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© Semiconductor Components Industries, LLC, 2009
April, 2009 − Rev. 0
1 Publication Order Number:
AND8382/D
AND8382/D
WOLA Filterbank
Coprocessor: Introductory
Concepts and Techniques
This tutorial is applicable to: Toccata Plus™,
Orela® 4500 Series, BelaSigna® 2xx Series
This Application Note details the concepts of WOLA
filterbank processing and the configuration of the WOLA
filterbank coprocessor for any application. For the sake of
consistency, the example of a hearing aid application is used
throughout to demonstrate these concepts. However, the
WOLA filterbank coprocessor can be configured creatively
within it’s constraints to benefit a wide variety of audio and
other applications.
INTRODUCTION
This tutorial is dedicated to the WOLA filterbank
coprocessor, which is integrated in the SignaKlara® DSP
architecture. The goal of this document is to address the
theoretical aspects of the WOLA filterbank, and describe the
influence of each involved parameter. A good level of
understanding at signal processing level is required in order
for the user to properly select the appropriate filterbank
configuration in a specific application. Providing basic
concepts, extensive examples and illustrations, this text
guides the user in this task. The tutorial is organized in the
following manner:
Signal Processing Aspects:
• Multirate filterbanks: the tree−structured
decomposition, an introductive example
• Complex−modulation filterbank: original and
complex−bandpass interpretations
• Weighted overlap−add implementation: the WOLA
• Prototype filter design
Filterbank Design: Playing with the Filterbank Parameters
(Using the MATLAB® WOLA Toolbox)
• Typical hearing−aid configurations (16 bands)
• Configurations with refined frequency resolution
• Overlap−add configurations (short−term discrete fourier
transform)
• Performing FFTs with the WOLA filterbank
• Using special microcodes
SIGNAL PROCESSING ASPECTS
This section introduces the basic signal processing
principles involved in multirate filterbanks. As a starting
point, a simple tree−structured filterbank is described for
didactical purpose, going through basic concepts and
tackling the time−frequency duality in filterbanks. Then, the
complex−modulation filterbank solution is introduced,
showing both the original and the complex−bandpass
structures.
The WOLA filterbank, as integrated in the SignaKlara
architecture, is an efficient realization of the
complex−modulation filterbank, in its complex−bandpass
version. The following sections will describe the structure of
the WOLA filterbank and the design of the filters involved
in the processing. The filter design is an important aspect of
filterbanks.
Multirate Filterbanks: the Tree−Structured
Decomposition, an Introductive Example
In order to set the initial ideas, consider at first the simplest
approach in the filterbank theory, namely the
tree−structured filterbank. A tree−structured filterbank
splits the input time−domain signal into M sub−band signals,
using several cascaded stages of decomposition, as shown
on Figure 1 for M=4.
In the first decomposition stage, the input signal is split in
two time−domain signals, which are the respective results of
a low−pass and a high−pass filtering process. Both filters
have Fs/4 cut−off frequency (half−band filters). After
filtering, decimation can be applied to those two signals,
because their bandwidth is now reduced. Typically,
decimation by factor 2 is performed, setting the sampling
frequency of both signals to Fs’ = Fs/2. Doing so, and
assuming ideal filter characteristics, the sampling frequency
is reduced to its minimum. This is the critically−sampled
situation.
Then, for both sub−bands signals, a new stage of
decomposition can be performed, including half−band
filtering and decimation. In this way, four sub band are
obtained, with sub band signals having sampling
APPLICATION NOTE
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