According to impulse response theor

According to impulse response theory, when you apply a Dirac deltafunction to the input of a system, the output of the system is the impulseresponse. You can think of the Dirac delta function δ(x) as a function thathas the value of infinity for x = 0, the value zero elsewhere, and a totalintegral of one. However, generating an ideal Dirac delta function isunrealistic.If you apply an approximate impulse with a small duration to the input of asystem, the output of the system is the approximation of the impulseresponse of the system. The smaller the duration of the impulse, the closerthe output of the system is to the true impulse response. However, animpulse carries little energy and might not excite the system, and noisemight corrupt the output of the system. An impulse with a large amplitudeand duration can improve the signal-to-noise ratio of the output signal.However, the large amplitude impulse can damage the hardware of thesystem, and a long-duration impulse leads to inaccuracy. For these reasons,the System Identification Toolkit uses the least squares method and thecorrelation analysis method to estimate the impulse response.