Integral of Transfer function in Laplace domain

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I have a Transfer function of a system in Laplace domain(T(s)), I need to compute the absolute value to the power of two and integral from minus infinity to positive infinity in the frequency domain. ∫|T(jw)|²,from -ꚙ to +ꚙ Do anyone have any suggestion,Thanks

Answers (1)

Ayush Aniket
Ayush Aniket on 24 Dec 2024
To compute the integral of the squared magnitude of a transfer function over the frequency domain, you can use Parseval's theorem. This theorem relates the integral of the squared magnitude of a function in the time domain to the integral of its squared magnitude in the frequency domain.
Additionally, in the time domain, it is equivalent to the energy of the impulse response of the system. Here's how you can compute it in MATLAB:
% Assuming you have the transfer function (sys) defined using the tf function
% Compute the impulse response
[impulseResponse, time] = impulse(sys);
% Calculate the energy of the impulse response
energy = trapz(time, impulseResponse.^2);
The trapz function performs numerical integration to compute the energy of the impulse response, which corresponds to the integral of ∫|T(jw)|² over all frequencies.

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