IFT6080 Homework 1 Overview

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IFT6080 Homework 1 Overview

• Rebecca Fiebrink
• 20 February 2006

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Part 1 DFT/IDFT

• Implementation of DFT Do summation as a
  multiplication of an NxN matrix with an Nx1
  vector

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Part 1 DFT/IDFT
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Part 2 Period

• Period
• Filter signal into six bands 50-301Hz,
  301-1000Hz, 1000-2500Hz, 2500-8000Hz,
  8000-15000Hz, 15000-22050Hz for 44.1kHz SR
• Adjust all but 50Hz limits for other sample rates
• Store each passband output to a file
• Do beat-finding algorithm for all passbands, and
  use a self-assigned score for how well detection
  performed
• Pick the beat with the highest score

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Part 2 Period

• Detecting the beat in a passband, p
• Perform auto-correlation
• Throw away the first half of the signal
• Low-pass filter the signal

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Part 2 Period

• Autocorrelation processed for peak detection

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Part 2 Period

• Detecting the beat in a passband, p
• Perform auto-correlation
• Throw away the first half of the signal
• Low-pass filter the signal
• Assume peak n is higher than peak n1
• Find peaks 1 through 7, and record distance
  between subsequent peaks

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Part 2 Period
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Part 2 Period
10
Part 2 Period
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Part 2 Period
12
Part 2 Period
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Part 2 Period
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Part 2 Period
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Part 2 Period

• Detecting the beat in a passband, p
• Perform auto-correlation
• Throw away the first half of the signal
• Low-pass filter the signal
• Assume peak n is higher than peak n1
• Find peaks 1 through 7, and record distance
  between subsequent peaks
• Throw out high and low distance values, keep the
  middle three values beatsp b1p, b2p, b3p

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Part 2 Period

• Detecting the beat in a passband, p
• Perform auto-correlation
• Throw away the first half of the signal
• Low-pass filter the signal
• Assume peak n is higher than peak n1
• Find peaks 1 through 7, and record distance
  between subsequent peaks
• Throw out high and low distance values, keep the
  middle three values beatsp b1p, b2p, b3p
• Rank beat detection for each passband
• Scorep (standard deviation (beatsp)) /
  mean(beatsp))
• The passband with the lowest score wins

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Part 2 Period

• Period Results

Within 5 17 of 18 Within 10 18 of 18
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Part 2 Period

• Comments
• Low-pass filtering is inefficient
• Scheirers method (convolve with half-Hann
  window) is much better
• Peak-detection is easily broken
• Very sensitive to all beats having same strength
• Requires several (5) beats to be present
• Use of score for beat detection goodness really
  improves robustness
• Works very well for these examples

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Part 2 Pitch

• Pitch
• Goal Find fundamental frequency, the lowest of
  the harmonically related partials present
• Assumes no missing fundamental Wont
  correspond to perception in this case
• Uses same passbands as period finding
• Collects spectral peaks from all passbands, then
  tries to infer which is the fundamental based on
  peak strengths and harmonic relationships

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Part 2 Pitch

• Pitch finding procedure
• Collect top five spectral peaks from each
  passband
• Pick three potential harmonics (highest peaks).
  For each
• Look for subharmonics of this harmonic, of at
  least 40 magnitude of the largest peak
• If found, iteratively look for subharmonics of
  this subharmonic
• This results in three potential fundamentals. For
  each, collect support for the proposition that
  this is the true fundamental
• Increase support according to magnitude of
  fundamental
• Increase support according to presence and
  magnitudes of upper harmonics, weighted linearly
  by frequency (because the noise is pink)
• The fundamental with the most support wins.

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Part 2 Pitch

• Pitch Results

Within 5 Within 5 D/H Within 10 Within
10 D/H
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Part 2 Pitch

• Comments
• Seemed to work quite well
• Looking down for subharmonics and looking up for
  harmonic support increase robustness
• Sensitive to several assumptions
• The fundamental is present
• The magnitude of the fundamental is at least X
  of the biggest peak
• The harmonics are tuned within Y of their
  expected values
• These values were set for good performance on
  this data (overtrained)
• Would be hurt by
• Broadband or high-frequency noise
• Missing or weaker fundamental
• (More) mistuned harmonics

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Part 3 Synthesis

• Didnt focus much on this part, kept it simple
• Allowed mis-tuned harmonics in the target
  samples, but enforced perfect tuning in the
  synthesized output
• Added very simple ADSR envelope to all
  instruments
• Played around with matrix manipulations of music
  (e.g., rounds)

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Part 3 Synthesis

• My ADSR envelope

D 25ms
A 50ms
S len - 100ms
R 25ms
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Part 3 Synthesis

• Example Code flute, fs wavread(flute-G4.wav
  )m rowrowrows makesong(m, flute, 395,
  fs)
• Result
• Comments
• Its very simple
• It doesnt sound horrible