WaveWarp 2.0 Component
      
Multirate:
Functional Description
A special-purpose upsampler for re-constructing the
high-frequency sub-band of a signal which
has been previously downsampled to half the original sample-rate.
(By comparison, a conventional upsampler
restores the previously-downsampled
low-frequency sub-band of a signal to its original sample-rate.)
It uses an upsampler in combination with a high-pass (rather than
low-pass) IIR anti-aliasing filter.
The output sample rate is twice the
input sample rate. This component is identical in function
to the high-frequency synthesis
branch of a two-channel IIR filter bank (hence the name "Hi").
IMPORTANT: This component should be used with care.
It should not be used to upsample
an arbitrary signal. Rather, it should only be used to upsample a
signal which has been previously downsampled via the
high-frequency analysis branch of a compatible two-channel filter bank (i.e.
originating
from the output of an IIR Hi DownSampler or from the first output
of an IIR HiLo DownSampler).
It is most usefully employed in the construction of a multirate equaliser
when only a simple gain factor has been applied in the way of signal
processing on the downsampled high-frequncy sub-band,
so that the signal reconstruction has not been 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 upsampler 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 last (i.e. at the higher sample rate), preceded
by the upsampling (inserting (M-1) zero-valued
samples between successive inputs). 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 upsampling 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:
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