User Manual

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21.3 Reference
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h(t
)
H(ω
)
fout(t
)
Fout(ω
)
Output
fin(t
)
Fin(ω
)
Input
Stationary Linear System
Application of Fourier transform (transfer function, unit-impulse
response)
As an application of Fourier transform, this section describes a steady-state
response in a static linear system.
fin(t): time function of input (source signal)
fout(t): time function of output (response function)
h(t): unit impulse response of linear system
t,τ: time
fout(t) =
fin(τ)･h(t-τ)dτ
The relationship between the input and output is expressed as follows:
This indicates that the response of the linear system can be determined just
by knowing the unit impulse response h(t) of the system.
In the frequency domain, Fin(ω), Fout(ω), H(ω), and ω are defined as
follows
Fin(ω): Fourier transformation of fin(t)
Fout(ω): Fourier transformation of fout(t)
H(ω): Fourier transformation of h(t)
ω: Angular frequency
Fout (ω) = Fin(ω)･H(ω)
Therefore, when fin(t) and fout(t) are measured, the system transfer function
H(ω) and the unit impulse response h(t) can be obtained by performing an
FFT operation and an inverse FFT operation.