Room Impulse Response

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

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response spectra

frequency - Bark0 5 10 15 20 25

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Music 318, Winter 2007, Impulse Response Measurement 2

Reverberation and LTI Systems

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direct path

early reflections


• 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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test signal

time - seconds

ampl

itude

test signal response

time - seconds

freq

uenc

y -

kHz

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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)


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)


Sine Sweep Measurement

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1

test signal

time - seconds

ampl

itude

test signal response

time - seconds

freq

uenc

y -

kHz

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processed chirp

time - seconds

ampl

itude

estimated impulse response

time - secondsfr

eque

ncy

- kH

z

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• Frequency trajectory (t), t [0,T], sine sweep s(t):

s(t) = sin (t), (t) = ( )d0

t

∫


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


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


sine sweep response

time - seconds

freq

uenc

y -

kHz

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5

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15

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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)


exponential sweep response

time - seconds

freq

uenc

y -

kHz

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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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1processed response

time - secondsam

plitu

de


time - seconds

freq

uenc

y -

kHz

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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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1processed response

time - seconds

ampl

itude


time - seconds

freq

uenc

y -

kHz

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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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0.5sine sweep, s(t)

ampl

itude

freq

uenc

y -

kHz

sine sweep spectrogram

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5

10

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0.5sine sweep response, r(t)

time - milliseconds

ampl

itude

time - milliseconds

freq

uenc

y -

kHz

sine sweep response spectrogram

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5

10

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0

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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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0.5sine sweep, s(t)

ampl

itude

freq

uenc

y -

kHz

sine sweep spectrogram

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5

10

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0

0.5

1sine sweep response, r(t)

time - milliseconds

ampl

itude

time - milliseconds

freq

uenc

y -

kHz

sine sweep response spectrogram

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5

10

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0

0.02

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0.08measured impulse response

time - milliseconds

ampl

itude

CCRMA Lobby Measurment Example

s(t)

r(t)

ˆ h (t)


Impulse Response Measurement Analysis

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time - milliseconds

direct path

early reflections


• 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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1impulse response

time - milliseconds

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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.


Echo Density Psychoacoustics

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6impulse responses

time - milliseconds

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echo density profile, 20-msec. frames.

time - msec.


Late-Field Time-Frequency Analysis

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response spectra


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0response spectra, 70-msec. interval between frames.

frequency - kHz



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0response power spectrum, Bark-spaced frequencies.

time - milliseconds


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0measured, modeled response energy profile

time - milliseconds

Late-Field Decay Rate Estimation


Equalization and Reverberation Time

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0q - resonance spectrum.

frequency - kHz

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101T_{60} - 60-dB decay time.

frequency - kHz


EMT140 Plate Reverberator Responses

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EMT140B response spectra, various damping settings


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101T_{60} - 60-dB decay time, various low-frequency absorption settings.

frequency - kHz

impulse response spectrograms

late-field decay times

Room Impulse Response

Documents

response t

t sine

t music

e e t t

t monotonic

inverse t

r t sk t

golay t