User`s guide

Transforming Between D iscrete-Time and Continuous-Time Representations
A delay in the discrete-time model that corresponds to an actual delay in the
continuous-time model is stored in the in the
InputDelay property of the
resulting continuous-time model. Typically, this
InputDelay is (nk-1)/Ts,
where
nk is the delay of the discrete-time system a nd Ts is the sampling
interval.
Note Unlike for discrete-time models, the nk property of continuous-time
model is only used to flag when immediate response to s te p changes is present;
nk is not u sed to store input delays greater than or equal to 1. When nk(i)=0,
then there is an immediate response to a step change in the input
ith. When
nk(i)=1, then there is no immediate response to the input.
Effects on the Noise Model
c2d, d2c,andd2d change the sampling interval of both the dynamic model and
the noise model. Resampling a m odel affects the variance of its noise model.
A parametric noise model is a time -se ries model with the follow ing
mathematical description:
yt Hqet
Ee
() ( ) ()=
=
2
λ
The n oise spectrum is computed by the following discrete-time equation:
Φ
v
iT
TH e()ωλ
ω
=
()
2
where
λ
is the variance of the white noise e(t),and
λT
represents the spectral
density of e(t). Resampling the noise model preserves the spectral density
λ
T
. The spectral density
λ
T is invariant up to the Nyquist f requency. For more
information about spectrum normalization, see “Understanding Spectrum
Normalization” on page 3-11.
d2d resampling of the noise model affects simulations w ith noise using
sim. If you resample a m odel to a faster sampling rate, simulating this
model results in higher noise level. This higher noise level results from the
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