Acoustic and Psychoacoustic issues in Room Correction

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Acoustic and Psychoacoustic issues in Room
Correction

• James D. (jj) Johnston
• Serge Smirnov
• Microsoft Corporation

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This talk is in two parts

• First, JJ will discuss some basic acoustics, some
  psychoacoustic issues, and explain how that
  impacts the idea of room correction.
• Then, Serge will explain how we actually
  implement these principles in the Vista room
  correction algorithm.

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Acoustics- What does a room do?
Diffuse tail
Direct signal
Early Reflections
Unpleasantly large Late reflection
Early reflections are those more or less under
the 10 msec mark. late (specular) reflections
create a problem with perception, more on that
later. The example here is egregious.
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What else does a room do?

• That diffuse field
• It is not frequency-flat
• Almost always, high frequencies roll off much
  faster (lower t60) than lower frequencies.
• It is (mostly) uncorrelated at the two ears, even
  taking into account ITDs

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A point to recall

• Because high frequencies decay faster than low
  frequencies (even on a cold, dry day in the
  desert)
• If you measure the early arrival frequency
  response, it will show a different frequency
  balance than that of the entire tail
• If you compare the early and late responses, the
  difference will be even bigger.
• Were used to listening to things that way, too,
  because its what we grow up with.

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And a loudspeaker

• Radiation patterns of loudspeakers are quite
  different at different frequencies
• Typically, there is little directivity at bass
  frequencies
• As frequency goes up, there is more directivity.
• Many (consumer) speakers have fairly narrow
  high-frequency radiation patterns

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So, what does that mean?

• Many speakers, both consumer and professional,
  are not power flat in terms of polar response.
• The total radiation from the speaker, not the
  front radiation, is what is added to the
  reverberant field.
• This means that the reverberant field almost
  always gets proportionally less energy injected
  at high frequencies than low.

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Well, now we combine the two

• Several things happen
• Due to both the lower t60 at higher frequency and
  the radiation pattern of the loudspeaker there is
  less energy in the diffuse field at high
  frequencies.
• So, what do we equalize? First arrival at high
  frequencies or the whole thing?
• What happens if we get that wrong?
• There is a first-arrival
• There may be a delayed reflection of a first
  arrival.
• There are a variety of early reflections

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So, we equalize what?

• The long-term frequency response?
• The short-term frequency response?
• Some combination of both?
• How exactly do we equalize the frequency
  response
• How important is inter-channel matching
• Vs
• Flattening all responses?

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Some other acoustical issues

• What do we measure?
• If we use an omni, we record only pressure.
• There are also 3 other variables at the same
  point, the volume velocities in each of X, Y, Z
• If we use a cardioid, we record one combination
  of volume velocity and pressure
• Specifically, we record half of the volume
  velocity in the direction of the microphone
• plus
• Half of the pressure at the front of the
  microphone

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So what do we correct?

• Good question
• Some things to remember
• The eardrum converts PRESSURE into mechanical
  movement
• The head, to some extent, converts velocity to
  pressure at the ear canal
• Our head affects the measurement when its
  there listening.

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Even more acoustical issues

• Sharp zeros in frequency response
• This does not mean signal is absent.
• It means that there is no PRESSURE (presuming
  omni measurement mike) at the point in question
• It means that volume velocity is at a peak at
  that point
• The ENERGY in the room is there, but its in the
  (mostly) wrong form for the ear at THAT POINT IN
  THE ROOM.
• Adding more energy, therefore, is not a very good
  solution.
• The only time a zero is not a room storage issue
  is when the loudspeaker has a zero at that
  frequency
• So fix it, already!
• Once more, with feeling adding more energy to
  the room while its storing energy at that
  frequency is not a solution!

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Finally, a note about speakers and linear systems

• Speakers are not linear devices
• Speakers really arent linear devices
• Speakers, in fact, are rather far from anything
  approximating a linear device.
• So, it is a good idea to keep the energy at any
  one frequency low.
• Sweeps dont do that
• Allpass sequences spread out the energy at any
  one frequency across time. This is a good thing.

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NOW WHAT?

• No, dont abandon ship, the water is only up to
  your beltline!

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For useful answers, we look to the perceptual
issues
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What do the ears care about?

• With the ear, both monaurally and binaurally
  FIRST ARRIVAL rules.
• The precedence effect, which goes by any number
  of other names, shows that arrivals on the
  cochlea just after an attack are masked, even if
  they are quite a bit larger.
• They do contribute to overall timbre
• This means that most really early arrivals are
  masked

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Ear Continued

• The first-arrival provides a very strong
  localization effect binaurally.
• This localization applies to anything that is
  correlated at the two ears, including with ITD
  range delays.
• Signals that are not correlated at the two ears
  are not localized, and are, rather, heard as
  envelopment

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Localization vs. Intensity

• After the time cues are considered, intensity
  provides us with a variety of spatial cues
• First, HRTFs provide a variety of front/back,
  up/down cues.
• Mismatched intensity at the two ears at higher
  frequencies moves the stereo image.
• Remember, though, first arrival rules.

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• Remember Specular reflections are correlated at
  the two ears.
• The diffuse tail is not.
• Some rooms are far, far, far from satisfactorily
  diffuse, hence flutter echo and like problems.
  This is not an easy problem to fix.
• In the diffuse tail, bass hangs over much more
  strongly than high frequencies, both initially
  (due to loudspeaker radiation pattern) and more
  so later, due to lossy transmission and
  reflection of sound.

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Diffuse perception

• Signals that are not correlated (either by
  waveform at low frequencies or envelope at high
  frequencies) at the two ears are heard as
  diffuse or surrounding.
• This means that we hear the diffuse response of
  the room as a different (set of) auditory objects
  than the direct sounds.
• We are USED to the diffuse sounds being heavily
  colored in timbre.

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Low frequencies

• We live, day in and day out, in environments that
  provide a huge variation in the low-frequency
  environment.
• Were used to it
• Nonetheless, huge excursions, especially peaks,
  are very annoying.
• Again, remember the rule dont add energy if
  theres already too much stored.

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So, the message is?

• Equalize the direct arrival at high frequencies.
• Since we are also used to hearing bumps and dips
  at low frequencies
• Equalize the overall frequency response at low
  frequencies, dont invert the whole thing
• Whatever you do, dont try to completely invert
  the system, i.e. correct both phase and magnitude.

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Why not?

• First, what are you inverting? Pressure? Volume
  velocity? Some of each? Does it relate to what
  your head/ear does in the soundfield? (Hint NO
  )
• Second, if you try to invert phase, youll
  introduce pre-echo unless your fit and inversion
  are good to 60dB.
• Even if it was when you did it, it wont be when
  you exhale and change the humidity in front of
  your head.

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What matters most to the ear?

• First arrival timbre
• Large peaks should be equalized
• Large, sharp dips are not to be touched, remember
  the energy storage issue
• Broad dips can be equalized out for a broader
  listening area

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Where are we?

• Obviously, you need to equalize
• Gain from each speaker
• Delay from each speaker
• Frequency response, but within limits
• But in what way?
• Exact?
• Relative?
• Try to cancel, to some extent, that single first
  later reflection, but only at low frequencies.

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Why only at low frequencies?

• As the listener moves, the mic moves, etc, that
  delay will change
• If you equalize at high frequencies, a mic in the
  center of your head will be wrong for both ears.
• If you equalize only below 500Hz or so, you get a
  .5 foot radius space, give or take, where the
  cancellation makes some sense.
• You only do SOME cancellation. Even some
  cancellation removes the boxiness, and does not
  provide a bizarre experience out of the sweet
  spot.

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The practical outcome

• At low frequencies, youre adjusting the overall
  response of the room, not the details.
• At high frequencies, youre concerned only with
  the direct signal and the early reflections. This
  is almost speaker plus speaker stand correction
• In any case, you correct whatevers most
  egregious, speaker, room, whatever.
• Fix what you can, and dont touch the rest.

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Relative vs. Flat correction

• Relative correction
• Reduces the image shift and spread
• Fixes first arrival (time, frequency response,
  gain) cues in the soundfield
• Does not require a calibrated microphone
• Provides very good stereo imaging
• Flattening each channel individually
• Requires a calibrated microphone
• Does not assure channel matching, in fact, the
  best flattening solution for each speaker will
  not in general assure best relative match
• Fixes first arrival cues for gain and time just
  like relative systems
• Does provide the measurably flattest response

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Relative or Flat

• Flat costs more for equipment
• Flat requires more CPU if done accurately
• Flat doesnt fix imaging as well, unless relative
  is also added, in which case you need even more
  CPU
• Relative is cheaper, both in equipment and CPU
• Relative corrects the most obvious defects.

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First Reflection Cancellation

• This is an individual adjustment for each channel
• It removes the boxy sound to some extent
• Fixing this for the listening location means that
  we do put more impairments elsewhere in the room.
• Can be adjusted to avoid obvious impairments and
  still have some productive effect.
• Can clean up boom to some extent as well.

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Conclusions

• At low frequencies, correct the overall room
  response
• At high frequencies, correct the first arrival
• Always, obviously, correct gain and delay between
  channels
• Relative correction between channels does more
  perceptually than the same amount of CPU applied
  to flattening the system analytically.
• Too much correction is bad
• Long-window corrections at high frequencies cause
  the dentist drill experience, because the
  system will be equalized to provide way, way too
  much correction at high frequencies for the
  first-arrival signal.

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After the break

• Serge Smirnov tells us
• How to implement a room correction that addresses
  the perceptual issues
• How to keep the CPU load down at the same time

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The Break

• Well do door prizes after the break
• Please take a 15 minute stretch.

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Sequence of operations

• Generate probe signals
• Measure delays
• Measure gains
• Measure frequency response
• Identify first reflection
• (delays are measured from one set of captures,
  the rest are measured from a second set of
  captures)

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Probe generation

• Synthesized in Frequency (Discrete Fourier)
  domain
• Magnitude the same at all frequencies
• Phase is continuous across frequency including at
  pi and zero
• Extent of time spread is limited by phase change,
  no window necessary
• DFT values at a negative and positive frequencies
  are complex conjugates to generate real signal
• Transformed to time domain using inverse complex
  FFT
• Imaginary part of complex time domain signal is
  zero
• Real part of complex time domain signal is the
  probe signal

but see next slide
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Narrowband vs. Wideband Probe

• We actually generate two probes
• The wideband probe used for identifying the
  system impulse response
• A narrowband probe used as a matched filter to
  capture time and delay, while rejecting low and
  high frequency interference (noise)

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Probe Generation
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Characteristics of the Probe Signal
Autocorrelation
Time Domain
Unwrapped phase
Spectrum
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Cross-channel delay probing

• silence between probes (for room to settle)
• extra marker probe at the end to detect timing
  glitches in audio capture/playback
• LS/RS could be LR/RR
• Can also do 7-channel or other arrangement, using
  same method

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Capture from mic for delay probing
Can you find the pulses?
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Delay analysis Hilbert (aka Analytic) envelope
What comes out
Probe Autocorrelation
Note the noise rejection
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Gain, Freq response, etc. measurements (this
happens for each channel separately)
N takes are used for wide probe in case sporadic
room noises interfere
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Gain analysis (per channel, per take)
Gain is derived from the 800-2000Hz average of
power spectrum coefficients Only the first N
(128) samples of the impulse response are
used Then, for each channel, throw away outliers
and average the rest Finally, normalize all gains
relative to the channel with the highest/lowest
gain Reject the results if there is too much
variation
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Frequency domain deconvolution

1. Power spectrum of captured signal
2. Power spectrum of captured signal complex-divided
   by FFT of probe
3. First 400 samples of IFFT ( FFT ( capture ) / FFT
   ( probe ) )

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Frequency response analysis (per channel, per
take)
Deconvolution by way of division in the frequency
domain Then, for each channel, throw away
outliers and average the rest Finally, if
relative response correction is specified,
normalize all responses relative to the average
of all channels
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Computation of FIR correction filter (with
apologies)

• Separate correction filters are computed for low
  vs high frequencies
• Each filter assumes that the part it doesnt do
  is flat
• Durbin LPC is used to obtain all-zero inverse
  filters (normally Durbin LPC is used to obtain
  all-pole direct filters)
• transition between the low high is done in
  log(power spectrum) domain
• Low- and high-freq correction filters are
  convolved to obtain final filter
• final filter is then (not shown) normalized for
  unity avg gain 800-2000Hz

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Location of First reflection

• Computed from analytic envelope

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Denominator of all-pole reflection cancellation
filter

• Reflection correction filter has a trivial
  numerator (1)
• Denominator uses (upside down) the coefficients
  of a specially crafted M-tap symmetric low-pass
  FIR positioned at a distance determined by
  reflection delay. I.e., it recursively subtracts
  LP-filtered version of echo.

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The Low Pass filter

• Provides a wider sweet spot
• Avoids flutter echo problems off-axis
• Ensures 100.00 filter stability
• The data for the filter is internal to the
  rendering engine
• The stored information is only gain and delay,
  which can be trivially tested for stability at
  startup time

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The Rendering Engine

• applies per-channel gain, delay, FIR filter
  (frequency response correction), IIR filter
  (reflection cancellation)
• Is low complexity in CPU, RAM, ROM
• Allows application of a partial profile (say to
  2 channels of a 7.1 profile)
• Allows limited application of a profile generated
  for a different sample rate

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• Questions ?