Hioki MR8827, Инструкция по эксплуатации

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A
14
FFT Definitions
Representing the above relationship on a complex flat surface produces the following figure.
Imaginary component
Real component
F(k)
ø(k)
│
F(k)
│
■ Linear Time-Invariant Systems
Consider a linear time-invariant (LTI) system y(n) that is a response to discrete time-domain signal x(n).
In such an LTI system, the following expression applies to any integer Ai when the response to xi(n) is
𝑦𝑦
𝑖𝑖
(𝑛𝑛) = 𝐿𝐿[𝑥𝑥
𝑖𝑖
(𝑛𝑛)] .
L
[
A
1
x
1
(
n
) +
A
2
x
2
(
n
)] =
A
1
y
1
(
n
) +
A
2
y
2
(
n
) ............................................. (6)
If the system function of an LTI system is
h(n), the input/output relationship can be obtained by the next
expression.
𝑦𝑦(𝑛𝑛) = ∑ ℎ(𝑛𝑛)𝑥𝑥(𝑛𝑛 − 𝑚𝑚) =
∞
𝑚𝑚=0
∑ ℎ(𝑛𝑛 − 𝑚𝑚)𝑥𝑥(𝑚𝑚)
∞
𝑚𝑚=−∞
.................... (7)
Therefore, when a unit impulse
δ
(
n) (which is 1 when n = 0, and 0 when n
≠ 0) is applied to
x(n), the input/
output relationship is:
y ( n ) = h ( n )
...................................................................................... (8)
This means that when the input signal is given as a unit impulse, the output is the LTI system characteristic
itself. The response waveform of a system to a unit impulse is called the impulse response .
On the other hand, when the discrete Fourier transforms of x(n), y(n) and h(n) are X(k), Y(k) and H(k),
respectively, expression (7) gives the following:
Y ( k ) = X ( k ) H ( k ) ............................................................................... (9)
H(k) is also called the transfer function, calculated from X(k) and Y(k). Also, the inverse discrete Fourier
transform function of H(k) is the unit impulse response h(n) of the LTI system.
The impulse response and transfer function of this instrument are calculated using the relationships of
expression (9).
Input
(Analysis channel 1)
Output
(Analysis channel 2)
x(n)
X(k)
y(n)
Y(k)
h(n)
H(k)
LTI System