title: The relationship between the auditory brain-stem response and its reconstructed waveforms following discrete wavelet transformation.
abstract: OBJECTIVE
  To examine the relationship between the auditory brain-stem response (ABR) and its reconstructed waveforms following discrete wavelet transformation (DWT), and to comment on the resulting implications for ABR DWT time-frequency analysis.
  
  
  METHODS
  ABR waveforms were recorded from 120 normal hearing subjects at 90, 70, 50, 30, 10 and 0 dBnHL, decomposed using a 6 level discrete wavelet transformation (DWT), and reconstructed at individual wavelet scales (frequency ranges) A6, D6, D5 and D4. These waveforms were then compared for general correlations, and for patterns of change due to stimulus level, and subject age, gender and test ear.
  
  
  RESULTS
  The reconstructed ABR DWT waveforms showed 3 primary components: a large-amplitude waveform in the low-frequency A6 scale (0-266.6 Hz) with its single peak corresponding in latency with ABR waves III and V; a mid-amplitude waveform in the mid-frequency D6 scale (266.6-533.3 Hz) with its first 5 waves corresponding in latency to ABR waves I, III, V, VI and VII; and a small-amplitude, multiple-peaked waveform in the high-frequency D5 scale (533.3-1066.6 Hz) with its first 7 waves corresponding in latency to ABR waves I, II, III, IV, V, VI and VII. Comparisons between ABR waves I, III and V and their corresponding reconstructed ABR DWT waves showed strong correlations and similar, reliable, and statistically robust changes due to stimulus level and subject age, gender and test ear groupings. Limiting these findings, however, was the unexplained absence of a small number (2%, or 117/6720) of reconstructed ABR DWT waves, despite their corresponding ABR waves being present.
  
  
  CONCLUSIONS
  Reconstructed ABR DWT waveforms can be used as valid time-frequency representations of the normal ABR, but with some limitations. In particular, the unexplained absence of a small number of reconstructed ABR DWT waves in some subjects, probably resulting from 'shift invariance' inherent to the DWT process, needs to be addressed.
  
  
  CONCLUSIONS
  This is the first report of the relationship between the ABR and its reconstructed ABR DWT waveforms in a large normative sample.
authors.affiliation: Division of Audiology, School of Health and Rehabilitation Sciences, Faculty of Health Sciences, University of Queensland, Brisbane, Qld 4072, Australia. w.wilson@shrs.uq.edu.au
authors.forename: W J
authors.initials: WJ
authors.lastname: Wilson
mesh_terms: D000328:Adult; D000368:Aged; D016057:Evoked Potentials, Auditory, Brain Stem; D006801:Humans; D008875:Middle Aged; D011930:Reaction Time; D012815:Signal Processing, Computer-Assisted