Simulation of Dynamic Systems with MATLAB® and Simulink®, 3rd Edition

4.5Frequency Response of LTI Continuous-Time Systems

The response of LTI continuous-time systems to sinusoidal inputs is of interest because it provides an alternative to time domain methods based on the impulse response function to characterize the system’s dynamics. A nonperiodic signal f(t) can be resolved into sinusoidal functions over a continuum of frequencies according to Jackson (1991)

$f (t) = \frac{1}{2 π} \int_{- \infty}^{\infty} F (j ω) e^{j ω t} d ω$	(4.295)

where the sinusoidal functions are the complex exponentials

$e^{j} ω t = cos ω t + j sin ω t (- \infty < ω < \infty)$	(4.296)

and the function F(jω) is given by

$F (j ω) = \int_{- \infty}^{\infty} f (t) e^{j ω t} d t$	(4.297)

The complex-valued function F(jω) is called the Fourier integral or Fourier transform of the signal f(t). Entire books have been written on the ...

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