Digital Signal Processing Reference
In-Depth Information
If the band width of the band pass filter is set narrower and narrower by means of the
quality Q - z.B. Q = 6 and Q = 10 - and the steepness of the sides increases, the sweep
curve no longer shows the frequency response apparently because the
UP
has been
contravened. The output signal u
out
rather reflects the diffuse oscillations as a reaction to
the sweep signal but not the amplitude frequency response.
We can escape from this dead end thanks to a modicum of intelligence and better methods
(computer-assisted!). Apparently the bandpass signal of a higher quality Q has already
signalled by its behaviour in the time domain what transfer properties it has in the
frequency domain. It has to some extent shown by its behaviour in its transient response
(in the time domain) what its behaviour in the frequency domain will be.
This should be stated more precisely. By means of the sweep signal gradually (altogether
t = 1s) all the frequencies - sinusoidal signals - of the frequency range to be examined
with a constant amplitude are directed to the input. The output signal must contain all the
frequencies with a certain uncertainty, which have passed the bandpass filter with a
certain strength (amplitude) and phase shift.
Û
out
should therefore be subjected to an FT by means of the computer. The result is
shown in Illustration 106. The “erroneous” sweep curve “distorted” by transient
responses in the frequency domain apparently shows the frequency response of the
narrow band pass represented as an amplitude spectrum. According to this the information
is contained in the output signal u
out
- but this information can only be recognised via an
FT.
Preliminary conclusions:
•
The transmission features of circuits/components/systems can only
be deduced inaccurately and in a very time-consuming way with
traditional measuring instruments - analog function generator and
analog oscilloscope.
•
Above all the possibility to use FT and IFT (inverse FT) is lacking.
This is however easily possible with the digital signal processing sys-
tem (DSP) by means of the computer.
•
There is only one correct path from the time domain to the frequency
domain and vice versa - FT and IFT!
The future of modern signal generation and processing and the analysis of signals and
systems lies therefore in computer-aided digital signal processing (DSP). Analog signals
can be stored digitally and evaluated according to the desired criteria and represented
graphically by means of a straightforward sound card and the DASY
Lab
S-version.
Modern test signals
In this age of computer-based signal processing other test signals are gaining in practical
significance on account of their theoretical importance because each theoretical
mathematical process can be implemented in a real sense via a certain progam algorithm.
