1. Background Matching Pursuit Signal Decomposition Matching pursuit (MP) gives a representation of a signal as the sum of a number of “atoms” selected from a predefined “dictionary”. Following Jedrzejczak et al, (2004), in this study, transient-evoked otoacoustic emission (TEOAE) waveforms are decomposed into atoms, each of which is a toneburst with a Gaussian envelope, and is parameterised by amplitude, frequency, phase, latency, and duration (Fig. 1 & 2) In this study, the use of MP to characterise non-linear changes in waveform morphology is explored. TEOAE latency reduces with stimulus level One way of defining TEOAE latency (within a given frequency band) is by filtering the waveform, extracting the envelope, and measuring the time to the maximum of the envelope. Other (related) methods use time-frequency analysis (e.g., Tognola et al., 1997; Sisto & Moletti, 2007). All these methods show a reduction in TEOAE latency with stimulus level, which is qualitatively consistent with the theory that cochlear tuning broadens with stimulus level, due to compressive non-linearity of the cochlear amplifier. I/O-slope reduces with latency The slope of the input-output (I/O) function in dB/dB serves as an index of compressive non-linearity, with 1 dB/dB indicating prefect linearity, and 0 dB/dB indicating perfect saturation. When I/O-slope is calculated in different time segments, it has been found that the later the time segment, the lower the I/O-slope (e.g., Rutten, 1980), and thus the greater the compression. This non-linear phenomenon may arise from some of the same mechanisms underlying the latency-level phenomenon: both imply a relative shift of energy from longer to shorter latencies. Fig 1: TEOAE waveform de-composed as 11 atoms. Here the reconstructed signal captures 95% of the original signal power. The signal power of each atom is shown as a percentage of the total power. Note that as the atoms are not orthogonal, the total power may not necessarily equal the sum of the atomic powers. Results Tracking atoms across stimulus levels For a given ear, the atoms at one level were compared with those at the next level up. Where the atoms matched up (to within a pre-set tolerance), they were deemed to be the same atom. On average 60% of atoms at one level could be identified at the level 5 dB above. An example level series of the waveforms and their atomic time-frequency representations are shown in Figs. 3 and 4. Variation of atoms across stimulus levels As stimulus level increases, individual atoms show little variation in latency or duration. However, there is a tendency for long-latency atoms to die away more rapidly than short latency atoms (Fig 5) due to their reduced I/O-slope. Changes in latency with stimulus level When the latency of an identifiable atom is tracked across levels there is little or no change (Fig 6B). However, due to the increased number of short- relative to long- latency atoms at higher levels, there is an overall reduction in average latency as level increases. This holds both overall, and within frequency bands (Fig 6). Effect of stimulus level on the morphology of transient-evoked otoacoustic emission waveforms analysed by matching pursuit signal decomposition Ben Lineton 1 and Lucy Cooper 1 1 ISVR, University of Southampton, UK Research Questions The aim was to decompose TEOAE waveforms into toneburst “atoms” using a matching pursuit algorithm, in order to investigate how the atoms are affected by stimulus level, and, more generally whether this technique provides a useful way of representing TEOAEs. Specifically: Do atoms show a continuous trajectory on the time-frequency plane as stimulus level increases? How is an atom’s latency (and its other parameters) affected by stimulus level? How does the well-known reduction in latency of TEOAE waveforms with stimulus level manifest itself in the matching pursuit representation? Experimental Methods and Data Analysis TEOAEs were measured at 7 levels (60-90 dBpeSPL in 5 dB steps) in 20 normally- hearing ears from 10 subjects, using the ILO-292 in “linear” mode. A matching-pursuit algorithm was used to decompose the waveforms into atoms comprising Gabor functions: tonebursts with a Gaussian envelope. Fig 3: Example level series: TEOAE waveforms from 60 to 90 dB peSPL. (normalised w.r.t. rms amplitude). Fig 4: Example of changes in atomic properties with level changes. Only the three strongest atoms at each level are shown. Fig 5: A. Schematic diagram showing the typical trajectory of a long and short latency atom. B. Actual trajectories for one ear. Atomic frequency is coded by colour. Fig 6: Median atomic latency over all atoms and all ear, in 1-kHz frequency bands. Fig 7: Median rates of latency reduction over all ears. Blue line: average down- ward slope of lines in Fig 6. Red line: average downward slope of lines as per Fig. 5B. Conclusions On average, 60% of atoms at one level could be identified at a stimulus level 5 dB greater. Thus it was possible to “track” most atoms across levels. When a typical atom was tracked across levels, it showed little change in latency or duration with increased stimulus level. Thus, the overall change in signal latency did not show up as a shift in atomic latency. The reduction in signal latency with level manifested itself as a reduction in the median latency of all the atoms, due to the change in relative proportion of short- to long latency atoms, rather than to changes in individual atomic latencies. References Jedrzejczak WW, Blinowska KJ, Konopka W, Grzanka A & Durka PJ (2004). Identification of otoacoustic emissions components by means of adaptive approximations. J Acoust Soc Am. 115, 2148-58 Sisto R, Moleti A (2007). Transient evoked otoacoustic emission latency and cochlear tuning at different stimulus levels. J Acoust Soc Am. 122, 2183-90 Tognola G, Grandori F, Ravazzani P (1997). Time-frequency distributions of click-evoked otoacoustic emissions. Hear. Res. 106 112-22 Rutten WL (1980). Evoked acoustic emissions from within normal and abnormal human ears: comparison with audiometric and electrocochleographic findings. Hear Res. 2, 263-71. Acknowledgements The authors are grateful to Thomas Blumensath for supplying the matching pursuit algorithm. Fig 2: The atoms in Fig 1 plotted as ellipses on the time-frequency plane, with signal power coded as line thickness. Atomic latency is defined as the time to the centre of the atom.