Room Impulse Response Measurement and Analysis. Music 318, Winter 2010, Impulse Response Measurement

Transcription

1 Room Impulse Response Measurement and Analysis

2 Reverberation and LTI Systems α(t) = L{ a(t) }, β(t) = L{ b(t) } superposition, linearity { } = α(t) + β(t) L{ γ a(t) } = γ α(t) L a(t) + b(t) time invariance { } = α(t τ) L a(t τ) Reflected source signals are sensitive to the details of the environment geometry and materials. Reverberation is roughly linear and time-invariant, and thus characterized by its impulse response. 2

3 LTI System Measurement amplitude test signal time - seconds test signal response 1 s(t) = δ(t) ˆ h (t) = r(t) frequency - khz Impulsive test signal: time - seconds Limited input amplitude poor noise rejection 3

4 LTI System Measurement Methods k s k (t) s k ( t) = γ δ(t) ˆ h (t) = 1 γ k s k ( t) r k (t) Repeat measurement, average results MLS, Golay s k (t) = δ(t), k = 1,2, γ ˆ h (t) = 1 γ Smear impulse over time allpass chirp, sine sweep k r k (t) s(t) = γ a(t), a( t) a(t) = δ(t) ˆ h (t) = 1 γ s( t) r(t) 4

5 Sine Sweep Measurement amplitude test signal time - seconds test signal response 1 amplitude processed chirp time - seconds estimated impulse response 1 frequency - khz frequency - khz time - seconds time - seconds Frequency trajectory ω(t), t [,T], sine sweep s(t): t s(t) = sinθ(t), θ(t) = ω(τ)dτ 5

6 Sine Sweep Generation Monotonic frequency trajectory ω(t), t [,T] Sine sweep s(t), "inverse" σ(t): t s(t) = sinθ(t), θ(t) = ω(τ)dτ σ(t) = v( t) sinθ( t), v(t) = 2 dω dt For ω(t) monotonic, slowly varying, ω [ω, ω T ] s(t) σ (t) δ(t), bandlimited to ω [ω,ω T ] 6

7 Measurement Bias, SNR Gain Impulse response estimate ˆ h (t) = σ (t) r(t) = [σ(t) s(t)] h(t) + σ (t) n(t) = h(t) + σ (t) n(t) Expected value (zero-mean noise assumed) E{ h ˆ (t)} = h(t) + σ (t) E{n(t)} = h(t) SNR gain (sweep, noise uncorrelated) Γ(ν) 1/ 2 dω dt 7

8 Nonlinear Measurement Example sine sweep response 2 15 frequency - khz time - seconds Speaker generates harmonic series k ( t ) r(t) = g(t) β(ω k )sin ω k (τ)dτ, ω k (t) = k ω(t) 8

9 Exponential Sweep (Farina, 2) exponential sweep response 1 1 ω(t) = ω e ηt, η = 1 T log ω ω T frequency - khz 1 ω k (t) = k ω e ηt = ω e η(t + 1 log k) η time - seconds = ω(t + 1 log k) η Sweep harmonic trajectories isomorphic; appear as time-offset exponential sweeps 9

10 Exponential Sweep Response 1 processed response amplitude time - seconds exponential sweep response 1 1 frequency - khz time - seconds Processing using the sweep inverse produces a series of time-shifted responses, one for each harmonic present. The "linear" response is the impulse response; the remaining responses are used to estimate THD. 1

11 System Linear Portion 1 processed response amplitude time - seconds exponential sweep response frequency - khz preamp nonlinearity time - seconds Power nonlinearities generate even/odd harmonic series, depending on the sense of p; e.g., for p odd, cos p ωt = 2 1 p ( p 1)/2 k = p k cos( p 2k) ωt The time-separated "linear" response may not be the desired system linear portion. 11

12 Acoustic Tube Measurment Example.5 sine sweep, s(t) 1 sine sweep spectrogram s(t) amplitude frequency - khz 5 r(t) amplitude sine sweep response, r(t) time - milliseconds frequency - khz sine sweep response spectrogram time - milliseconds.2 measured impulse response.15 ˆ h (t) amplitude time - milliseconds 12

13 CCRMA Lobby Measurment Example.5 sine sweep, s(t) 1 sine sweep spectrogram s(t) amplitude frequency - khz 5 r(t) amplitude sine sweep response, r(t) time - milliseconds frequency - khz sine sweep response spectrogram time - milliseconds.8 measured impulse response.6 ˆ h (t) amplitude time - milliseconds 13

14 Impulse Response Measurement Analysis The impulse response of a reverberant environment will often have a direct path, followed by a few early reflections and the late-field reverberation. 14

15 Echo Density Profile Echo density can be measured along an impulse response by comparing the percentage of taps lying outside the local standard deviation to that expected for Gaussian noise. 15

16 Echo Density Psychoacoustics 16

17 Late-Field Time-Frequency Analysis 17

18 Late-Field Time-Frequency Analysis 18

19 Late-Field Time-Frequency Analysis 19

20 Late-Field Decay Rate Estimation 2

21 Equalization and Reverberation Time 21

22 EMT14 Plate Reverberator Responses impulse response spectrograms late-field decay times 22

23 Late-Field Spatial Impression estimated arrival energy microphone arrays 23

24 Late-Field Spatial Characteristics Lateral energy fraction (LEF) LEF(t) = t +β τ = t β t +β τ = t β h 8 2 (τ) h 2 (τ) figure-of-8 omni-directional Inter-aural cross coherence (IACC) IACC(t) = t +β τ = t β t +β τ = t β h L (τ) h R (τ) h L 2 (τ) t +β τ = t β h 2 R (τ) 1/ 2 right ear binaural 24