1. Auditory Nerve Laboratory: What was the Stimulus? Bertrand Delgutte HST.723 – Neural Coding and Perception of Sound

2. Real and Idealized Spike Trains Spike train from inferior colliculus of awake rabbit (Devore) Fundamental assumption: All the information is contained in the timing of spikes Idealized spike trains are modeled mathematically as point processes

3. Peri-Stimulus Time Histogram Auditory-Nerve Fiber, 400-ms Pure Tone

4. Interspike Interval Histogram Homogeneous Poisson process with 0.6-ms dead time 0400 ms Dead time ISIH also useful with pure tones. ISIH modes can be used to estimate stimulus period.

5. Period Histogram 20 ms Nonhomogeneous Poisson Process, 500-Hz Pure tone SI = 0.85 Period needs to known to compute a period histogram

6. Spike-Train Analysis with Histograms HistogramDescriptionUseful forProcessing Peri-Stimulus Time (PST) Distribution of spikes over time course of stimulus All stimuli (transient, periodic, stationary, time- varying) Spectrum (for transient and periodic stimuli) Spectrogram for time-varying stimuli (First-order) Interspike Interval Distribution of intervals between successive spikes Stationary and periodic stimuli Spectrum Period Histogram Distribution of spikes over stimulus cycle Periodic stimuli with known period Spectrum, Synchronization Index Reverse Correlation (“Revcor”) Average stimulus waveform preceding each spike Noise with known waveform Spectrum

7. Determine the average (most likely) stimulus waveform preceding a spike. Measured by “spike-triggered averaging” with a white noise stimulus. Revcor functions of low-CF auditory-nerve fibers resemble the impulse response of a bandpass filter centered at the CF. Fourier transforms of revcor functions match the tip of pure-tone tuning curves over a wide range of noise levels. The revcor is an estimate of the crosscorrelation between stimulus and response. The reverse correlation (“revcor”) method (de Boer) Evans (1977) Pickles (1988)

8. Reverse correlation and Wiener filters Given a linear system, the crosscorrelation of the response r(t) with a stationary, white noise input w(t) is proportional to the system’s impulse response h(t): System identification: Given, two signals r(t) and s(t), the linear filter h(t) which does the best job (in a least- squares sense) of predicting r(t) from s(t) is known as the Wiener filter. In the special case when s(t) is white noise, h(t) is the crosscorrelation function between input and output (except for a scale factor). The revcor is an estimate of the Wiener filter in the special case when r(t) consists of impulses (spikes).