WaveWarp 2.0 Component
      
Multirate:
Functional Description
A special-purpose downsampler for storing the
high-frequency sub-band of a signal at half the input sample-rate.
(By comparison, a conventional downsampler
stores the
low-frequency sub-band of a signal at a reduced sample-rate.)
It uses a downsampler in combination with a high-pass (rather than
low-pass) IIR anti-aliasing filter.
The output sample rate is half the
input sample rate. This component is identical in function
to the high-frequency analysis
branch of a two-channel IIR filter bank (hence the name "Hi").
IMPORTANT: This component should be used with care. The output signal
cannot be treated as a "conventional" signal in the sense that
any processing performed on the signal may destroy the
possibility of re-constructing the original signal by later upsampling
via the IIR Hi UpSampler (the only upsampler appropriate for this purpose).
The component is most usefully employed in the construction of a multirate equaliser,
whereby only a simple gain factor is required in the way of signal processing,
and thus later signal reconstruction via the IIR Hi UpSampler is not adversely affected.
Algorithm
In the current implementation, the IIR high-pass
anti-aliasing filter is
"hard-wired" (i.e. cannot be changed by the user).
It is designed and implemented according to the method
described in
[VaCo]
(with a sign-change in the all-pass circuit to convert the design
from low-pass to high-pass).
Concerning the particulars of this method for the present
application, it is found that the use of two cascaded elementary
all-pass sections is sufficient for reasonable performance.
The downsampler implementation
is highly-efficient, since the use of all-pass subfilters allows
the system to be structured in polyphase form (not generally possible
for IIR filters)
such that the filtering is computed at the lower
(i.e. the output) sample rate. The end result is the same as if the
filtering was performed first (i.e. at the higher sample rate), followed
by the downsampling (retaining only every Mth filtered sample).
The real-time output from each polyphase IIR filter branch is computed by direct
evaluation of the cascaded all-pass elements.
See
[CrRa]
and
[StNg]
for a detailed treatment
of multirate signal processing.
For a specific discussion
on downsampling by an integer factor, see
section 2.3.2 of
[CrRa]
and chapters 1 & 3 of
[StNg].
For a specific discussion
on two-channel filter banks (FIR only), see
[StNg]
chapter 4.
For design methodologies for
IIR (recursive) filters suitable for sample rate conversion,
see, for example,
[VaCo],
[ReSa1],
and
[ReSa2].
Signal Implementations
| Audio signals | Control signals | Description |
|---|
| Single input mono single output mono | n/a | Converts the sample rate of the mono signal |
| Single input stereo single output stereo | n/a | Converts the sample rate of the stereo signal |
Related components:
Example DrawingBoards illustrating usage:
|
