Power Reduction by Varying Sampling Rate
William R. Dieter
Electrical and Computer
Engineering Department
University of Kentucky
Lexington, KY 40506–0046
dieter@engr.uky.edu
Srabosti Datta
Electrical and Computer
Engineering Department
University of Kentucky
Lexington, KY 40506–0046
sdatt1@engr.uky.edu
Wong Key Kai
Electrical and Computer
Engineering Department
University of Kentucky
Lexington, KY 40506–0046
kkwong0@uky.edu
ABSTRACT
The rate at which a digital signal processing (DSP) system
operates depends on the highest frequency component in the
input signal. DSP applications must sample their inputs at
a frequency at least twice the highest frequency in the in-
put signal (i.e., the Nyquist rate) to accurately reproduce
the signal. Typically a fixed sampling rate, guaranteed to
always be high enough, is used. However, an input signal
may have periods when the signal has little high frequency
content as well as periods of silence. When the input signal
has no perceptible high frequency components, the system
can reduce its sampling rate, thereby reducing the number
of samples processed per second, allowing the CPU speed to
be scaled down without reducing output quality. This paper
describes how to reduce power consumption in DSP appli-
cations by varying the amount of processing based on the
input signal, and reports results of experiments with a pro-
totype implementation. Experiments with a prototype show
that when the system performs little processing, the added
overhead of the variable sampling rate technique increased
power consumption. When the system performs more pro-
cessing, 18 FIR filters per frame, the power consumption was
reduced to 40 % of the power required for a static sampling
rate, while not reducing sound quality.
Categories and Subject Descriptors
C.3 [Special-Purpose and Application-Based Systems]:
Real-time and embedded systems; C.3 [Special-Purpose
and Application-Based Systems]: Signal processing sys-
tems; J.7 [Computers in Other Systems]: Real time
General Terms
Performance, Experimentation
Keywords
Power-aware, digital signal processing, frequency scaling,
voltage scaling, real-time audio
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1. INTRODUCTION
Digital signal processing (DSP) has found its way from
high-performance applications like radar systems, afford-
able only by a few, to consumer-level applications like cell
phones and power drills. Many of these new applications are
portable battery-powered devices. However, the usefulness
of these devices is limited by battery life, which depends on
the device’s power consumption.
Strategies for reducing power take advantage of opportu-
nities at all levels of system design from transistors all the
way up through the application software [15]. At the tran-
sistor level, the dynamic power consumed by a CMOS device
is proportional to the clock frequency and the square of the
supply voltage, i.e.:
P ∝ V
2
dd
f,
where V
dd
is the supply voltage, and f is the clock fre-
quency [9]. Halving the clock frequency without changing
V
dd
cuts power consumption in half, but does not affect the
total energy consumed.
Energy is the time integral of power, so energy consump-
tion is not reduced as long as the same number of clock
cycles are required to do the same work. However, reducing
clock frequency allows V
dd
to be reduced [3, 17] leading to
energy savings. Though static power is an increasing frac-
tion of total power, dynamic power is still the majority of
power consumed. Thus, varying frequency and voltage can
significantly reduce power and energy consumption.
The dynamic voltage (and frequency) scaling (DVS) al-
gorithms proposed in the literature [2, 5, 6, 13, 14] exploit
the relationship between power, voltage, and frequency to
reduce energy consumption. Typical real-time DVS algo-
rithms try to run the processor as slowly as possible while
still guaranteeing that all jobs meet their deadlines. This
strategy works well, especially when the average execution
times of jobs is less than their worst case execution times.
Though they can exploit slack produced by varying exe-
cution times, these algorithms do not directly change the
number of clock cycles required by each job.
Many DSP applications have a fairly simple structure
where a number of filters are periodically applied to a frame
of samples. Most filters are a set of equations involving
points in each input frame, with highly predictable execution
times. DVS may seem less applicable because the amount
of computation required for a given filter with a fixed buffer
size does not vary more than a few cycles. However, the
amount of work required of the system does vary based on
the frequency content of the signal sampled in each frame.
In this work, we use a TI DSP to emulate a digital hearing
aid to demonstrate the concept and measure results on real
hardware.
A digital hearing aid provides an example of this concept,
though any DSP application requiring significant process-
ing power can use the same technique as long as there is
variation in the frequency content of the input signal. For
example, the audio frequency content in the typical office
environment varies greatly. Sometimes the room is quiet.
Conversation generates audio signals with primarily low fre-
quency content. Other events like a telephone ringing, an
alarm sounding, or music playing can add higher frequency
content. A DSP-based hearing aid can exploit this fact
by temporarily reducing its effective sampling rate during
times when no significant high-frequency content is audible.
Fewer input samples per second mean less computation for
the filters to do on each frame, which leads to lower power
consumption. Whenever a high frequency input is detected,
the hearing aid can increase its sampling rate and processing
speed to process the input at a rate high enough to preserve
signal fidelity.
The hearing aid application takes advantage of human
perception of sound to determine how much processing the
signal needs. The psychoacoustic model and overall sys-
tem design used in this application are described in Sec-
tion 2. Section 3 describes the system implementation for
this prototype, including hardware shortcomings we experi-
enced. Measurements from running the system are given in
Section 4. Section 5 discusses related work, and Section 6
concludes the paper.
2. SYSTEM MODEL
A hearing aid only needs to process those signals that a
person with normal hearing would be able to hear. A per-
son with normal hearing does not perceive every frequency
equally well, for example. A hearing aid designed with the
knowledge of this and other traits of the human auditory sys-
tem can use less computationally intense filters than might
otherwise be required. Like lossy audio compression algo-
rithms, the system can introduce noise into the signal, as
long as the noise does not affect the perceived quality of the
output signal.
2.1 Absolute Threshold of Hearing
Though the frequency range of human hearing is generally
considered to be 20 Hz to 20 KHz, not all frequencies are
heard equally well. For example, tones at the extreme fre-
quencies are more difficult to hear. Furthermore, the human
ear can detect differences in pitch better at lower frequencies
than at higher frequencies.
The Absolute Threshold of Hearing (ATH) indicates the
quietest sound a person with normal hearing can perceive [12,
23]. The following equation has been found to approxi-
mate the absolute threshold of hearing, based on experi-
ments playing a sinusoidal tone at a very low power:
AT H(f) = 3.64
„
f
1000
«
−0.8
− 6.5e
(
−0.6
f
1000
−3.3
)
2
+10
−3
„
f
1000
«
4
,
where f is the frequency of the input tone in hertz. Fre-
quency components with power levels that fall below the
ATH (measured in sound pressure level) can be discarded,
as a listener with normal hearing will be unable to hear
them. Moreover, the system can add noise to the output sig-
nal without reducing the signal’s perceived quality, as long
as the total power at each frequency stays below the ATH
curve.
2.2 Hearing Aid Model
A simple digital hearing model aid consists of a micro-
phone, A/D converter, DSP processor, D/A converter, and
a speaker. The A/D converter converts analog signals from
the microphone into digital samples, which are then pro-
cessed by the DSP, converted to analog signals by the D/A
converter, and sent to a speaker. According to sampling
theory a signal must be sampled at a rate at least twice its
bandwidth to be exactly reconstructed from its samples [19].
This sampling frequency is often called the Nyquist sam-
pling frequency or the Nyquist rate. A form of distortion
called aliasing occurs if the bandwidth of the sampled sig-
nal exceeds twice sampling frequency. In practice, systems
use sampling rates slightly above the Nyquist rate. Since
human hearing is generally considered to cover a range of
20 Hz to 20 KHz, typical audio sampling rates are 44.1 KHz
or 48 KHz.
Samples are grouped into frames of approximately 20 ms
worth of data, and filtered one frame at a time. At any given
time the hearing aid is simultaneously transferring samples
from the A/D converter to an input buffer, processing data
from the previously sampled frame, and transferring samples
from the previously processed buffer to the D/A converter.
The 20 ms frame size is long enough to produce stationary
signals, while not adding noticeable delay [21].
An ideal variable sampling rate hearing would sample the
analog input signal at the minimum rate required to avoid
aliasing for the current input frame. In other words, the
sampling frequency would be lowered for frames when the
signal has no audible high frequency components and raised
when high frequency components are present. Processing
would be carried out as in the standard hearing aid, with fil-
ter coefficients adjusted for the current sampling frequency.
The execution time of the filters on a DSP depends on the
number of samples and coefficients, but is independent of
the filter coefficient values. At lower sampling rates, fewer
samples are taken per 20 ms frame. Thus the system could
slow down the CPU in proportion to the number of sam-
ples, so that the filter finishes computing the filtered frame
as close to 20 ms as possible.
The most difficult theoretical question in building a vari-
able sampling rate system is, “When should the A/D con-
verter take the next sample?” Ideally, the system could
adjust its frequency with each sample taken. However, de-
termining the signal’s frequency on a per sample basis would
be difficult with existing hardware. For example, changing
the A/D converter’s sampling rate takes longer than the
time between samples. When working with frames of sam-
ples, the frequency can be determined for each frame and
be kept constant over an entire frame. However, there is no
way to determine the frequency content of the end of the
frame when the beginning of the frame is sampled.
The A/D converter in our prototype runs at a constant
speed, sampling every frame at a rate, f
max
, high enough
to guarantee no aliasing. It then examines the entire frame
to determine the highest audible frequency present, f
a
. The
system selects the precomputed filter set with the lowest ef-
fective sampling rate, f
i
≥ 2f
a
, the minimum rate at which
a frame can be sampled without aliasing, and resamples the
frame for the selected filter set. The filter sampling fre-
quencies, f
i
, are chosen to be integer multiples of f
max
, so
resampling the frame is a matter of selecting every k
th
sam-
ple, where k = f
max
/f
i
.
To determine the maximum audible frequency, f
a
, in a
frame our prototype transforms the frame to the frequency
domain with a Fast Fourier Transform (FFT). The FFT
determines how strong the signal is at a discrete set of fre-
quencies up to f
max
/2. The prototype finds the highest fre-
quency in the transformed signal with power greater than
the ATH curve, described in Section 2.1. Hearing aids that
do their filtering in the frequency domain already have to
do an FFT, so the only added overhead would be comparing
the FFT output to the ATH curve.
Often hearing aid filters are implemented in the time do-
main. If an FFT is too expensive, a set of time domain fil-
ters, with cutoff frequencies corresponding to the f
i
’s, could
be used to find f
a
. Starting with the highest cutoff fre-
quency, each high pass filter can be applied to the input
buffer. The energy of the signal above the given frequency
can be estimated by summing the square of the filtered sam-
ple values. The signal contains significant high frequency
signals if the energy of the filtered signal is above a thresh-
old determined by the ATH.
The prototype implementation described in this paper,
computes f
a
using an FFT. If the amount of computation
required to determine f
a
is greater than the amount of power
saved due to frequency and voltage scaling, then scaling fre-
quency and voltage is not worthwhile. As will be seen in
Section 4, the payoff varies with the amount of computation
required by the hearing aid filters.
3. IMPLEMENTATION
Measurements for the variable sampling rate hearing aid
are based on a TI TMS320C5510 DSP Starter Kit. The TI
TMS320C5510 is typical of DSP’s used in digital hearing
aids. The starter kit is based on a printed circuit board
with a TMS320C5510 DSP processor and a stereo codec
(a combined A/D and D/A converter) capable of sampling
audio at rates from 32 KHz to 96 KHz. The DSP core
can be scaled to many different frequencies from 6 MHz to
200 MHz. It can run at 1.1 V at frequencies less than or
equal to 72 MHz. Otherwise it must run at 1.6 V [4, 20].
To get maximum benefit from frequency scaling, the sys-
tem should support a different voltage for each frequency.
Though our prototype only has two voltage choices, dis-
carding unneeded samples reduces total energy consumed
because the computational complexity of the filters is di-
rectly proportional to the number of samples per frame.
Moreover, battery capacity depends non-linearly on the dis-
charge rate. In lithium ion batteries, for example, not only
does battery capacity decrease at high discharge rates, it
also becomes more sensitive to peak power consumed than
to average power [10]. Even if the voltage cannot be reduced,
reducing the clock frequency reduces the peak power within
each frame, compared with running the clock full speed and
putting the CPU to sleep until the next frame.
The TMS320C5510 DSP Starter Kit has several problems
related to frequency scaling. The TMS320C5510 uses an
internal phase-locked loop (PLL), controlled by CPU regis-
ters, to generate the CPU clock frequency from a 24 MHz
crystal oscillator. Calculations based on specifications from
TI and experiments with frequency scaling have shown that
locking to a new frequency can take from 20 µs to 80 µs.
When the frequency changes, the function units within the
CPU cannot communicate with each other until the PLL
locks to the new frequency.
One of the affected function units is the direct memory
access (DMA) controller that transfers samples to and from
the codec. In the constant frequency implementation, the
DMA controller moves an entire frame in the background
while the DSP filters the current frame. The variable sam-
pling rate implementation attempts to do the same thing,
and thus does not run reliably at all the data points. If
the function units could continue to run while the frequency
changes, or the frequency change could complete between
two samples, the power consumption would be the same as
is reported here.
The time required for the PLL to lock to a new frequency
is often longer than the time between samples, depending
on the frequency to which it is changing. With a sampling
rate of 48 KHz the time between samples is approximately
20.83 µs. Slowing the sampling rate to 32 KHz, the min-
imum sampling frequency supported by the codec, would
increase the intersample time to 31.25 µs, which is still not
long enough to guarantee that a frequency change transition
will complete before the next sample is ready.
One way around this problem would be to use two PLL’s
connected to a CPU controlled multiplexer. While the CPU
uses one PLL as it’s clock, the other PLL can change to
an arbitrary frequency. When the second PLL has stabi-
lized, the CPU can switch to the second PLL quickly. IBM
PowerPC 750FX RISC Microprocessor offers this feature.
It can switch between two PLL’s in three clock cycles with
all function units continue to operate normally during the
switch [7]. Unfortunately, the PowerPC 750FX would not be
suitable for this application because draws at least an order
of magnitude more power than the TMS320C5510, though
it is a much faster processor.
Another alternative is to use a frequency divider to gener-
ate lower frequencies from a constant high frequency. Since
no phase locking is required the frequency divider can quickly
switch frequencies.
The experimental setup consists of a PC sound card to
supply repeatable inputs to the “line in” on the starter kit.
The starter kit provides a jumper to which a wire loop is con-
nected to measure current and supply voltage of the CPU
core. A Tektronix current probe and AM503B current probe
amplifier connected to a Tektronix TDS 3012B digital oscil-
loscope measured current through the loop, while the second
channel on the oscilloscope measured the core voltage. RMS
power was computed using the oscilloscope’s multiply and
RMS functions. The RMS window was set wide enough to
cover several frames. Multiple power consumption measure-
ments were taken for each tested configuration and aver-
aged. Energy consumption can be estimated by multiplying
the average power measurement by the desired amount of
time.
A CD recording of music provided a repeatable audio in-
put source. The music test [18] represents a difficult case,
because it frequently contains audible high frequency com-
ponents not present in speech only signals.
Each of the data points was measured with a sampling
rate of f
max
= 48 KHz with a frame size of 1024, giving
21.3 ms per frame. Downsampling was implemented by di-
viding f
max
by a power of two. Thus possible effective sam-
pling rates are 48 KHz, 24 KHz, 12 KHz, 6 KHz, 3 KHz,
1.5 KHz, 750 Hz. Lower frequencies were not used because
the filters used do not operate on fewer than 16 samples.
Digital hearing aids often use filters like frequency shap-
ing, adaptive noise reduction, interaural time delay, and
multichannel amplitude compression to process their input
signals [21]. To give a generic characterization of the tech-
nique as a function of processing load, we used a series of
finite impulse response (FIR) filters applied to the input
buffer repeatedly as a dummy processing load. In practice,
each channel (left and right) uses between 1 and 50 FIR
filters with 50 to 200 taps for frequency shaping, with 14
filters being common [21]. Similar filtering techniques are
used for the other types of processing.
The FIR filter [22] is hand-tuned in assembly language
for maximum execution speed. It is designed to use the
TMS320C5510 pipeline efficiently including the the dual mul-
tipliers, which give the load a power consumption character-
istic similar to highly optimized signal processing code.
4. RESULTS
Overhead and load execution time were measured using TI
Code Composer Studio’s profiling clock. Clock cycle counts
stayed constant as the CPU frequency changed because all
code and data are located in on-chip memory. The on-chip
memory can be accessed in a single cycle using the same
clock as the rest of the CPU. The FFT used to determine the
maximum frequency content in the input signal was taken
from the TI TMS320C55x DSPlib library [22]. It was mea-
sured to take less than 64,000 cycles on the TMS320C5510.
Postprocessing to upsample the output waveform was mea-
sured to take less than 57,000 cycles. The FIR filter used to
load the processor was also taken from the TI TMS320C55x
DSPlib library [22]. It consistently took about 110,000 cy-
cles to execute for 208 taps and 1024 samples.
Figure 1 compares the power consumed by the standard
hearing aid model to the variable sampling rate hearing aid
as a function of the number of FIR filters run on each frame.
The standard hearing aid was run at the smallest constant
frequency required to guarantee the FIR filters had time to
run during each frame. The variable sampling rate hearing
aid scaled the frequency for each frame to the minimum
required to run all the FIR filters on the possibly reduced
size frame. A third curve represents a standard hearing aid
sampling at 24 KHz, half the maximum sampling rate of the
other two hearing aids.
At low loads the standard hearing aid uses less power than
the variable rate hearing aid because both the constant rate
and the variable rate hearing aid can run at a frequency low
enough that V
dd
is always 1.1 V. The savings from scaling
are small in this case because there is not a lower voltage for
the variable rate hearing aid to use. Around 14 FIR filters,
constant rate hearing aid consumed approximately 2.5 times
more power than the variable rate hearing aid because the
constant rate hearing aid is forced to run at a frequency
that requires 1.6 V. Most frames contain little enough high
frequency content that the variable sampling rate hearing
aid can run at 1.1 V most of the time.
All of the curves show an increase in power consumption
when the processor has to shift from running at 1.1 V to
0
20
40
60
80
100
120
140
160
180
200
0 5 10 15 20 25 30 35
Power Consumed (mW rms)
FIR Filters
Static Sampling Rate
Variable Sampling Rate
Static Sampling (24 KHz)
Figure 1: Graph of system power as a function of
load for the standard hearing aid model and the
variable sampling rate hearing aid.
0.1
1
10
100
0.75 1.5 3 6 12 24 48
Percent of Frames
Effective Sampling Frequency (KHz)
Figure 2: Measured distribution of effective sam-
pling rates for music test.
1.6 V. For a given load, the fixed sampling rate hearing aid
only needs one voltage level, just high enough to run at a
speed fast enough to complete processing just in time for
the next frame. The variable sampling rate hearing aid,
however, would benefit from more voltage levels. Ideally a
different voltage level would be available for frame size to
maximize the power savings of switching frame sizes.
Though the standard hearing aid running at 24 KHz uses
less power than the variable sampling rate hearing aid for
many cases, it loses audible signals above 12 KHz. The his-
togram in Figure 2 shows, in log-log scale, how often the
variable rate hearing aid is able to use each of the sampling
rates from 750 Hz to 48 KHz. The 24 KHz and 12 KHz ef-
fective sampling rates are most commonly used. Both lower
and higher sampling rates are also present, but represent
fewer than 1 % of the frames.
The dotted curve in Figure 1 shows that reducing the fixed
sampling rate hearing aid’s sampling frequency to 24 KHz
would compete well with the variable sampling rate hearing
aid. This tradeoff may be worthwhile when less than one
percent of the samples need to be sampled at a rate higher
than 24 KHz. Even so, the variable rate hearing aid uses
less power for high loads. The variable sampling rate sys-
tem would likely also do better if more voltage levels were
available, since the largest advantage is seen when it is able
to switch to a lower voltage than the static sampling rate
system much of the time. Optimization of the up and down
sampling code would also improve the variable rate hearing
aid’s performance.
5. RELATED WORK
Most DVS algorithms [2, 5, 6, 13, 14] estimate the slack
available at scheduling points and adjust the clock frequency
to keep the CPU busy at as low a clock frequency as possi-
ble. Rather than only updating slack at scheduling points,
AbouGhazaleh, Childers, et. al [1] introduce compiler sup-
port to insert power management points into a program.
At each power management point the compiler provides
updated WCET information, which is periodically used to
update the current clock frequency. This method is dif-
ferent than typical DVS scheduling algorithms in that the
power management points allow the system to get informa-
tion about the amount of dynamic slack available from a job
before the job finishes.
Multimedia applications often take advantage of limita-
tions of human perception. For prerecorded video streams,
buffering extra frames before processing them has been shown
to increase slack time in the system when the amount of
compressed video data per frame varies widely [8]. Buffer-
ing several frames lets the scheduler spread longer jobs over
several periods, taking slack from periods with lower ex-
ecution time requirements. Buffering could be applied in
addition to varying the sampling rate, but the added delay
may become noticeable in the hearing-aid application.
All of these algorithms use static and dynamic slack in
the schedule to reduce energy consumption. In contrast, our
method introduces slack into the schedule by changing the
amount of work the application requires based on the cur-
rent input. Other DVS techniques could be combined with
ours to take advantage of this slack. For example, compiler
inserted power management points would remove the need
for the programmer to manually determine the clock fre-
quency for each filter speed. Other DVS algorithms could
schedule variable sampling rate signal processing tasks with
other tasks in a system with other real-time tasks.
In cases where schedulability cannot be guaranteed, pre-
vious work has studied how to maximize system value while
meeting energy and timing constraints for jobs that com-
plete [16]. Frames with little high frequency content could be
viewed as having lower value, thus getting less computation.
Even though some samples are discarded, the difference in
signal output should be indistinguishable from a frame in
which all samples were processed, so the discarded work had
zero value. Moreover, all frames are guaranteed to be pro-
cessed by their deadlines, regardless of the clock frequency.
In other words, the techniques described in previous work
trade quality for energy consumption. This work reduces
energy consumption without reducing perceived quality.
Lossy audio compression algorithms [12, 23] commonly
use psychoacoustic principles to reduce the amount of data
in a stored or transmitted audio stream. Our approach is
similar in that we improve the economy of the system by
imperceptibly changing the signal. It is different in that
we reduce the amount of computation required to process
the signal, rather than reducing the amount of space re-
quired to store it. Compression algorithms ideally remove
the maximum amount of information, which can take a sig-
nificant amount of computation. In contrast, our method
seeks to discard inaudible high frequency signal components
with minimal extra computation.
6. CONCLUSIONS AND FUTURE WORK
The variable sampling rate technique reduces power re-
quired to as little as 40 % of the power required for the static
sampling rate, depending on the amount of processing per
frame. As the amount of computation per frame decreases
the technique becomes less effective due to the overhead of
determining the frequency content of a frame. Optimiza-
tions of the current prototype should increase the range for
which this technique is useful. A wider range of voltages
and less computationally complex method for determining
the sampling frequency would increase the effectiveness of
the technique.
Faster frequency switching or a codec that can buffer sev-
eral samples is needed to avoid missing samples. Many
DVS algorithms proposed by others only change frequency
at longer intervals. In those cases the 20 µs to 80 µs to
change frequencies is reasonable. Even for the hearing aid
application the frequency switching time is only a small per-
centage of the frame size. Buffers in the codec to hold sam-
ples while the CPU is unavailable or a second PLL would
prevent dropped samples.
We are currently developing a set of time domain band-
pass filters, which we expect to require much less computa-
tion than the FFT/ATH combination. Low power switched
capacitor filter banks have been used to measure frequency
response in several bands [11]. Adding such circuitry to the
A/D converter could dramatically increase the efficiency of
determining the highest frequency components in the sys-
tem. If the processing stage operates in the frequency do-
main, then a filter bank is unnecessary because the FFT is
essentially free.
Digital hearing aids are just one energy sensitive DSP ap-
plication. The variable sampling rate technique can be ap-
plied to any signal processing application with significant
variation in input frequencies for which the CPU power is a
substantial portion of the entire system power.
7. ACKNOWLEDGMENTS
The authors would like to thank Kevin Donohue and Art
Radun for use of lab space and test equipment used in mea-
suring results. Mike Strain at Digital Spectrum and Todd
Sanning at TI were of assistance in troubleshooting our
starter kit.
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