Digital Signal Processing Reference
In-Depth Information
Illustration 106:
Sweep - a method of measuring with pre-programmed errors
Here we see the three sweep signal responses from Illustration 105 once again. In the time domain they are
very different from each other; above all in the lower series “mysterious” effects occur.
By contrast the FT of these “spoilt” signals shows the frequency response very precisely; accordingly the
correct information on the frequency response must be present in u
out
(see next section: Transients). The
FT seems, therefore, to be the only suitable means of saying anything precise about the frequency
behaviour of a circuit/process. Now the signal in the lower series is easy to explain. As the bandpass filter
is extremely narrow here (
-
>
0) it can practically only let one frequency through - see bottom left -
and as a result of
UP
u
out
must also last longer.
As a result of
UP
the sweep method contains too many errors - unless measuring is carried out very slowly
- because the envelope possibly does not reflect the true amplitude curve. As can be seen on the right all
three band pass filters have the same mid- frequency 50Hz.
Δϕ
In Illustration 105 the sweep measurement is carried out using band pass filters with
different bandwidths or qualities Q. The quality Q of a simple band pass filter is a mea-
surement of the abililty to filter out in as narrow a band width as possible or a yardstick
for measuring the steepness of the sides of the filter. First a “poor quality” i.e broad width
band pass filter without steep sides (Q = 3) is swept. The frequency response can be
recognised here clearly via the amplitude curve. As a result of the large bandwidth
B =
Δ
f all the instantaneous frequencies were sufficiently long so that
Δϕ
∗ Δ
t
≥
1 was
fulfilled (
UP
).
Think of a curve which connects the upper maximum values (i.e. the amplitudes of the
“instantaneous frequencies”) with each other. This curve is intended to represent the
frequency response (of the amplitude) of the filter.
