This paper presents a method to analyze and filter digital signals of finite duration by means of a time-frequency representation. This is done by defining a purely invertible discrete transform, representing a signal either in the time or in the time-frequency domain, as simply as possible with the conventional discrete Fourier transform between the time and the frequency domains. The wavelet concept has been used to build this transform. To get a correct invertibility of this procedure, we have proposed orthogonal and periodic basic discrete wavelets. The properties of such a transform are described, and examples on brain-evoked potential signals are given to illustrate the time-frequency filtering possibilities.

In this study, a frequency domain formulation of continuous loop averaging deconvolution (CLAD) of overlapping evoked potentials is developed and applied for the extraction of transient responses from recordings obtained at high stimulation rates. This formulation allows for a faster execution of CLAD by using fast Fourier transform algorithms. The frequency characteristics of the deconvolution filter depends exclusively on the stimulus sequence and determines whether the noncoherent noise is amplified or attenuated in different frequencies. A formula for calculating the signal-to-noise ratio (SNR) achieved by the deconvolution process is developed. The newly developed theory and the methodology is applied to the extraction of the auditory brainstem and middle latency responses using various sequences. The effects of the sequence used and the number of sweeps averaged in ongoing acquisition on SNR are examined by using single sweep recordings. The results verify the deconvolution theory and the methodology and show its limitations. Depending on the frequency characteristics of the sequence, the deconvolution process can amplify or attenuate the EEG noise. Proper selection of the stimulus sequence can increase the SNR enhancement obtained with conventional averaging.

We recorded pattern electroretinograms (PERGs) simultaneously from each eye in mice using binocular stimulation and a common noncorneal electrode. The PERG was derived simultaneously from each eye in 71 ketamine/xylazine anesthetized mice (C57BL/6J, 4 months old) from subcutaneous needles (active, snout; reference, back of the head; ground, root of the tail) in response to contrast-reversal of gratings (0.05 cycles/deg, >95% contrast) generated on two custom-made light-emitting diode (LED) tablets alternating at slight different frequencies (OD, 0.984 Hz; OS, 0.992 Hz). Independent PERG signals from each eye were retrieved using one channel continuous acquisition and phase-locking average (OD, 369 epochs of 492 ms; OS, 372 epochs of 496 ms). The PERG was the average of three consecutive repetitions. Binocular snout PERGs had high amplitude (mean, 25.3 μV, SD 6.6) and no measurable interocular cross-talk. Responses were reliable (test-retest variability within-session, 14%, SD 7; between sessions, 25%, SD 9; interocular asymmetry within-session, 9%, SD 7; between sessions, 13%, SD 5). Retinal ganglion cells (RGCs) were the main source of the binocular snout PERG, as optic nerve crush in three mice abolished the signal. The PERG, a sensitive measure of RGC function, is used increasingly in mouse models of glaucoma and optic nerve disease. Compared to current methods, the binocular snout PERG represents a substantial improvement in terms of simplicity and speed. It also overcomes limitations of corneal electrodes that interfere with invasive procedures of the eye and facilitates experiments based on comparison between the responses of the two eyes.