Echo Generation and Simulated Reverberation

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Echo GenerationandSimulated Reverberation

• R.C. Maher
• ECEN4002/5002 DSP Laboratory
• Spring 2002

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Recirculating Delay Line

• Recall that a simple delay FIFO (first-in,
  first-out) queue can be implemented using a
  modulo buffer
• Now, consider a recirculating buffer

output can also be taken here
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Recirculating Delay (cont.)
xn
yn
N poles equally spaced around circle (radius k1/N)
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Recirculating Delay (cont.)

• Example unit sample response (N8, k0.8)

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Recirculating Delay (cont.)

• Frequency response of system
• A comb filter

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Echo Generator

• If length N is short, comb filter effect (audio
  coloration) is noticeable
• If length N corresponds to a time delay of 200ms
  or more, output perceived as an echo of the input
• Scaling of input is typically needed to prevent
  overflow

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Acoustics

• Sound propagates through air as a longitudinal
  wave
• Speed of sound
• 343 m/s _at_ 20C (331 m/s _at_ 0C)
• About 1125 ft/s
• About 1 ft/ms (light travels about 1 ft/ns)
• About 5 seconds per mile
• Audible wavelengths 1.7cm to 17m

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Human Hearing Characteristics

• Frequency sensitivity roughly 20 Hz 20kHz
• 3 decades, or 10 octaves
• Compares to less than one octave for human visual
  system (wavelengths 3800 7600 angstroms)
• Amplitude sensitivity roughly 20?Pa 20Pa
• Atmospheric pressure 105 Pa
• Minimum audible sound corresponds to motion a
  fraction of diameter of hydrogen atom!
• Any better, and we would hear thermal noise
• Difference judgments good, absolute judgments poor

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Acoustical Transfer Function

• Linear Time-Invariant (LTI) systems can be fully
  described by an impulse response
• Fourier Transform of the impulse response is the
  transfer function
• Acoustical path from a sound source to the
  listeners ear is LTI, so we can describe the
  acoustical system with a transfer function

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Reflections and Reverberation

• Direct sound arrival is followed by reflections
  from room surfaces
• Overlapping reflections are heard as
  reverberation
• Direct-to-Reverberant ratio gives cues to size of
  room, type of room surfaces, and distance from
  source

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Direct Sound and Reflections
Sound Source
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Reverb Simulation

• Method 1 obtain impulse response of real room,
  then convolve with input signal
• Results can be good, but computation and storage
  requirements are high impulse response sequence
  for 3-5 seconds is 200k
• Method 2 use recirculating delay lines to
  create an artificial impulse response
• Less computation and storage, but tricky to get
  satisfactory sound quality

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Reverb Simulation (cont.)

• For good reverb
• echo density (echoes per second) must increase as
  time goes on
• response should be quasi-random (no spectral
  coloration)
• high frequencies typically decay faster than low
  frequencies

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Reverb Simulation (cont.)

• Plan use parallel recirculating delay lines
  with incommensurate delays

Delay Line (z-N1)
k1
Delay Line (z-N2)
k2
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Other Improvements

• Cascade of all pass recirculators

-k
Delay Line (z-N)
N poles and zeroes equally spaced around
circle (pole radius k1/N, zero radius k-1/N)
k
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Other Improvements (cont.)

• Add lowpass filter to feedback path shortens
  high frequency reverb time more like natural
  reverberation

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EVM Note External Memory

• To use external memory on EVM, need to program
  the bus control register and the address
  attribute register 0 (see 56300 Family Manual)
• movep 040821,xM_AAR0 Compare 8 most
  significant bits
• Look for a match with address
• Y0000 0100 xxxx xxxx xxxx xxxx
• No pack, no mux, Y enabled
• P and X disabled
• AAR0 pin active low
• movep 012421,xM_BCR One ext. wait state
• Access to external memory is slower than internal
  memory wait state stalls processor