5.3 Methods for Analysis and Processing of Discrete Biosignals

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175

Fig. 5.18: Discrete-time impulse response with a period length Np: Discrete impulse response g(n)

with N = 4 values (top), impulse response gp(n), Np = 4 without g(n) overlap (middle), impulse

response gp(n), Np = 3 with g(n) overlap (bottom).

Then for the finite output signal y(n) according to Equation 5.51 we obtain:

y(0) = x(0)gp(0) + x(1)gp(2) + x(2)gp(1) = 3.125

y(1) = x(0)gp(1) + x(1)gp(0) + x(2)gp(2) = 2.75

y(2) = x(0)gp(2) + x(1)gp(1) + x(2)gp(0) = 2.25 ,

respectively for the vectors x, y and the matrix cycl{gp}:

[[

[

y(0)

y(1)

y(2)

]]

]

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

y

= ^[[

[

gp(0)

gp(2)

gp(1)

gp(1)

gp(0)

gp(2)

gp(2)

gp(1)

gp(0)

]]

]

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

Zykl{gp}

󳐂^[[

[

x(0)

x(1)

x(2)

]]

]

⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟⏟

x

= ^[[

[

3.125

2.75

2.25

]]

]

.

5.3.2 Signal Analysis in the Frequency Domain

In section 5.2 various transformations (especially the Fourier-transformations) were

described with which a signal can be described not only as a function of time but