**The morphology of the electroretinogram (ERG) can be altered as a result of normal and pathological processes of the retina. However, given that the ERG is almost solely assessed in terms of its amplitude and timing, defining the shape of the ERG waveform so that subtle, physiologically driven, morphological changes can be systematically and reproducibly detected remains a challenging problem. We examined if the discrete wavelet transform (DWT) could meet this challenge. Normal human photopic ERGs evoked to a broad range of luminance intensities (to yield waveforms of various shapes, amplitudes, and timings) were analyzed using DWT descriptors of the ERG. Luminance-response curves that were generated using the various DWT descriptors revealed distinct ( p < 0.05) luminance-dependence patterns, indicating that the stimulus luminance differently modulates the various time-frequency components of the ERG and thus its morphology. The latter represents the first attempt to study the luminance-dependence of ERG descriptors obtained with the DWT. Analyses of ERGs obtained from patients affected with ON or OFF retinal pathway anomalies were also presented. We show here for the first time that distinct time-frequency descriptors can be specifically associated to the function of the ON and OFF cone pathway. Therefore, in this study, the DWT revealed reproducible, physiologically meaningful and diagnostically relevant descriptors of the ERG over a wide range of signal amplitudes and morphologies. The DWT analysis thus represents a valuable addition to the electrophysiologist's armamentarium that will improve the quantification and interpretation of normal and pathological ERG responses.**

^{−2}. Photopic hills were obtained in response to graded intensities of stimulation (ranging between −0.8 and 2.64 log cd.s.m

^{−2}in 14 steps of ∼0.26 log-units; average of 10 flashes per intensity; flash duration: 20 μs; white light; interstimulus interval: 1.5 s; prestimulus baseline: 20 ms) in 15 of the 25 subjects. ERGs evoked to seven dimmer flash intensities (ranging between −2.23 and −1.00 log cd.s.m

^{−2}in 0.2 log-unit steps; average of 50 to 300 flashes; flash duration: 20 μs; white light; interstimulus interval: 0.3 s; prestimulus baseline: 20 ms) were obtained from the other 10 subjects. Background light and integrated flash luminances were measured with a research radiometer (IL1700; International Light, Newburyport, MA). ERGs from both eyes were averaged to yield a single waveform and imported in MATLAB R2014a software (Mathworks, Natick, MA) for further analyses.

^{−2}; rod-desensitizing background light: 30 cd.m

^{−2}) ERGs obtained from patients (

*n*= 20) affected with Type-1 CSNB (

*n*= 10) or congenital postreceptoral cone pathway anomaly (CPCPA;

*n*= 10). These patients were selected for two main reasons. Firstly, the selected ERG waveforms show, upon visual inspection, strikingly different morphological features that, we claim, will be captured by the DWT descriptors. Secondly, the functional anomaly of patients affected with CSNB is known to specifically reside with the ON-pathway (based on electroretinographic (Langrova et al., 2002; Miyake, Yagasaki, Horiguchi, & Kawase, 1987; Quigley et al., 1996) and molecular (Bech-Hansen et al., 2000; Dryja et al., 2005; Gregg et al., 2007; Pusch et al., 2000) findings and complementary, the functional anomaly of patients affected with CPCPA is believed to lie on the OFF-pathway (Garon et al., 2014; Lachapelle et al., 1998). We hypothesize that retinal conditions affecting the ON (CSNB) and OFF (CPCPA) pathways will affect different DWT descriptors.

^{−2}starts at near-zero values (Levels 1 to 3), rapidly increases (steepest increment between Levels 5 and 6) to reach a maximum at Level 7, which is then followed by a final decrease in the value of the wavelet variance. This graphic representation allowed us to identify the delta-variance (Δ-variance) descriptor, the computation of which is presented in Appendix A and illustrated in Figure 1D. The Hölder exponent (also termed scaling exponent) represents another descriptor that can be computed using the WVA of DWT (Abry, Flandrin, Taqqu, & Veitch, 2002). This descriptor, which is amplitude-independent, characterizes the irregularity (or roughness) of the signal, a feature often associated to the complexity of a given waveform (Bishop, Yarham, Navapurkar, Menon, & Ercole, 2012; Sen, Litak, Kaminski, & Wendeker, 2008). The computation procedure of the Hölder exponent is detailed in Appendix A and illustrated in Figure 1E.

^{−2};

*n*= 15 subjects) followed by post hoc Bonferroni-paired

*t*tests for multiple hypotheses testing with repeated measures. Statistical analysis of the wavelet variance descriptors (Hölder and Δ-variance) was obtained using one-way (stimulus intensity) within-subjects ANOVAs (between −0.8 to 2.64 log cd.s.m

^{−2};

*n*= 15 subjects). Multiple comparisons (based on Bonferroni-paired

*t*test for repeated measurements) were used to compare the values of selected pairs of means obtained under different stimulus luminances. The pathological ERG groups (CSNB and CPCPA) were compared to control and between them using unpaired two-sample

*t*tests. The coefficient of variation (CV) of selected group data was computed as the standard deviation divided by the mean and multiplied by 100. Finally, Pearson correlation coefficients (i.e.,

*r*for rho) were used to compare the similarities between ERG waveforms or between LR functions. The significance level of each test was fixed at 0.05.

^{−2}stimulus in Figure 2C and delimited with white borders in the other scalograms) show that, irrespective of the intensity of the stimulus, the maximal energy of the signal is always contained within a time-frequency region delimited by these descriptors. Therefore, irrespective of the amplitude of the ERG signal, LWM associated with the a-wave (20a, 40a), b-wave (20b, 40b) and OPs (80ops, 160ops) remained quantifiable (as per color scale). Of interest, as shown in Figure 2D, when the total LWM energy (i.e., ΣEnergy = 20a + 40a + 20b + 40b + 80ops + 160ops) of each ERG waveform is plotted against the intensity of the stimulus, the shape of the resulting function is reminiscent of the PH obtained when only the amplitude of the b-wave is considered (as in Figure 2B)—both functions reaching their maximal values with the ERG evoked to the 0.39 log cd.s.m

^{−2}stimulation. This confirms that, as hypothesized, the PH-like shape (originally evidenced with TD measures of the b-wave; blue curve of Figure 2B) continues to remain a signature feature of the cone ERG LR function when the ERG response is quantified in the time-frequency domain.

*SD*) photopic a- and b-wave LR functions obtained using the LWM descriptors weighing the a-wave (20a, 40a; Figure 3A) and b-wave (20b, 40b; Figure 3B) energy levels. As seen in Figure 3A, the 20a and 40a descriptors follow distinct LR patterns; the 20a descriptor first increases slowly (from −0.8 to 0.39 log cd.s.m

^{−2}) and then more abruptly (from 0.39 to 1.4 log cd.s.m

^{−2}) before reaching a plateau with the four brightest intensities. In contrast, the 40a descriptor appears to follow a logistic-like growth function. As shown in Figure 3D, the growth pattern obtained by summating the 20a and 40a DWT descriptors is almost identical to that obtained using TD measurements of the a-wave (Pearson's correlation coefficient = 0.9983). A similar decomposition of the b-wave (Figure 3B) reveals that the LR functions of the two frequency components (i.e., 20b and 40b) follow distinct PH-like shapes. First, the peak of the 20b is flat compared to the sharper peak of the 40b LR function, and second, while the maximal energy value for the 20b descriptor is reached with the 0.64 log cd.s.m

^{−2}stimulus, that of the 40b component is attained at 0.39 log cd.s.m

^{−2}. Again, as shown in Figure 3E, the growth function obtained by summating the 20b and 40b DWT descriptors is nearly identical (Pearson's correlation coefficient = 0.9988) to that obtained using the TD measurements of the b-wave (the so-called PH shown in Figure 2B). Statistical analysis revealed that the interaction effects (frequency band × stimulus intensity) were significant for both the a-wave (

*df*= 13;

*F*= 37.16;

*p*< 0.00001) and b-wave (

*df*= 13;

*F*= 27.28;

*p*< 0.00001). Of interest, post hoc analysis revealed that, depending on the intensity of the stimulus used, the energy level concealed in the 40 Hz a-wave parameter (40a) was either significantly higher (

*p*< 0.05) or equal (

*p*> 0.05) to that concealed in the 20 Hz a-wave parameter (20a). Similarly, the 40-Hz b-wave parameter (40b) was either significantly higher (

*p*< 0.05), equal (

*p*> 0.05), or significantly lower (

*p*< 0.05) than the 20-Hz b-wave parameter (20b). These significant intensity-dependent differences (indicated by the black asterisks in Figure 3A, B) in the energy level of the LWM descriptors indicate that the intensity of the stimulus significantly modulates the time-frequency composition of the ERG. As shown in Figure 3C, a similar PH pattern was also obtained with the higher frequency components of the ERG (80ops and 160ops), both attaining maximal values with the 0.39 log cd.s.m

^{−2}stimulus. Statistical analysis revealed that the interaction effect (frequency band × stimulus intensity) was significant (

*df*= 13;

*F*= 28.98;

*p*< 0.00001). Post hoc tests indicated that irrespective of the intensity, the magnitude of 80 Hz OPs energy descriptor (80ops) was significantly higher (

*p*< 0.05) than the 160 Hz (160ops) one. Finally, as shown in Figure 3F, the LR function obtained by summating the 80ops and 160ops descriptors covaried (Pearson's correlation coefficient = 0.9831) with that obtained using the TD measurement of the SOPs.

*SD*) LR function of the Hölder exponent. With progressively brighter stimuli, the value of the Hölder exponent first increases, reaches a maximal value (e.g., maximal complexity of the ERG waveform) at 0.64 log cd.s.m

^{−2}, which is then followed by a gradual decrease with brighter stimuli. The main effect of the stimulus intensity was found to be significant (

*df*= 13,

*F*= 51.26;

*p*< 0.00001). Of note, though the Hölder exponent is amplitude-independent, its LR function is reminiscent of the PH obtained with TD measure of b-wave amplitude, which is shown in Figure 4C. There are, however, important differences, such as (a) the peak value is reached at slightly brighter stimulus intensity (i.e., 0.64 compared to 0.39 log cd.s.m

^{−2}) and (b) the absence of a plateau effect with the brightest stimuli (compare Figure 4A, C).

^{−2}flash and does not plateau with the brightest stimuli. This main effect of the stimulus intensity was also found to be significant (

*df*= 13,

*F*= 22.54;

*p*< 0.00001).

^{−2}stimulus, the shapes of the resulting LR functions differed significantly; the peak of the Hölder exponent function being smoother compared to the sharper peak of the Δ-variance function. Supportive of the latter, post hoc analysis revealed that Hölder values immediately adjacent (i.e., evoked at 0.39 and 0.9 log cd.s.m

^{−2}) to the peak value (0.64 log cd.s.m

^{−2}) were not significantly different from this peak value (

*p*> 0.05), while the peak value of the Δ-variance descriptor was significantly larger (

*p*< 0.05) than that of the values from the two neighboring intensities.

^{−2}, while the corresponding DWT scalograms are presented at the right-hand side of each waveform. As shown in Figure 5B, the amplitude of the a- and b-waves thus obtained grows progressively (a-wave: from 0.6 to 5.0

*μ*V; b-wave: from 0.9 to 10.75

*μ*V) with brighter stimuli to reach, in response to the −1 log cd.s.m

^{−2}stimulus, values that are slightly lower (a-wave: 5.0

*μ*V; b-wave: 10.75

*μ*V) than values obtained at −0.8 log cd.s.m

^{−2}(a-wave: 7.41; b-wave: 18.24

*μ*V; e.g., Figure 2A, B). Similar to what was shown with the larger amplitude ERGs (see Figure 2C), DWT scalograms of the low-voltage ERGs also reveal that the maximal energy of the ERG signal remains localized in the time-frequency region that is delimited with the six LWM descriptors (white borders) defined above (i.e., 20a, 20b, 40a, 40b, 80ops, 160ops). Similarly, each DWT descriptor (Figure 5C through F) grows progressively with brighter stimuli to reach, in response to the −1 log cd.s.m

^{−2}stimulus a value slightly lower than the value obtained at −0.8 log cd.s.m

^{−2}(see Figures 3 and 4), confirming that DWT descriptors can be used to monitor the ERG over a wide range of amplitudes (i.e., in this study: from less than 1

*μ*V to more than 100

*μ*V).

^{−2}(mean SNR in the TD: 1.62 ± 0.82) and 0.64 log cd.s.m

^{−2}(mean SNR in the TD: 19.65 ± 6.77). A 92% reduction in the SNR values, increased (i.e., seen from right to left in Figure 6C) the CV of the a- and b-wave measurements by 125% and 98%, respectively, using the TD approach, compared to 50% and 31% using the DWT approach.

*SD*s below the control value for CSNB and CPCPA, respectively. Of note, out of the 10 descriptors presented in Table 2, it is also the Hölder exponent that had the least variability in control subjects (CV of 4.14%), which could explain its superior sensitivity to pathological changes. Moreover, from a TD point of view, the amplitude of the a- and b-waves (TD a and TD b parameters in Table 2) of both patient groups was significantly reduced (apart from the normal a-wave amplitude found in CPCPA patients). However, these parameters were only the fifth and sixth most affected descriptors (for the TD b parameter of CPCPA and CSNB, respectively), suggesting that these traditional ERG parameters are less sensitive than DWT ones (maximum of 1.2 and 2.5

*SD*s below the mean for TD a and TD b, respectively, compared to a maximum of 8

*SD*s below the mean for the Hölder exponent).

*p*< 0.00001) in CSNB and CPCPA, respectively. As a result, while in control the 40b-to-20b ratio (i.e., 40b divided by 20b; shown in Figure 7D) was found to be almost unity (1.05 ± 0.06), that of CSNB patients was found to be of 2.01 ± 0.30 (i.e., 40b > 20b), and that of CPCPA of 0.43 ± 0.06 (i.e., 20b > 40b). Use of this ratio significantly reduced intersubject variability (CV of control is 5.71% for 40b-to-20b ratio compared to 18.18% and 14.92% for 20b and 40b, respectively) and significantly emphasized the effect size seen between the two patient groups (% difference = 367.44% for 40b-to-20b ratio compared to 129.42% and 101.39% for 20b and 40b, respectively).

*μ*V; Figures 3 and 4) and low- (<1

*μ*V; Figure 5) voltage ERGs, a feature of diagnostic relevance especially if one wishes to use the ERG to monitor disease progression in severe degenerative retinopathies (such as Retinitis Pigmentosa), whose final outcome is often characterized by very low-amplitude ERGs, or even extinguished ERGs (Rispoli, Iannaccone, & Vingolo, 1994). Our results indicate that the LR functions that were generated using the DWT descriptors that quantified ERG components concomitant with the b-wave (i.e., 20b and 40b) presented with PH-like shapes that complemented the traditional TD measurement of the b-wave (TD b-wave curve in Figure 3E). A similar match was also found between the DWT and TD descriptors of the a-wave. The fact that we were able to mimic the characteristic PH, a signature trait of the cone ERG LR function (traditionally generated from TD measures), using DWT descriptors suggests that selected DWT descriptors appraised physiological attributes of the cone ERG that covaried (see Pearson coefficients in Figure 3) with those obtained with TD measures.

^{−2}(maximal values for 40b, 80ops, 160ops, and ΣEnergy; Peak 1 in Figure 8) and another one at 0.64 log cd.s.m

^{−2}(maximal values for 20b, Hölder exponent and Δ-variance; Peak 2 in Figure 8). In a previous study, we also showed that the flash intensity required to reach the maximal b-wave amplitude and to optimally develop the photopic OP response (i.e., where OP2, OP3, and OP4 are fully developed) was (approximately) 0.3 and 0.6 log cd.s.m

^{−2}, respectively (Lachapelle et al., 2001). The brighter intensity also generated the most complete response (in terms of number of detectable ERG components), a claim in accord with our finding that the Hölder exponent (descriptor of roughness or complexity of a waveform) also peaks at the brighter flash intensity (0.64 log cd.s.m

^{−2}). Moreover, as it can be seen in Figure 8, while some DWT descriptors (40b, 80ops, 160ops, and ΣEnergy) reached a plateau with the brightest stimuli (from 1.63 to 2.23 log cd.s.m

^{−2}), others either continued to decrease (Hölder and Δ-variance) or slightly increased (20b).

*r*= 0.9831) between TD and DWT OPs measurements (see Figure 3F). Obviously, we might have obtained better fits by selecting which coefficients to include on a case-by-case basis (cherry-picking approach), a strategy that would have required some data interpretation from the user or more complex interventions from the algorithm, all of which could potentially lead to undesired artifacts, subjectivity and variability. Although our OPs descriptors (80ops and 160ops) do not, unlike band-pass filtering, permit the analysis of the photopic OPs individually, our results (see Figure 3C) did show that the two OP frequency bands differed in their respective energy level, suggesting that they might monitor different features of the high-frequency components of the ERG. Of interest, another wavelet study (Forte et al., 2008) previously revealed that rat OPs also comprised two frequency components (i.e., 70–80 Hz and 120–130 Hz). This study also showed that the two OP components had distinct LR functions, suggesting that they might be evoked by different retinal sources. Similarly, Zhou, Rangaswamy, Ktonas, and Frishman (2007) reported that the photopic OPs of primates also contained two distinct frequency bands, namely the slow OPs (presumably generated by the amacrine cells) oscillating at 80 Hz and the faster OPs (presumably generated by the ganglion cells) oscillating at 150 Hz (Zhou et al., 2007). Like our study, the slower OPs were of the highest energy level. In our study, the LR functions of the 80ops and 160ops DWT descriptors followed a PH-like function, suggesting an intimate tie linking the genesis of the b-wave with that of the OPs, a claim previously advanced using TD measures (Guite & Lachapelle, 1990; Lachapelle, 1987, 1990; Lachapelle & Benoit, 1994; Lachapelle & Molotchnikoff, 1986).

*p*< 0.00001) from each other. This result indicate that the low- (80 Hz) and high-frequency (160 Hz) OP bands can be differently affected by a given disease process and suggest a potential association of the low- (80 Hz; i.e., 80ops descriptor) and high-frequency (160 Hz; i.e., 160ops descriptor) OP descriptors to the OFF- and ON-pathway, respectively. In a recent study, Dimopoulos et al. (2014) reported that the light-adapted OPs were separated into two frequency bands and suggested the possibility of ON and OFF system representation. Data presented herein would support this claim.

^{−2}, suggesting that it could allow us not only to detect subtle pathological changes at disease onset, but also to facilitate the monitoring (and severity grading) of changing ERG morphologies as the disease progresses towards nearly extinguished responses. This claim is best supported with the gradual decline in the value of the Hölder exponent seen with progressively smaller ERGs in normal subjects (Figure 5E) as well as with the significantly attenuated values obtained from pathological responses (Figure 7; Table 2).

*SD*s below the mean) than the traditional TD parameters (maximum of 2.5

*SD*s below the mean). The latter would suggest that DWT descriptors could also potentially detect subtle ERG anomalies even when the TD measures (amplitudes and timing) are still normal. Previous studies conducted on more specialized types of ERG signals further support the latter claim. For example, Miguel-Jimenez et al. (2010) used the DWT decomposition to reconstruct mfERG waveforms into various frequency bands and demonstrated the higher sensitivity of this approach to detect changes in glaucoma patients, compared to classical Humphrey visual field tests. Similarly, Rogola and Brykalski (2005) previously showed that DWT coefficients were superior to traditional TD measures in segregating normal from pathological PERG waveforms. Results presented in Figure 7 and Table 2 also indicate that certain disease can affect specific DWT descriptors. As shown, the photopic ERGs of CSNB patients suffered from a pronounced attenuation of the low-frequency b-wave component (20b) compared to the better preserved high-frequency b-wave component (40b), and conversely, CPCPA patients were characterized by opposite findings (40b specifically reduced compare to the better preserved 20b). Of interest, given that patients affected with CSNB and CPCPA have a specific anomaly of the ON and OFF retinal pathway (Bech-Hansen et al., 2000; Dryja et al., 2005; Garon et al., 2014; Gregg et al., 2007; Lachapelle et al., 1998; Langrova et al., 2002; Miyake et al., 1987; Pusch et al., 2000; Quigley et al., 1996) and that we found a specific attenuation of the 20b and 40b in CSNB and CPCPA, respectively, our results suggest that the 20b and 40b descriptors might therefore be more closely related to the ON (20b) and OFF (40b) cone pathway contribution to the ERG response, respectively.

*μ*V) was reached at the intensity of 0.64 log cd.s.m

^{−2}, where both the ON (20b) and OFF (40b) pathway are equally (and maximally) contributing to the response.

*(pp. 39–88). New York: Wiley.*

*Wavelets for the analysis, estimation, and synthesis of scaling data, self-similar network traffic and performance evaluation**, 130, 155–163.*

*Theory in Biosciences**, 26, 319–323.*

*Nature Genetics**, 81, 207–214.*

*Jama Ophthalmology**, 117, 810–821.*

*Anesthesiology**, 8, 106–113.*

*Canadian Journal of Ophthalmology**About Wavelab*. Palo Alto, CA: Department of Statistics, Stanford University. Retrieved from http://statweb.stanford.edu/∼wavelab/Wavelab_850/AboutWaveLab.pdf

*(pp. 125–150) New York: Springer-Verlag.*

*Wavelet and statistics**. Philadelphia, PA: Society for Industrial and Applied Mathematics.*

*Ten lectures on wavelets**, 32, 122–138.*

*Clinical Electroencephalography**, 102, 4884–4889.*

*Proceedings of the National Academy of Sciences, USA**, 169, 191–200.*

*Journal of Neuroscience Methods**, 52, 3061–3074.*

*Computational Statistics & Data Analysis**, 129, 9–16.*

*Documenta Ophthalmologica: Advances in ophthalmology**, 121, 177–187.*

*Documenta Opthalmologica**2014, 246096, 1–11, doi:10.1155/2014/246096.*

*BioMed Research International**, 98, 3023–3033.*

*Journal of Neurophysiology**, 75, 125–133.*

*Documenta Ophthalmologica: Advances in Ophthalmology**Theory and applications of the shift-variant, time-varying and undecimated wavelet transforms (Masters thesis)*. Rice University, Houston, TX. Retrieved from https://scholarship.rice.edu/handle/1911/13954

*, 70, 53–59.*

*Journal of the Optical Society of America**, 47, 2968–2972.*

*Vision Research**, 96, 526–534.*

*American Journal of Ophthalmology**, 44, 20–28.*

*Japanese Journal of Ophthalmology**, 22, 354–361.*

*Canadian Journal of Ophthalmology**, 75, 73–82.*

*Documenta Ophthalmologica: Advances in Ophthalmology**, 86, 33–46.*

*Documenta Ophthalmologica: Advances in Ophthalmology**, 63, 337–348.*

*Documenta Ophthalmologica: Advances in ophthalmology**, 95, 35–54.*

*Documenta Ophthalmologica: Advances in Ophthalmology**, 102, 157–162.*

*Documenta Ophthalmologica: Advances in Ophthalmology**, 42, 1475–1483.*

*Vision Research**, 2, 219–229.*

*Applied and Computational Harmonic Analysis**. Houston, TX: Academic Press.*

*A wavelet tour of signal processing the sparse way*(3rd ed.)*, 130, 1–12.*

*Documenta Ophthalmologica: Advances in ophthalmology**, 32, 617–622.*

*Medical Engineering & Physics**(pp. 31–41). New York: Springer.*

*Degenerative retinal diseases**, 31, 81–87.*

*Japanese Journal of Ophthalmology**. New York: Wiley.*

*Self-similar network traffic and performance evaluation**, 82, 619–631.*

*Biometrika**, 30, 982–992.*

*Journal of Neurophysiology**, 26, 324–327.*

*Nature Genetics**, 92, 159–165.*

*Documenta Ophthalmologica: Advances in ophthalmology**, 114, 376–390.*

*Clinical Neurophysiology**, 88, 27–37.*

*Documenta Ophthalmologica: Advances in Ophthalmology**, 8, 238–246.*

*Pattern Analysis & Applications**, 43, 1405–1412.*

*Vision Research**, 45, 2321–2330.*

*Vision Research**, 104, 231–248.*

*Documenta Ophthalmologica: Advances in Ophthalmology**, 18, 033115.*

*Chaos: An Interdisciplinary Journal of Nonlinear Science**. Wellesley, MA: Wellesley Cambridge Press.*

*Wavelet and filter banks**, 11, 1085–1094.*

*IEEE Transactions on Biomedical Engineering**, 79, 61–78.*

*Bulletin of the American Meteorological Society**, 54, 1263–1280.*

*Journal of Modern Optics**, 80, 335–345.*

*Documenta Ophthalmologica: Advances in Ophthalmology**, 47, 2021–2036.*

*Vision Research**DWT*(

*j*,

*k*) represents the wavelet coefficients localized at discrete scales (indexed with

*j*and corresponding frequencies in [(

*Fs*/ 2)2

^{−}

*, (*

^{j}*Fs*/ 2)2

^{−}

^{j}^{+1}], where

*Fs*is the sampling frequency) and discrete time

*k*,

*x*(

*t*) designates the raw ERG time series, and ψ̄ denotes the complex conjugate of the mother wavelet. The DWTs were computed using the fast wavelet transform algorithm of Mallat (2009) implemented with MATLAB and Wavelab 850 routines (Buckheit, Shaobing, Donoho, Johnstone, & Scargle, 2005). Prior to DWT computation, each ERG was padded with 256 constant samples (by repeating the first and last value of the signal) on both sides of the response, in order to reduce edge effects (Torrence & Compo, 1998). With our parameters (i.e., 1,024 samples per padded signal and

*F*s of 3413.33 Hz), we were able to obtain 10 levels of decomposition per DWT. Only the first eight levels were displayed and the padding was discarded after computation (obtaining an eight-level time-frequency plan of 150 ms in length). Finally, several mother wavelets could have been used to extract the DWT descriptors described herein. However, one should be aware that use of different wavelets may affect the output of the DWT (such as the energy level), and hence, the same mother wavelet should be applied to normal subjects and patients for clinical decisions. In this study, we opted for the Haar wavelet to analyze the LWM descriptors of the ERG and for the symmetric Daubechies wavelet (set with two vanishing moments) to compute the WVA descriptors. Rationale for the use of these mother wavelets is indicated in the Methods section (see subsection “Selection of mother wavelets”).

*Var*(

*d*) ∼ 2

_{j}*. Accordingly, the Hölder exponent H (also termed scaling exponent) can be estimated from the DWT variance-level plot, such as that illustrated in Figure 1D (Abry et al., 2002). Briefly, we process the natural logarithm of the variance-level curve (Figure 1D) to obtain the log-variance plot, such as the one shown in Figure 1E. This logarithm linearizes the curve (compare Figure 1D, E). The measurement of the Hölder exponent is then reduced to the calculation of the slope over the alignment region in the log-variance diagram. In this study, the linear fitting was achieved between Levels 2 to 6 (red line in Figure 1E) as this region of the curve offered the best linear fitting.*

^{jH}