VTI Instruments Corp.
320
EX1629 Filtering
The Matched Z-transform
Under most circumstances, the BLT is superior to the matched Z-transform (MZT).
The
principal disadvantage of the BLT is that the frequency scale is “warped” so that, for a low-pass
filter:
0 Hz
In the analog domain maps to 0 Hz in the digital domain
f
c
In the analog domain maps to
f
c
in the digital domain
∞ Hz
In the analog domain maps to
f
s
/2 in the digital domain
where
f
c
is the corner frequency and
f
s
is the sampling frequency
Typically, this is what is desired of a low-pass or bandpass filter: a response which is exactly zero
at the Nyquist frequency (
f
s
/2). For a high-pass filter, a response equal to unity at this frequency is
also desirable.
The one exception to this is the Bessel filter. The advantage of a Bessel filter over a Butterworth
or Chebyshev filter is that the phase response is nearly linear throughout the passband (the group
delay is almost constant throughout the passband). The “warping” inherent in the BLT method
upsets this linearity. The MZT does not warp the frequency scale, so a digital Bessel filter
designed by this method will have a near-linear phase characteristic.
In fact, a low-pass filter designed by MZT is impulse-invariant with the analog prototype. With
the same impulse response, it behaves identically to the corresponding analog filter. This stands
true only if aliasing is ignored. If the response of the digital low-pass filter is not negligible at
f
s
/2,
the response in the vicinity of this frequency will be disturbed by the spurious response at
frequencies above
f
s
/2, which are folded down into the band below
f
s
/2. This is why it is advisable
to check the frequency response graphs carefully if this method is used.
A further advantage of the MZT is that the number of zeros is reduced, in comparison with the
BLT. A low-pass filter designed by MZT has no
z
-plane zeros.
To summarize: matched Z-transform may be used if:
a Bessel filter is required with an optimally linear phase response; or
efficiency is more of a concern than the quality of the frequency response.
Содержание EX1629
Страница 310: ...VTI Instruments Corp 310 EX1629 Command Set...
Страница 342: ...VTI Instruments Corp 342 EX1629 Onboard Memory...