Digital Signal Processing Reference
In-Depth Information
Together with addition and multiplication by a constant, delay forms a triad of elemental
signal processing. If you take a closer look, many extremely complex (linear) processes
merely consist of a combination of these three basic processes. A good example are digital
filters. Chapter 10 will demonstrate exactly how they work and how they are designed.
Differentiation
Differential and integral calculus are where „higher mathematics“ is generally thought to
begin. Both types of calculus are important because the most important natural laws and
technological relationships can only be modelled by using this.
But do not worry - we will not use formal mathematics. This forces us to describe the
substance of a problem and not simply point casually to „trivial“ mathematics.
You should therefore simply recognise by means of Illustration 127 what differentiation
as a technical signal process in the time domain actually means. Try to answer the
following questions:
•
At what points of time of u
in
do local maxima and minima occur in the
case of the differentiated signal u
out
•
What property does the input signal u
in
have at these points of time?
•
At what points of time of u
in
is the differentiated signal u
out
equivalent
to zero?
•
What property does the input signal u
in
have at these points of time?
•
In what way does u
in
differ at the places where u
out
has a positive local
maximum and a „negative local maximum“ (equal to a local
minimum)?
You should arrive at the following result:
The differentiated signal u
out
indicates how rapidly the input
signal u
in
is
changing
.
By way of example two of the most important laws of electrical engineering will be
mentioned in this context.
Law of induction
:
The faster current changes in a coil the greater the induced
voltage.
Law of capacity
:
The faster the voltage at the capacitor changes the greater the
current that flows in or out (charging current or discharge
current of a capacitor).
