Fundamentals in signal analysis of passive acoustic data
Dr Cédric Gervaise & Dr Lucia Di Iorio
Chaire CHORUS Remote sensing of Aquatic Environment By Passive Acoustics
Outline
• Introduction • Introduction to sound • Measurement chain • Spectral analysis of acoustic measurements • Time-frequency representation • Applied examples from our own research
gipsa lab Lucia Slide 1 Who are we ?
Cédric Lucia
Signal processing and Application of passive acoustics application to underwater Chair CHORUS to answer biological & acoustics Environmental ecological questions monitoring using Physical oceanography passive acoustics Animal behaviour Algorithm development Evolutionary biology/ecology Environmental monitoring Environmental monitoring
gipsa lab Lucia & Cedric Slide 2 Why sound in a time series conference?
hosts medium
Services deriving from the hydrosphere : 20 900 billions $ / year
The ocean: a vast still largely unknown environment Its observation : a priority of the 21st century gipsa lab Lucia Slide 3 Costanza, R.; d'Arge, R.; De Groot, R.; Farber, S.; Grasso, M.; Hannon, B.; Limburg, K.; Naeem, S.; O'Neill, R.; Paruelo, J. & others (1997), 'The value of the world's ecosystem services and natural capital', Nature 387(6630), 253--260.
gipsa lab Why sound in a time series conference?
Emitter = sources Receiver
Soundscape
Propoagation
AQUATIC ENVIRONMENT = ACOUSTIC SOUNDSCAPE
gipsa lab Cedric slide 4 • Pijanowski, B.; Villanueva Rivera, L.; Dumyahn, S.; Farina, A.; Krause, B.; Napoletano, B.; Gage, S. & Pieretti, N. (2011), 'Soundscape ecology: the science of sound in the landscape', BioScience 61(3), 203--216.
• Radford, C.; Stanley, J.; Tindle, C.; Montgomery, J. & Jeffs, A. (2010), 'Localised coastal habitats have distinct underwater sound signatures', Mar. Ecol. Prog. Ser. 401, 21-29
• Kennedy, E.; Holderied, M.; Mair, J.; Guzman, H. & Simpson, S. (2010), 'Spatial patterns in reef generated noise relate to habitats and communities: Evidence from a Panamanian case study', Journal of Experimental Marine Biology and Ecology 395 (1 2), 85 92.
• Gervaise, C.; Di Iorio, L.; Grall, J.; Chauvaud, L. ; Jolivet, A. ; Clavier, J. (2012),’La polyphonie côtière : des sons au fonctionnement des écosystèmes’, Chapitre HDR
gipsa lab Why sound in a time series conference?
- Recent technological advances in sound acquisition - Long-term monitoring, - Continuous recordings, - High resolution, - Deployment in areas/substrates difficult to access, - Relatively cost-effective, - Real-time acquisition possible….
gipsa lab • Lucia slide 5 Why sound in a time series conference?
gipsa lab Cedric slide 6 Why sound in a time series conference?
Soundscape
Propagation
Combination of ocean science and computational science
Environmental Characterisation of Sounds description & sound sources and knowledge propagation channel
Passive acoustic monitoring of the marine environment
Passive acoustic monitoring = an indirect measurement that needs processing! gipsa lab Cedric slide 7 Outline
• Introduction • Introduction to sound • Measurement chain • Spectral analysis of acoustic measurements • Time-frequency representation
• Applied examples from our own research
gipsa lab What is a wave ?
A mechanical WAVE
Initial information Propagation of information Oscillation of a particle Transmission of oscillation Different possible waves to explore the marine environment: - electromagnetic - optic - acoustic gipsa lab • Cedric slide 8 Why acoustic waves?
2 2 I0 (W/m ) I (W/m ) r
with α = coefficient of absorption (here in cm 1)
gipsa lab Cedric slide 9 Why acoustic waves?
Frequency 50Hz, range 20000km! Frequency 18Hz, range > 3000km
Frequency
Absorption
Range
Wavelength gipsa lab • Lucia slide 10 Munk, W.; Spindel, R.; Baggeroer, A. & Birdsall, T. (1994), 'The Heard Island Feasibility Test', The Journal of the Acoustical Society of America 96(4), 2330-2342.
Clark, C. W. & Gagnon, G. J. 2004. Low frequency vocal behaviors of baleen whales in the North Atlantic: Insights from integrated Undersea Surveillance System detections, locations, and tracking from 1992 to 1996. Journal of Underwater Acoustics (USN), 52 .
gipsa lab What is an acoustic wave ?
The equation of wave propagation is obtained from: - the law of conservation of mass - the law of conservation of momentum - the law of fluid dynamics (linking P to ρ) and from their 1st order linearization around the equilibrium pressure + v=0ms -1
1 ∂2p p − = 0 Wave equation c 2 ∂t 2
ρc 2 = p p = power/m 2 r ∂v r source Piezo electric ρ0 + ∇p = 0 receiver ∂t v
gipsa lab cédric slide 11 Jensen, F. (1994), Computational ocean acoustics, Amer Inst of Physics.
gipsa lab What is a sound ? Level (received µPa, emitted µPa@1m ?) in decibel as a function of:
1 0.8 0.6 0.4 Sound intensity level: 0.2 0
signal P 0.2 P =10log ( ) 0.4 dB re P0 10 Time domain Time 0.6 P0 0.8 1 0 200 400 600 800 1000 1200 1400 1600 1800 2000 temps T Time-frequency Frequency domain 1
0.9 T = 1/f
0.8
0.7
0.6
0.5
dsp V2/Hz 0.4
0.3
0.2
0.1
0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 gipsa lab f (Hz) Cedric slide 12 Sound speed
1 ∂2p air, c=330 ms 1 p − = 0 c 2 ∂t 2 water, c=1500 ms 1 ρc 2 = p rock, c =4000 ms 1
Sea water sound velocity c= G(T,p,S)=H(T,z,S)
Take home message (for T= 0 °C and S = 35 ° /°° ) • c increases with T (4.6m/s for T = 1 °C) • c increases with S (1.4m/s for S = 1 ° /°° ) • c increases with p and z (1.7m/s for S = 1000m) gipsa lab Cedric /Lucia slide 13 Sound speed
If sound velocity c changes with depth z, sound waves do not propagate on a straight line, they are refracted.
Sound waves always tend to converge towards the sound speed minimum.
gipsa lab Cedric slide 14 Sound speed
Polar profile c Shallow water / continental shelf profile c z
z
Deep water / temperate profile c
z
gipsa lab Cedric slide 15 Temperate deep water sound popagation
x10 4
gipsa lab Cedric slide 16 Temperate shallow water propagation
gipsa lab Cedric slide 17 The intensity of sound
p = force/m 2
v Power = strength x velocity
Intensity = amount of power transmitted through a unit area (m 2) = pressure x speed (W/m 2)
For planar waves : I
gipsa lab Cedric slide 18 The intensity of sound
Example = sound wave with an amplitude of 1 Pa
In water: ( ρ=1000kg/m 2; c=1500ms 1) => I =6.10 7W/m 2 eau I 2 1 3 2 In air: ( ρ=1.2kg/m ; c=330ms ) => Iair =2,5.10 W/m
Iair / Ieau = 4166 !!!!!!!!!!!
Air : compressible gaz Water : incompressible fluide
gipsa lab Lucia slide 19 Decibels – unit of Sound (pressure) Level
J represents a quantity and Jref a reference quantity
if J is an amplitude
if J is an intensity
Decibels are used to represent and compare amplitude quantities. The sound level in dB is a scale based on multiples of 10 (logarithmic scale):
10dB = 1* 10 -11 W/m 2 -> acoustic pressure increases 10 times 20dB = 1* 10 -10 W/m 2 -> acoustic pressure increases 100 times 40dB = 1* 10 -8 W/m 2 -> acoustic pressure increases 10000 times
gipsa lab Lucia slide 20 Can Decibels be a source of confusion ? Yes or No ! Two sounds with the following levels:
Are the sound of equal amplitudes ?
The quantity is an amplitude:
remember The quantity is an intensity:
gipsa lab Cedric slide 21 Can Decibels be a source of confusion ? Yes or No ! The sound level in dB of a sum of acoustic signals is not equal to the sum of the sound levels of each signa l!!!!!!!!!!!!!!
Two independent sounds => intensity of the sum = sum of the intensities in a linear scale:
(son = sound)
then then
gipsa lab Cedric slide 22 Source Level & Reveived Level
Source Level Level heared if @ 1m form an Received Level SL dB re isotropic source RL dB ref 1 Pa 2@1m ….. 1 Pa 2…..
Emitter = sources Receiver
Soundscap e
Propagation gipsa lab Cedric slide 23 Acoustic intensity : The energetic budget of a singing blue whale
Mean source level of blue whale song note: 160 dB re 1 Pa @ 1m (188 dB peak), signal duration = 18s with 960 signals/day, energetic value of krill = 96kcal/100g.
gipsa lab Biophony From invertebrates… Range
1m - > 200m
10m - > 1km
> 100m - > 1000km
… to marine mammals gipsa lab Lucia slide 24 Geophony Wind & rain Sounds of breaking ice
Underwater earthquake
gipsa lab Lucia slide 25 Anthropophony
gipsa lab Lucia slide 26 Sound Levels
Source (SL) Mesure (RL) Wideband effective source Wideband effective received level (SL), level (RL),
2 2 SL =10log10 rl( ); dBref1µPa @1m RL =10log10 rl( ); dBref1µPa 1 1 sl = m )t( 2 dt rl = m )t( 2 dt T ∫ T ∫ T T
Narrowband source level Narrowband received level Power spectral density Power spectral density
2 2 γ SL )f( = dBref1µPa /Hz@1m γRL )f( = dBref1µPa /Hz
Sound exposure level (SEL)
2 SEL =10log10 (sel); dBref1µPa s sel = ∫m )t( 2 dt T
gipsa lab Lucia slide 27 An inventory initatied by 2nd world war and cold war
Source whoi.edu, Wenz 1962, Wenz 1972, Urick 1984 gipsa lab Cedric slide 28 Natural sources Abiotic Biotic
Anthropogenic sources
gipsa lab Cedric slide 29 Ambient noise Background noise from many different sources excluding individually identifiable sounds
gipsa lab Cedric slide 30 Verydynamic amplitude large
Very large frequency dynamic gipsa lab Cedric slide 31 Hildebrand, J. (2009), 'Anthropogenic and natural sources of ambient noise in the ocean', Marine Ecology Progress Series 395, 5--20.
Wenz, G. (1972), 'Review of underwater acoustics research: Noise', The Journal of the Acoustical Society of America 51, 1010.
Wenz, G. M. (1962), 'Acoustic Ambient Noise in the Ocean: Spectra and Sources', The Journal of the Acoustical Society of America 34(12), 1936-1956.
gipsa lab Outline
• Introduction • Introduction to sound • Measurement chain • Spectral analysis of acoustic measurements • Time-frequency representation • Applied examples from our own research
gipsa lab Some measurement devices
10 miles
1826, lake of Geneva: Calladon & Strum gipsa lab Lucia slide 32 Some measurement devices
Portable device
Amplifier
IN
IN OUT
Recorder Hydrophone
gipsa lab Lucia slide 33 Some measurement devices
Autonomous recorders
RT SYS, France Aural, Multi Electronique, Qc.
gipsa lab Lucia slide 34 Some measurement devices
Cabled systems http://www.medon.info/
Yves Gladu
SO und SU rveillance System
gipsa lab Lucia slide 35 The elements of the acquisition chain
RS 20 s1 =10 p s p RS 1 dB = dB +
Amplifier
G 20 s 2 = 10 s1 Analogue digital s s G converter 2 dB = 1 dB +
Recorder/player
s s = (E 2 2nb−1 ) 3 D 2nb−1 s = s + 20log10( ) 3 dB 2 dB D
Sound analysis tools
gipsa lab Cedric slide 36 Receiver sensitivity
RSdB ref1V /1µPa
gipsa lab Cedric slide 37 A key element : the analogue to digital conversion
It allows the use of digital technology to process the acquired data.
gipsa lab Cedric slide 38 The analogue to digital conversion
s(t) t : independent variable s : dependent variable Discrete or continuous variable
Numérique/numérisation = digital/digitalisation Echantillonnage = sampling rate gipsa lab Cedric slide 39 Sampling rate
fmax is the maximal frequency of a signal s(t) only if
∀f > fma x ,S(f) = 0
The sampling of a signal s(t) is reversible only if s(t) is low-pass and
fe>2f max
gipsa lab Cedric slide 40 Sampling rate
gipsa lab Cedric slide 41 Sampling rate – the anti aliasing Physical filter phenomenon
fmax
measurement noise
f>fmax receiver f >2f fc≈fmax e c d filter PB d ⊗ fc ×××Te gipsa lab Cedric slide 42 Quantification The 3 key parameters: Vmin Vmax Number of quantification levels N D : dynamic range q : quantification step Quantification rule: b : number of bits gipsa lab Cedric slide 43 Quantification errors Saturation Discretization s(t) sq(t)=s(t)+ ε(t) ε(t) The quantification error limited Evenly distributed over white noise -> constant spetral component high frequencies gipsa lab Cedric slide 44 How to set a quantification chain? Case: need to measure two signals: an intense (amplitude A1) and a low one (amplitude A2) A1 Choose Vmin, Vmax, N in order to : A2 1) Avoid saturation of the intense signal q=2A /N 1 2) Record the faint signal with a minimal signal to noise ratio (so that it is audible) A2 A1 gipsa lab Cedric slide 45 Choose Vmin, Vmax, N in order to : 1) Avoid saturation of the intense signal 2) Record the faint signal with a minimal signal to noise ratio (SNR) A1 Procedure to estimate quantification N A2 q=2A 1/N A2 A1 RSB = SNR N = quantification gipsa lab Cedric slide 46 Example Calculate the parameters of a measurement chain that allows to record dolphin whistles at 1000 meters of the hydrophone and simultaneously ship noise at 100 meters. SNR of dolphin signals = 20dB. Sampling rate : Low frequency ship noise, dolphin whistles (frequency range: few kHz to 30 kHz) => fs > 60kHz; we choose fs = 96kHz Quantification: 2 Intense signal: shipping noise => (180dB re 1 Pa /Hz@1m around f 0=50Hz, spherical transmission loss 20log10(f) => 156dB re 1 Pa 2 Faint signal: dolphin whistle => (110 dB re 1 Pa@1m, spherical transmission loss) => 50dB. 20 + 106 4 = 7log2( N) => log2( N) = 17 => 24 bit needed gipsa lab Cedric slide 47 Outline • Introduction • Introduction to sound • Measurement chain • Spectral analysis of acoustic measurements • Time-frequency representation • Applied examples from our own research gipsa lab Why ? To represent the measurements to a scientist in the best way to understand its information content and to process them adequately. gipsa lab Cedric slide 46 Spectral analysis Frequency : number of repetitions of a phenomenon per second The frequency representation (rhythm of the repetitions naturally occurring in the measurement) allows sometimes to better understand the content of acoustic signals gipsa lab Cedric slide 47 Spectral analysis Cato 2008, Proc Inst Acoust gipsa lab Lucia slide 48 Spectral analysis Example: Description of the conent of a mailing box (L. Di Iorio) Introduction to Fourier analysis Temporal represenation Mon Tue Wed Thu Fry Sat Sun Mon Tue Wed frequency Frequency represenation 1 daily newspaper J (1/day) at 8 am 1 newspaper with a weekly TV magazine (1/7 days) at 8am every friday gipsa lab Cedric slide 49 How ? Easy cos(2 πππf0t), sin(2 πππf0t), exp(j2 πππf0t) contain only the frequency f0 ! s(t) contains the frequency f 0 if it looks like cos(2 πππf0t), sin( 2π2π2πf0t), exp(j2 πππf0t) ! s1(t) looks like s 2(t) if their scalar products is high. (Linear Algebra) < s (t), s (t) >= s (t)s* (t)dt 1 2 ∫ 1 2 gipsa lab Cedric slide 50 < >= * s1 ),t( s2 )t( ∫s1 s)t( 2 )t( dt Case 1 I > 0 I > 0 + < s1(t),s2 (t) > > 0 + t - s2(t) Case 2 - s1(t) I > 0 I < 0 I < 0 I >0 < s1(t),s2 (t) > ≈ 0 + + s (t) + + 2 t - - - + s1(t) gipsa lab Cedric slide 51 How ? Analogue signal: Fourier transform (FT) Digital signal: Fourier transform via Fast FT (FFT) gipsa lab Cedric slide 52 How ? For digital signals: the discrete Fourier transform (DFT) can be implemented real-time! through the FFT algorithm (of N 2 operations at Nlog2(N) gipsa lab Cedric slide 53 The case of random signals • A random signal depends on time and hazard ε. • Two recordings carried out within exactly the same conditions produce different measurements. • m(t, ε) gipsa lab Cedric slide 54 s(t, ξξξ) !!!!!!! Index of time experiment random gipsa lab Cedric slide 55 The case of random signals • For random signals, the Fourier transform cannot be applied directly! Analogue signals : Fourier Transform gipsa lab Cedric slide 56 For random signals we estimate the power spectral density = frequency distribution of the power of a random signal Received level : dB re 1 Pa 2/Hz Source level: dB re 1 Pa 2/Hz@1m Energy of s(t) within the bandwidth B = [f 0 – 0.5, f 0+ 0.5] gipsa lab Cedric slide 57 A tool for power spectral density estimation: the autocorrelation function Γs (τ) =< s(t),s(t − τ) > Case 1 τττmax Γ(τ)Γ(τΓ(τΓ(τ))) s s is smooth on a period ~ τττmax around t0 τττmax t t τττ 0 Case 2 τττmax Γ(τ)Γ(τΓ(τΓ(τ))) s s is smooth on a period ~ τττmax around t0 τττmax t t τττ 0 ΓΓΓs( τττ) commands the dynamic of variation of s(t) Fast variation : high frequency gipsa lab Cedric Slow variation : low frequencyslide 5851 Autocorrelation function Γs (τ) =< ),t(s t(s − τ) > Autocorrelation function 1 T 2/ = lim t(s)t(s − τ)dt For Deterministic signals T→∞ ∫ T −T 2/ = t(s(E 0 ,ξ t(s) 0 − τ,ξ)) For random signals S.O2 2 γs )f( = (F Γs (τ));(V / Hz) Power spectral density 1 2 = lim ST )f( For Deterministic signals T→∞ T gipsa lab Cedric slide 59 Fourier transform of ‘classical’ signals 1 t f 1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1 0 100 200 300 400 500 600 f0 f0 f 2.5 2 1 1.5 1 0.5 0 0.5 1 1.5 2 2.5 0 20 40 60 80 100 120 140 f gipsa lab Cedric slide 60 The use of a PC to apply the theory to real measures Analogue signal with infinite temporal domain and infinite number of experiences Spectrum carrying information Signal carrying the entire information not usable Physical phenomenon inducing a magnitude to change s(t) Digital signal with finite temporal domain and one experience Signal not carrying the entire information usable gipsa lab Cedric slide 61 Frequency resolution How many propellers, blades ? Which states ? gipsa lab Lucia slide 63 Frequency resolution 1 line 1 line 2 lines ‚bad‘ frequency resolution: „ lines „blured“ ‚good‘ frequency resolution: 2 lines gipsa lab Lucia slide 64 FFT errors: The frequency resolution – separation of two close frequencies gipsa lab Cedric slide 65 FFT errors: The frequency resolution – separation of two close frequencies gipsa lab Cedric slide 66 FFT errors: The frequency resolution – separation of two close frequencies Frequency resolution is the ability to distinguish the presence of two components of similar frequencies 1 frequency resolution∝ T gipsa lab Cedric slide 66 trawler Domingo, Off Barcelona, Spain September 2006 • Radiale domingo + adobe gipsa lab Cedric slide 67 FFT errors: The amplitude resolution – simultaneous distinction of a faint and intense signal gipsa lab Cedric slide 68 FFT errors: The amplitude resolution – simultaneous distinction of a faint and intense signal s (t,ξ ), t ∈ ]− ∞ , + ∞ [ s(nT e ,ξ 0 ), n ∈ ,0[ N − ]1 si(t) = w(t) x s(t) w(t) Windows with smoothed or sharp shape (upward and downward front) gipsa lab Cedric slide 69 FFT errors: The amplitude resolution – simultaneous distinction of a faint and intense signal s (t,ξ ), t ∈ ]− ∞ , + ∞ [ s(nT e ,ξ 0 ), n ∈ ,0[ N − ]1 si(t) = w(t) x s(t) w(t) Windows with smoothed or sharp shape (upward and downward front) gipsa lab Cedric slide 70 Types of analysis windows gipsa lab Cedric slide 71 Take home message FFT errors 1] Frequency resolution: determines the ability to separate components of similar frequencies. The limiting value δf is inversely proportional to the duration of observation (window) and dependent on the type of the analysis window. 2] Amplitude resolution: determines the ability to detect a faint component in the presence of an intense one. It is dependent on the analysis window. In the case of a rectangular window, a component with a 5 times smaller amplitude compared to another component might not be detected. 3] To increase the amplitude resolution , We must chose a weighting Windows with a smooth shape. As a consequence, the size (duration) of the analysis window is reduced, implying a degradation of the frequency resolution. gipsa lab Cedric slide 72 Power spectral density of Random signal Periodogram s = 1,(s[ ξ1); (s 2,ξ1); (s 3,ξ1)...; (s N,ξ1)] ~ 1 2 γs )f( = FFT )s( Nfs Estimated with FFT => corrupted with error (frequency resolution, amplitude resolution, dispersion) gipsa lab Cedric slide 73 Types of spectra – choice depends on use Octave or 1/3 octave levels: Noise impact studies on mammalian ears (masking) Jensen et al.2012, JASA Narrowband (1Hz bands) levels: Ambient noise descriptions gipsa lab Lucia slide 74 From the narrowband to the wideband, octave and 1/3 octava band spectra 1/3 d’Octave band around f0 Octave band around f0 f0 1/ 6 f B = f[ = f, = 2 f ] 0 1 1/ 6 2 0 B = f[ 1 = f, 2 = 2f0 ] 2 2 Energy of s(t) within the bandwidth B = [f 0 – 0.5, f 0+ 0.5] f2 )B(sl = ∫ γ )f( df f1 gipsa lab Cedric slide 75 From the narrowband to the wideband, octave and 1/3 octava band spectra gipsa lab Lucia slide 76 Outline • Introduction • Introduction to sound • Measurement chain • Spectral analysis of acoustic measurements • Time-frequency representation • Applied examples from our own research gipsa lab Lucia slide 77 Time frequency representation Spectrogram gipsa lab Lucia slide 78 Introducing the spectrogram – why? Sound 1 Sound 2 1 0.9 0.8 0.7 0.6 0.5 dsp V2/Hz 0.4 0.3 0.2 0.1 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 f (Hz) • live gipsa lab Lucia slide 79 The limitations of the Fourier Transform for non stationary signals The Fourier transform transforms a temporal signal into a frequency signal It indicates the frequency content of a signal… …but does not date the frequency content! => Reasons why it is appropriate for stationary signals, with a stationary signal = a signal who’s frequency or spectral content do not change with respect to time! gipsa lab Cédric slide 79 Non stationary signals – frequency modulated signals Single frequency Varying frequency gipsa lab Cédric slide 80 Need of a time frequency representation: which frequency f(t) at time t ? We want to map the power of a signal in a time-frequency plane frequency Instantaneous frequency f(t) time gipsa lab Cédric slide 81 frequency time gipsa lab Cédric slide 82 For non stationary signals • Goal: for deterministic non stationary signals, how to get from a frequency to a time frequency representation • The frequency : number of cycles per second • Intrinsic problem : frequency is already time dependant in a time frequency representation we look for the instantaneous frequency (number of cycles during dt around t)…. gipsa lab Cédric slide 83 The short term Forurier Transform (STFT) The Spectrogram STFT corresponds to an adaptation of the Fourier transform – a spectral representation of consequent time segments S(t , f ) = s(t)× w (t − t )exp(−2πjf t)dt 0 0 ∫ T 0 0 S(t0 , f0 ) = F(s(t)× wT (t − t0 )) The spectrogram = the squared magnitude of the STFT of a signal s(t) 2 S pect (t0 , f0 ) = S(t0 , f0 ) The spectrogram = a map of signal energy in time frequency plane gipsa lab Cédric slide 84 The short term Forurier Transform (STFT) The Spectrogram s t1 t0 t ωL ωL S(t0 , f ) = F(s(t)×ωL (t − t0 )) S f t t1 t S(t , f ) 2 = spectrogra0 m gipsa lab 0 1 0.8 0.6 0.4 0.2 0 signal 0.2 0.4 0.6 0.8 1 0 200 400 600 800 1000 1200 1400 1600 1800 2000 temps ωL ωL S(t0 , f ) = F(s(t)×ωL (t − t0 )) gipsa lab The short term Forurier Transform (STFT) The Spectrogram Numerical implementation: S(iM , j) = FFTL (s(n)× wL (n − iM )), j ∈{0,.., L −1} t(s) = iM j f (Hz) = f L e M=(1 ov)L n L gipsa lab Cédric slide 85 • live, • Linear Frequency modulation • Dolphin’s whistles gipsa lab Cédric/Lucia slide 86 The short term Forurier Transform (STFT) The Spectrogram The degrees of freedom of the STFT window length : L window type : wL window overlap : ov The choice of the degrees of freedom determines the properties of the time frequency representation ov = 0.5 ? , L et wL ? M=(1 ov)L n L gipsa lab Cédric slide 87 f#1/ t gipsa lab Cédric slide 92 Frequency Frequency Time Time L= small: L= high : Good time resolution Bad time resolution Bad frequency resolution Good frequency resolution Short L Long L gipsa lab Cédric slide 93 The short term Forurier Transform (STFT) The Spectrogram The degrees of freedom of the STFT: the window length : L compromise between time and frequency resolution the type of window : wL compromise between frequency and amplitude resolution the window overlap : ov >0.5 gipsa lab Lucia slide 91 • live on real data : sifflement.wav gipsa lab Cédric slide 95 Extraction of key parts of a spectrogram gipsa lab Lucia slide 96 Extraction of key parts of a spectrogram gipsa lab Lucia slide 96 Extraction of key parts of a spectrogram Method – Compute a spectrogram – Segment the spectrogram into binary areas • 0=> H0 absence of target signal • 1=> H1 presence of target signal gipsa lab cédric slide 97 H0: signal absent, if D0 : good decision, if D1 : bad decision – false alarm (Pfa) H1: signal present, if D1 : good decision (Pd), if D0 : no bad decision gipsa lab cédric slide 98 General architecture of a signal detector Spectrogram gipsa lab cédric slide 99 T/H1 T/H0 gipsa lab cédric slide 100 T/H1 T/H0 gipsa lab cédric slide 101 Pfa et Pd +∞ +∞ P = pdf (α H0 d) α =1− cdf (λ H ) P pdf ( H d) cdf ( H ) fa ∫ Q Q 0 d = ∫ Q α 1 α =1 − Q λ 1 λ λ gipsa lab cédric slide 102 Detector with a constant false alarm rate • In many application of signal detection, f Q(q)|H1 is not well known. • We define a detector with constant false alarm rate Pfa =1− cdfQ (λ H 0 ) −1 λ = cdfQ 1( − Pfa H 0 ) −1 Pd =1− cdfQ (cdfQ 1( − Pfa H 0 ) H1) gipsa lab cédric slide 103 Interest of data processing for signal detection no processing processing gipsa lab cédric slide 104 gipsa lab cédric slide 105 gipsa lab The processing: computation of the spectrogram 1 q f H 0 (q) = exp(− ),q ≥ 0 Q Lσ 2 Lσ 2 For a stationary q Gaussian noise F H0 (q) =1− exp(− ) Q Lσ 2 2 λ = Lσ log(Pfa ) gipsa lab cédric slide 106 Before spectrogram computation ov =0.5 L = 1024 wL = kaiser 180 dB After spectrogram computation gipsa lab cédric slide 107 Processing gain = function (L, signal) gipsa lab cédric slide 108 Bottlenose dolphins, Molène LIVE adobe gipsa lab Cédric/Lucia slide 111 Pfa=10 -6 Example 2 : influence of L L=128 L=512 L=1024 L=8192 gipsa lab Lucia slide 113 Example 1 : influence of the Pfa L=1024 Pfa=1 e-6 -4 Pfa=10 -8 Pfa=10 Pfa=10 -6 Pfa=10 -3 gipsa lab Lucia slide 112 Specific literature General • R. Urick - Principles of Underwater Sound • W.W.L. Au & M.C. Hastings - Principles of Marine Bioacoustics Signal processing (detection, time-frequency) • Hlawatsch, F. & Boudreaux-Bartels, G. F. (1992), 'Linear and quadratic time-frequency signal representations', Signal processing magazine, IEEE 9(2), 21-67 . • Kay, S. (1998), Fundamentals of statistical signal processing, detection theory, Prentice Hall, New jersey . gipsa lab Outline • Introduction • Introduction to sound • Measurement chain • Spectral analysis of acoustic measurements • Time-frequency representation • Applied examples from our own research gipsa lab Environmental applications Molène 2011: dolphins & ships Use of ambient noise in ecology: FROM OCEAN SOUNDS TO COASTAL ECOSYSTEM MONITORING talk, friday 21st september @ 8h15 am gipsa lab Study site • weather station • models (weather, tides, currents…) gipsa lab Study site 6 10m 800 – 1000 animal species 300 - 400 species of algae & plants, (J. Grall, OSU Resident population of ~40 bottlenose dolphins RdB) (Tursiops truncatus ) Alpheus macrocheles Echinus esculentus 1000 / ha 2000 / ha (100mx100m) (Grall, J. OSU Brest, 2011) (Grall, J. OSU Brest, 2011) gipsa lab Objectives • How to describe the soundscape of Molène: which acoustic descriptors? Which algorithms ? • Reconstruct an acoustic landscape through time series (3x6 months) of the descriptors • Analyse the time series: their contribution to the description and understanding of the environment Biophony (bottlenose dolphin , benthic activity , ) Géophony (wind, rain) Anthropophony (mainly boats) gipsa lab Some numbers • 1 year = signal processing development & pilot experiments • 6 months observations ( 3 terabytes raw data, 3 recorders 3x15 k€ , boat trips ~ 6 k€) … 10s 10s 10s 10s 10s 10s 10s 10s … • two months of data processing & analysis => 35 days PC calculations => 1.5 Mio segments gipsa lab … 10s 10s 10s 10s 10s 10s 10s 10s … Processing algorithms Ambient noise Dolphin detection Acoustic descriptors gipsa lab Ambient noise vs. close sources Ambient noise Individually distinctive sources gipsa lab Algorithms – Ambient noise wideband analysis (RL, BNL, IR, IL) Energy based detector gipsa lab Algorithms – Frequency modulations whistle detections (WR) Spectrogram based detector gipsa lab Anthropogenic activity in the Parc Naturel Marin d’Iroise gipsa lab 24h spectrogram data inspection, choice of analysis band Small, identifiable boats night day Anthropogenic ambient noise – low frequencies gipsa lab Small, identifiable boats RL BNL> Seuil => binarization Energy based detector Analysis window size = 10min gipsa lab Anthropogenic background noise gipsa lab M_P3 M_P2 M_P4 gipsa lab M_P3 M_P2 M_P4 Affected site: Noise source: Rade Non affected site: 8dB between day & night de Brest – 8dB No, night day difference propagation?! between night & day gipsa lab Intermezzo… power apectral density of Molène ambient noise 1 0.9 0.8 0.7 0.6 0.5 dsp V2/Hz 0.4 0.3 0.2 0.1 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 f (Hz) P2 , july, september P1 , july, september gipsa lab Intermezzo… power apectral density of Molène ambient noise 1 0.9 0.8 0.7 0.6 0.5 dsp V2/Hz 0.4 0.3 Anthropophony 0.2 0.1 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 f (Hz) P2 , july, september Biophony P1 , july, september gipsa lab Habitat use by the bottlenose dolphins (Tursiops truncatus ) of the PNMI gipsa lab gipsa lab Algorithms – Frequency modulations whistle detections (WR) binarozation ov =0.5 L = 1024 Spectrogram based detector wL = kaiser 180 dB gipsa lab gipsa lab Acoustic presence – time HIGH LOW series of whistle detections 24h TIDES 6 months gipsa lab Comparison/com bination of dolphin vs. boat detections (close) 24h gipsa lab