Room Impulse Response Measurement and Analysisadnanm/SCI220/Music318ir.pdf · Music 318, Winter...
Transcript of Room Impulse Response Measurement and Analysisadnanm/SCI220/Music318ir.pdf · Music 318, Winter...
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Music 318, Winter 2007, Impulse Response Measurement
Room Impulse Response Measurementand Analysis
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1CCRMA Lobby Impulse Response
time - milliseconds
direct path
early reflections
late-field reverberation
power - dB
0
10
20
30
40
50
60
response spectra
frequency - Bark0 5 10 15 20 25
0
200
400
600
800
1000
1200
1400
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Music 318, Winter 2007, Impulse Response Measurement 2
Reverberation and LTI Systems
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1CCRMA Lobby Impulse Response
time - milliseconds
direct path
early reflections
late-field reverberation
• Reflected source signals are sensitive to the detailsof the environment geometry and materials.
• Reverberation is roughly linear and time-invariant,and thus characterized by its impulse response.
(t) = L a(t){ }, (t) = L b(t){ }
L a(t) + b(t){ } = (t) + (t)
L ⋅ a(t){ } = ⋅ (t)
L a(t − ){ } = (t − )
superposition, linearity
time invariance
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Music 318, Winter 2007, Impulse Response Measurement 3
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test signal
time - seconds
ampl
itude
test signal response
time - seconds
freq
uenc
y -
kHz
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2
4
6
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10
LTI System Measurement
Impulsive test signal:
– Limited input amplitude poor noise rejection
s(t)
LTI system
r(t)
test sequence
measured response
n(t)
h(t)
measurement noise
s(t) = (t) → ˆ h (t) = r(t)
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Music 318, Winter 2007, Impulse Response Measurement 4
LTI System Measurement Methods
• Smear impulse over time – allpass chirp, sine sweep
s(t)
LTI system
r(t)
test sequence
measured response
n(t)
h(t)
measurement noise sk (t) ∗ sk (−t) =
k∑ ⋅ (t)
→ ˆ h (t) =1
sk (−t) ∗ rk (t) k
∑
• Repeat measurement, average results – MLS, Golay
sk (t) = (t), k = 1,2,K → ˆ h (t) =
1rk (t)
k∑
s(t) = ⋅ a(t), a(−t) ∗ a(t) = (t) → ˆ h (t) =1
s(−t) ∗ r(t)
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Music 318, Winter 2007, Impulse Response Measurement 5
Sine Sweep Measurement
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0
1
test signal
time - seconds
ampl
itude
test signal response
time - seconds
freq
uenc
y -
kHz
0 0.5 1 1.5 20
2
4
6
8
10
0 0.5 1 1.5 2
0
0.5
1
processed chirp
time - seconds
ampl
itude
estimated impulse response
time - secondsfr
eque
ncy
- kH
z
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2
4
6
8
10
• Frequency trajectory (t), t [0,T], sine sweep s(t):
s(t) = sin (t), (t) = ( )d0
t
∫
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Music 318, Winter 2007, Impulse Response Measurement 6
s(t) ∗ (t) ≈ (t), bandlimited to ∈[ 0, T ]
Sine Sweep Generation
• Monotonic frequency trajectory (t), t [0,T]
• Sine sweep s(t), "inverse" (t):
s(t) = sin (t), (t) = ( )d0
t
∫
• For (t) monotonic, slowly varying, [ 0, T]
(t) = v(−t) ⋅ sin (−t), v(t) = 2d
dt
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Music 318, Winter 2007, Impulse Response Measurement 7
E{ ˆ h (t)} = h(t) + (t) ∗E{n(t)} = h(t)
Measurement Bias, SNR Gain
• Impulse response estimate
ˆ h (t) = (t) ∗ r(t) = [ (t) ∗ s(t)] ∗ h(t) + (t) ∗ n(t)
= h(t) + (t) ∗ n(t)
• Expected value (zero-mean noise assumed)
• SNR gain (sweep, noise uncorrelated)
Γ( ) ∝1/ 2d
dt
s(t)
LTI system
r(t)
test sequence
measured response
n(t)
h(t)
measurement noise
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Music 318, Winter 2007, Impulse Response Measurement 8
sine sweep response
time - seconds
freq
uenc
y -
kHz
0.2 0.4 0.6 0.8 1 1.2 1.4 1.60
5
10
15
20
Nonlinear Measurement Example
• Speaker generates harmonic series
r(t) = g(t) ∗ ( k)sin k ( )d0
t
∫( )k
∑ , k (t) = k ⋅ (t)
s(t)(·)
speaker
g(t)
room
r(t)
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Music 318, Winter 2007, Impulse Response Measurement 9
exponential sweep response
time - seconds
freq
uenc
y -
kHz
0.2 0.4 0.6 0.8 1 1.2 1.4 1.610-1
100
101
Exponential Sweep (Farina, 2000)
• Sweep harmonic trajectories isomorphic; appear astime-offset exponential sweeps
(t) = 0 ⋅e t, =1
Tlog 0
T
= (t + 1 log k)
k (t) = k ⋅ 0 ⋅e t
= 0 ⋅e(t + 1 log k)
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Music 318, Winter 2007, Impulse Response Measurement 10
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1processed response
time - secondsam
plitu
de
exponential sweep response
time - seconds
freq
uenc
y -
kHz
0 0.5 1 1.5 210-1
100
101
Exponential Sweep Response
• Processing using the sweep inverse produces a series oftime-shifted responses, one for each harmonic present.
• The "linear" response is the impulse response; the remainingresponses are used to estimate THD.
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Music 318, Winter 2007, Impulse Response Measurement 11
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0
0.5
1processed response
time - seconds
ampl
itude
exponential sweep response
time - seconds
freq
uenc
y -
kHz
0 0.5 1 1.5 210-1
100
101
System Linear Portion
• Power nonlinearities generate even/odd harmonicseries, depending on the sense of p; e.g., for p odd,
cosp t = 21− p p
k
cos( p − 2k)k =0
( p −1)/2
∑ ⋅ t
→ The time-separated "linear" response may not bethe desired system linear portion.
s(t)g(t)
room
(·)
mic preamp
r(t)
preamp nonlinearity
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Music 318, Winter 2007, Impulse Response Measurement 12
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0
0.5sine sweep, s(t)
ampl
itude
freq
uenc
y -
kHz
sine sweep spectrogram
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5
10
0 500 1000 1500-0.5
0
0.5sine sweep response, r(t)
time - milliseconds
ampl
itude
time - milliseconds
freq
uenc
y -
kHz
sine sweep response spectrogram
0 200 400 600 800 10000
5
10
0 5 10 15 20 25 30 35 40-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2measured impulse response
time - milliseconds
ampl
itude
Acoustic Tube Measurment Example
s(t)
r(t)
ˆ h (t)
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Music 318, Winter 2007, Impulse Response Measurement 13
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0
0.5sine sweep, s(t)
ampl
itude
freq
uenc
y -
kHz
sine sweep spectrogram
0 200 400 600 800 10000
5
10
0 500 1000 1500 2000-1
-0.5
0
0.5
1sine sweep response, r(t)
time - milliseconds
ampl
itude
time - milliseconds
freq
uenc
y -
kHz
sine sweep response spectrogram
0 500 1000 1500 20000
5
10
0 100 200 300 400 500 600 700 800 900 1000-0.04
-0.02
0
0.02
0.04
0.06
0.08measured impulse response
time - milliseconds
ampl
itude
CCRMA Lobby Measurment Example
s(t)
r(t)
ˆ h (t)
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Music 318, Winter 2007, Impulse Response Measurement 14
Impulse Response Measurement Analysis
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1CCRMA Lobby Impulse Response
time - milliseconds
direct path
early reflections
late-field reverberation
• The impulse response of a reverberant environmentwill often have a direct path, followed by a few earlyreflections and the late-field reverberation.
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Music 318, Winter 2007, Impulse Response Measurement 15
0 20 40 60 80 100 120 140 160 180 200-0.5
0
0.5
1impulse response
time - milliseconds
0 20 40 60 80 100 120 140 160 180 2000
0.2
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1
echo density profile, 20-msec. frames.
time - msec.
Echo Density Profile
• Echo density can be measured along an impulseresponse by comparing the percentage of tapslying outside the local standard deviation to thatexpected for Gaussian noise.
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Music 318, Winter 2007, Impulse Response Measurement 16
Echo Density Psychoacoustics
0 100 200 300 400 500 600 700 800 900-2
0
2
4
6impulse responses
time - milliseconds
0 100 200 300 400 500 600 700 800 9000
0.2
0.4
0.6
0.8
1
echo density profile, 20-msec. frames.
time - msec.
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Music 318, Winter 2007, Impulse Response Measurement 17
Late-Field Time-Frequency Analysis
power - dB
0
10
20
30
40
50
60
response spectra
frequency - Bark0 5 10 15 20 25
0
200
400
600
800
1000
1200
1400
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Music 318, Winter 2007, Impulse Response Measurement 18
Late-Field Time-Frequency Analysis
10-1 100 101-80
-70
-60
-50
-40
-30
-20
-10
0response spectra, 70-msec. interval between frames.
frequency - kHz
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Music 318, Winter 2007, Impulse Response Measurement 19
Late-Field Time-Frequency Analysis
0 200 400 600 800 1000 1200 1400-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0response power spectrum, Bark-spaced frequencies.
time - milliseconds
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Music 318, Winter 2007, Impulse Response Measurement 20
0 200 400 600 800 1000 1200 1400-120
-100
-80
-60
-40
-20
0measured, modeled response energy profile
time - milliseconds
Late-Field Decay Rate Estimation
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Music 318, Winter 2007, Impulse Response Measurement 21
Equalization and Reverberation Time
10-1 100 101
-10
-5
0q - resonance spectrum.
frequency - kHz
10-1 100 10110-1
100
101T_{60} - 60-dB decay time.
frequency - kHz
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Music 318, Winter 2007, Impulse Response Measurement 22
EMT140 Plate Reverberator Responses
power - dB
0
10
20
30
40
50
60
EMT140B response spectra, various damping settings
frequency - Bark0 5 10 15 20 25
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
10-1 100 10110-1
100
101T_{60} - 60-dB decay time, various low-frequency absorption settings.
frequency - kHz
impulse response spectrograms
late-field decay times