Image Processing Reference
In-Depth Information
The intuitive reason that determines the benefits of EIA is simple. Since EIA is capable of
processing large sets of data in a single interval-based simulation, the results are obtained
faster than in the separate computation of the numerical samples. Although the use of
intervals imposes a limitation of connectivity on the computation of the results, both the
speed and the accuracy are improved with respect to the numerical processing of the same
number of samples.
Section 3.1 discusses the cancellation problem in the analysis of digital filter structures using
IA, and justifies the selection of AA for such analysis, indicating the cases in which it can be
used, and under what types of restrictions. Section 3.2 examines how the Fourier Transform
is affected when uncertainties are included in one or all of the samples. Section 3.3 evaluates
the changes that occur in the parameters of the random signals (mean, variance and
Probability Density Function (PDF)) when a specific width is introduced in the samples, and
how these changes affect the computed estimates using the Monte-Carlo method. Finally,
Section 3.4 provides a brief discussion to highlight the capabilities of interval-based
simulations.
3.1 Analysis of digital filter structures using IA and AA
The main problem that arises when performing interval-based analyses of DSP systems
using IA is that the addition and subtraction operations always increase the interval widths.
If there are variables that depend on other variables through two or more different paths,
such as in z ( k ) = x ( k ) - x ( k ), the ranges provided by IA are oversized. This problem, called the
cancellation problem, is particularly severe when there are feedback loops in the
realizations, a characteristic which is common in most DSP systems.
Oversizing with IA
Signal names
and initial values
y
x
y
x
sv1
sv1
sv1
sv1
z 1
z 1
z 1
z 1
t sum
t sum
t sum
a 1 = 1
a 1 = 1
t a 1
t a 1
t a 1
sv2
sv2
sv2
z 1
z 1
z 1
z 1
a 2 = 0.75
a 2 = 0.75
t a 2
t a 2
t a 2
(a) (b)
Fig. 2. Interval oversizing due to the cancellation effect of IA: (a) Signal names and initial
(interval) values. (b) Computed intervals until the oversizing in the variable t sum is
detected. In each small figure, the abscissa axis represents the sampled time, and the
ordinate axis represents the interval values. A dot in a given position represents the
interval [0,0].
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