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In control theory the impulse response is the response of a system to a Dirac delta input. This proves useful in the analysis of dynamic systems; the Laplace transform of the delta function is 1, so the impulse response is equivalent to the inverse Laplace transform of the system's transfer function.
If a system initially rests at its equilibrium position, from where it is acted upon by a unit-impulse at the instance t=0, i.e., p(t) in the equation above is a Dirac delta function δ(t), () = | = =, then by solving the differential equation one can get a fundamental solution (known as a unit-impulse response function)
A short to moderate length FIR or infinite impulse response (IIR) filter can compensate for the falling slope of a CIC filter's shape. [5] Multiple interpolation and decimation rates can reuse the same set of compensation FIR coefficients, since the shape of the CIC's main lobe changes very little when the decimation ratio is changed. [5 ...
Use an exponential function as the impulse response for the support region of positive values as before. In this double-sided filter, also implement another exponential function. The opposite in signs of the powers of the exponent is to maintain the non-infinite results when computing the exponential functions.
The point spread function (PSF) describes the response of a focused optical imaging system to a point source or point object. A more general term for the PSF is the system's impulse response; the PSF is the impulse response or impulse response function (IRF) of a focused optical imaging system. The PSF in many contexts can be thought of as the ...
The impulse response can be computed to any desired degree of accuracy by choosing a suitable approximation for δ, and once it is known, it characterizes the system completely. See LTI system theory § Impulse response and convolution. The inverse Fourier transform of the tempered distribution f(ξ) = 1 is the delta function.
The time-domain impulse response can be shown to be given by: = where () is the unit step function. It can be seen that () is non-zero for all , thus an impulse response which continues infinitely. IIR filter example
The sinc function, the impulse response for an ideal low-pass filter, illustrating ringing for an impulse. The Gibbs phenomenon, illustrating ringing for a step function.. By definition, ringing occurs when a non-oscillating input yields an oscillating output: formally, when an input signal which is monotonic on an interval has output response which is not monotonic.