Most of the computations
the hearing aid is performing
Novel Numerical Representations for Low-Power Audio Signal Processing
Roger Chamberlain*†, Yen Hsiang Chew*, Varuna DeAlwis*, Eric Hemmeter*,
John Lockwood*, Robert Morley*, Ed Richter*, Jason White*, and Huakai Zhang*
*School of Engineering and Applied Science, Washington University, St. Louis, MO
†Hearing Emulations, LLC and BECS Technology, Inc., St. Louis, MO
Power Is Used Charging Capacitance
Hearing Aid Architecture
Multiplication vs. Addition
We can see from these examples that many more bits are
needed to perform a multiplication than to perform an
Using a logarithmic representation of the
audio signals allows us to take advantage
of this difference in the effort to reduce
By using a logarithmic representation we can replace the multipliers with
log(A x B) = log(A) + log(B)
However, then the adder must be modified as well.
Lets start with this:
We want log(A+B),
Since this would be harder to calculate than the original multiplication and
addition, this function is performed by a look-up table.
To eliminate even more
unnecessary calculations, the look-up table is only accessed if the two inputs to
the “adder”, i.e., the log multiplier, are significant with respect to each other.
other words, if one of the values is small enough to be negligible then the look-
up is skipped and the larger number passed through, thus saving more power.
One of the major technical issues facing the designers of modern digital
hearing aids is the need to minimize the power consumption of the
system to prolong battery life.
As new signal processing techniques are
proposed, the computational requirements invariably grow, putting
additional pressure on power consumption.
In this work, we investigate
the use of non-standard numerical representations for the audio signals
being processed, showing how the power consumption can be lowered
for audio signal processing while maintaining (and even improving)
overall signal quality.