Gravitational-wave observatories around the world are searching for continuous waves: persistent signals from sources, such as spinning neutron stars. These searches use sophisticated statistical techniques to look for weak signals in noisy data. In this paper, we demonstrate these techniques using a table-top model gravitational-wave detector: a Michelson interferometer where sound is used as an analog for gravitational waves. Using signal processing techniques from continuous-wave searches, we demonstrate the recovery of tones with constant and wandering frequencies. We also explore the use of the interferometer as a teaching tool for educators in physics and electrical engineering by using it as an “optical microphone” to capture music and speech. A range of filtering techniques used to recover signals from noisy data are detailed in the supplementary material of this article. Here, we present the highlights of our results using a combined notch plus Wiener filter and the statistical log minimum mean-square error (logMMSE) estimator. Using these techniques, we easily recover recordings of simple chords and drums, but complex music and speech are more challenging. This demonstration can be used by educators in undergraduate laboratories and can be adapted for communicating gravitational-wave and signal-processing topics to nonspecialist audiences.

1.
B. P.
Abbott
,
R.
Abbott
,
T. D.
Abbott
 et al, “
Observation of gravitational waves from a binary black hole merger
,”
Phys. Rev. Lett.
116
,
061102
(
2016
).
2.
S. J.
Cooper
,
A. C.
Green
,
H. R.
Middleton
 et al, “
An interactive gravitational-wave detector model for museums and fairs
,”
Am. J. Phys.
89
(
7
),
702
712
(
2021
).
3.
LIGO Scientific Collaboration
,
Virgo Collaboration
,
KAGRA Collaboration
, et al, “
GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run
,” e-print arXiv:2111.03606 (
2021
).
4.
LIGO Scientific Collaboration, Virgo Collaboration, KAGRA Collaboration
, et al, “
Observation of gravitational waves from two neutron star-black hole coalescences
,”
Astrophys. J.
915
(
1
),
L5
(
2021
).
5.
W. H. G.
Lewin
,
J.
van Paradijs
, and
E. P. J.
van den Heuvel
,
X-Ray Binaries
(
Cambridge U. P
.,
Cambridge
,
1997
).
6.
LIGO Scientific Collaboration and Virgo Collaboration
 et al, “
Search for gravitational waves from Scorpius X-1 in the second advanced LIGO observing run with an improved hidden Markov model
,”
Phys. Rev. D
100
(
12
),
122002
(
2019
).
7.
S.
Suvorova
,
P.
Clearwater
,
A.
Melatos
 et al, “
Hidden Markov model tracking of continuous gravitational waves from a binary neutron star with wandering spin. II. Binary orbital phase tracking
,”
Phys. Rev. D
96
(
10
),
102006
(
2017
).
8.
When introducing the acoustic analogy to lay audiences, it is important to emphasize that gravitational waves are not sound. For example, gravitational waves can propagate in a vacuum. whereas sound cannot. Gravitational waves also travel at the speed of light and are not longitudinal waves.
9.
Piotr
Jaranowski
,
Andrzej
Królak
, and
Bernard F.
Schutz
, “
Data analysis of gravitational-wave signals from spinning neutron stars: The signal and its detection
,”
Phys. Rev. D
58
(
6
),
063001
(
1998
).
10.
A.
Viterbi
, “
Error bounds for convolutional codes and an asymptotically optimum decoding algorithm
,”
IEEE Trans. Inf. Theory
13
(
2
),
260
269
(
1967
).
11.
Ralph P.
Muscatell
, “
Laser microphone
,”
J. Acoust. Soc. Am.
76
(
4
),
1284
(
1984
).
12.
A photodiode is an electrical component that acts as a regular diode when no light is incident on it, blocking any current flow in the reverse direction. As the intensity of incident light rises, it becomes increasingly conductive in the reverse direction.
13.
Steven M.
Kay
,
Fundamentals of Statistical Signal Processing: Estimation Theory
(
Prentice-Hall, Inc
.,
New York
,
1993
).
14.
Yi
Hu
and
P. C.
Loizou
, “
Subjective comparison of speech enhancement algorithms
,” in
2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings
(
IEEE
,
2006
), Vol.
1
, pp.
I
I
.
15.
Wilson
Ching
, LogMMSE for <https://github.com/wilsonchingg/logmmse>,
2019
.
16.
Hatem M.
Elfekey
and
Hany Ayad
Bastawrous
, “
Design and implementation of a new thin cost effective AC hum based touch sensing keyboard
,” in
2013 IEEE International Conference on Consumer Electronics (ICCE)
(
IEEE
,
2013
), pp.
602
605
.
17.
Benjamin P.
Abbott
,
R.
Abbott
,
T. D.
Abbott
 et al, “
Exploring the sensitivity of next generation gravitational wave detectors
,”
Classical Quantum Gravity
34
(
4
),
044001
(
2017
).
18.
T.
Sekiguchi
, “
Study of low frequency vibration isolation system for large scale gravitational wave detectors
,” Ph.D. thesis (
Tokyo University
,
2016
).
19.
S. L. H.
Verhoeven
,
M. M. J.
van de Wal
,
IrTAE.
Oomen
, and
O. H.
Bosgra
, “
Robust control of flexible motion systems: A literature study
,” DCT Rep. (
2009
).
20.
Daniel
Dzibela
and
Armin
Sehr
, “
Hidden-Markov-model based speech enhancement
,” e-print arXiv:1707.01090 (
2017
).
21.
Santiago
Pascual
,
Antonio
Bonafonte
, and
Joan
Serrà
, “
SEGAN: Speech enhancement generative adversarial network
,” e-print arXiv:1703.09452 (
2017
).
22.
Guy P.
Nason
and
Bernard W.
Silverman
, “
The stationary wavelet transform and some statistical applications
,” in
Wavelets and Statistics
(
Springer
,
New York
,
1995
), pp.
281
299
.
23.
Z.
Tufekci
and
John N
Gowdy
, “
Feature extraction using discrete wavelet transform for speech recognition
,” in
Proceedings of the IEEE SoutheastCon 2000, Preparing for the New Millennium (Cat. No. 00CH37105)
(
IEEE
,
2000
), pp.
116
123
.
24.
Johnson Ihyeh Agbinya.
Discrete wavelet transform techniques in speech processing
,” in
Proceedings of Digital Processing Applications (TENCON'96)
(
IEEE
,
1996
), Vol.
2
, pp.
514
519
.
25.
E. T.
Jaynes
,
Probability Theory: The Logic of Science
(
Cambridge U. P
.,
Cambridge
,
2003
).
26.
See supplementary material at https://www.scitation.org/doi/suppl/10.1119/10.0009409 for further resources and a detailed explanation and discussion of the different signal-processing techniques used for speech enhancement of the recordings from the optical microphone, including techniques not presented in the main text.

Supplementary Material

AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.