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Overshoot (signal)


In signal processing, control theory, electronics, and mathematics, overshoot is the occurrence of a signal or function exceeding its target. It arises especially in the step response of bandlimited systems such as low-pass filters. It is often followed by ringing, and at times conflated with the latter.

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."

In control theory, overshoot refers to an output exceeding its final, steady-state value. For a 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 context.

The percentage overshoot is a function of the Damping ratio ζ and is given by

The damping ratio can also be found by

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.

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

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

Also see the definition of overshoot in a control 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, 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. 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; 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 terms, this is a low-pass filter.


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