of decreasing circuitrise time can conflict.
3. The magnitude of overshoot depends on time through a phenomenon called"damping." See illustration understep response.
4. Overshoot often is associated withsettling time, how long it takes for the output to reach steady state; seestep response.

Also see the definition ofovershoot in acontrol theory context.

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, aFourier series or an expansion inorthogonal polynomials, the approximation of the function by a truncated number of terms in the series can exhibit overshoot, undershoot andringing. 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;^[5] this is known as theGibbs phenomenon. For theFourier transform, this can be modeled by approximating astep function by the integral up to a certain frequency, which yields thesine integral. This can be interpreted as convolution with thesinc function; insignal processing terms, this is alow-pass filter.

Insignal processing, overshoot is when the output of afilter has a higher maximum value than the input, specifically for thestep response, and frequently yields the related phenomenon ofringing artifacts.

This occurs for instance in using thesinc filter as an ideal (brick-wall)low-pass filter. The step response can be interpreted as theconvolution with theimpulse response, which is asinc function.

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 havegain. The value of a convolution at a point is alinear combination of the input signal, with coefficients (weights) the values of the kernel. If a kernel is non-negative, such as for aGaussian kernel, then the value of the filtered signal will be aconvex 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 anaffine combination of the input values, and may fall outside of the minimum and maximum of the input signal, resulting in undershoot and overshoot.

Overshoot is often undesirable, particularly if it causesclipping, but is sometimes desirable in image sharpening, due to increasingacutance (perceived sharpness).

A closely related phenomenon isringing, when, following overshoot, a signal then fallsbelow 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 thesettle time.

Inecology,overshoot is the analogous concept, where a population exceeds thecarrying capacity of a system.

• Step response
• Ringing (signal)
• Settling time
• Overmodulation
• Integral windup

• Percentage overshoot calculator

• Transient response characteristics
• Classical control theory

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