System analysis - Signals, Processes, and Systems - page 146

Illustration 105: Frequency-dependent reaction of a bandpass filter to the sweep signal
The upper series shows the sweep signal which is connected in the same way with the input of three
bandpass filters. They all have the same mid-frequency (!), but are of different quality (2nd series Q = 3;
3rd series Q = 6 and 4th series Q = 10).
The sweep response u out of the three bandpass filters does not tell us very much. In the second series - of
BP with Q = 3 - it is apparently possible to to see exactly at what temporary frequency the bandpass filter
reacts most strongly, the amplitude curve seems to correspond to the frequency response of the filter.
In the third series the maximum is further to the right although the bandpass filter has not changed its
mid-frequency. The frequency seems unlike the sweep signal not to change from left to right. Finally, in the
lower series - of the BP with Q = 10) - the sweep response u out clearly has the same instantaneous
frequency over the whole period. The sweep response certainly does not reproduce the frequency response.
Thus, the circuit is gradually tested with all the frequencies of the frequency range with
which we are concerned here. In Illustration 104 the whole sweep signal is represented on
the screen, on the left the starting frequency and on the right the stop frequency. In this
way the curve of u out on the screen shows not only the time curve but also indirectly the
frequency response of the system under examination.
But careful! Never forget the Uncertainty Principle UP . The FOURIER transform of this
sweep signal shows the consequences of beginning a signal suddenly, changing rapidly
and ending abruptly. The sweep signal ought really to result in a clearly rectangular
frequency response. Hopefully, you now know that this is not possible. The faster the
sweep signal changes, the shorter the “ instantaneous frequency ” and the more inaccurate-
ly it is measured.