Digital Signal Processing Reference
In-Depth Information
Exercises on chapter 10
Exercise 1
What difference between an analog and a digital filter is immediately striking?
Exercise 2
(a)
Which components in an analog filter determine its frequency-dependent behaviour
and how can this be described?
(b)
Why are there no high-quality analog filters?
(c)
Where is it certain that analog filters will be used in future?
Exercise 3
(a)
Describe the structure and way of functioning of the FFT filter consisting of three
components (modules)
(b)
What must be taken into account in the case of the FFT filter to make sure that the
desired conducting state region of the filter is set correctly.
(c)
Why does the selectivity or edge steepness of the FFT filter extend to the physical
limit imposed by the Uncertainty Principle?
(d)
What are the advantages and disadvantages of the FFT filter?
Exercise 4
Experiment with the bandpass circuit as in Illustration 206 and establish how the envelope
(Si-function) and the mid-frequency changes with the pulse response. How can the filter
properties of the bandpass be seen clearly from the pulse response in the time domain?
Exercise 5
At first glance the FFT filters appear not to be “causal” as the output signal - the pulse
response - seems to appear before the input signal - the
δ
-pulse - appears at the output.
Why can the computer not do this differently?
Exercise 6
(a)
What idea leads to the digital signal which filters directly in the time domain and
thus avoids transformation into the frequency domain and back again my means of
the FFT?
(b)
Explain the principle of digital filters on the basis of the overlapping of Si-shaped
pulse responses of all discrete measurements (see Illustration 209).
(c)
A filter restricts the bandwidth and for this reason a correspondingly long lasting
discrete pulse response also occurs in the case of digital filters. What signalling
processes are required to produce a longer lasting discrete pulse response
“artificially” from a
δ
-pulse?
