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. Author manuscript; available in PMC: 2011 Jan 31.
Published in final edited form as: J Acoust Soc Am. 2005 Nov;118(5):3261–3266. doi: 10.1121/1.2047228

Intelligibilities of 1-octave rectangular bands spanning the speech spectrum when heard separately and paired

Richard M Warren 1,a, James A Bashford Jr 1, Peter W Lenz 1
PMCID: PMC3031245  NIHMSID: NIHMS28535  PMID: 16334905

Abstract

There is a need, both for speech theory and for many practical applications, to know the intelligibilities of individual passbands that span the speech spectrum when they are heard singly and in combination. While indirect procedures have been employed for estimating passband intelligibilities (e.g., the Speech Intelligibility Index), direct measurements have been blocked by the confounding contributions from transition band slopes that accompany filtering. A recent study has reported that slopes of several thousand dBA/octave produced by high-order finite impulse response filtering were required to produce the effectively rectangular bands necessary to eliminate appreciable contributions from transition bands [Warren et al., J. Acoust. Soc. Am. 115, 1292–1295 (2004)]. Using such essentially vertical slopes, the present study employed sentences, and reports the intelligibilities of their six 1-octave contiguous passbands having center frequencies from 0.25 to 8 kHz when heard alone, and for each of their 15 possible pairings.

I. INTRODUCTION

The relative contributions to intelligibility made by the different regions of the speech spectrum is of major interest for theory and for practical applications such as telephony, hearing aids, cochlear implants, and architectural acoustics. There has been considerable research devoted to determining passband intelligibilities since the pioneering work at Bell Telephone Laboratories in the early twentieth century (see Fletcher, 1929; French and Steinberg, 1947; Fletcher and Galt, 1950). These studies have led to the development of a widely used method for estimating passband intelligibilities heard singly and together. This was accomplished by employing calculations based upon intelligibility measurements of high-pass and low-pass speech partially masked by noise. The procedure was used to construct the American National Standard Institute’s Articulation Index (AI) (ANSI S3.5, 1969) and its updated successor, the Speech Intelligibility Index (SII) (ANSI S3.5, 1997). At the time the AI/SII procedure was being developed, it was recognized that the intelligibility of speech bands was determined by contributions from both the passband and the flanking transition bands produced by filters available at that time (see Kryter, 1960). However, the design of the AI/SII procedure minimized the contribution of the transition bands and permitted the use of shallow filter slopes: The instructions for deriving AI state: “For the purpose of this standard, the slope of the filter skirts should be equal to or greater than 18 dB/octave” (ANSI S3.5, 1969, p. 7). The AI/SII calculations were amended by the Speech Transmission Index (STI) (Steeneken and Houtgast, 1980; 2002) to compensate for distortions such as echoes and reverberation and also to permit evaluation of speech transmission quality. The Speech Recognition Sensitivity (SRS) model (Müsch and Buus, 2001a; 2001b) amended the AI/SII calculations to account for both the “synergistic and redundant interactions among spectral bands of speech.”

Although there have been many estimates, there have been no direct measurements of the intelligibilities of passbands spanning the speech spectrum. The present study was undertaken to obtain such measurements for passbands heard singly and in pairs. In order to avoid confounding the passband information with out-of-band input, it was necessary to eliminate contributions from the transition-band slopes that accompany all filtering. Despite dwindling amplitude and distortions of normal spectral profile, transition bands can provide considerable information. This is demonstrated by the high intelligibility of narrow-band speech consisting solely of transition bands. Everyday sentences restricted to a wedge-shaped band consisting of high-pass and low-pass filter slopes of 48 dBA/octave meeting at a common cutoff frequency of 1.5 kHz were reported to have ceiling intelligibility scores of over 95% (Bashford, Riener, and Warren, 1992), and when, in a subsequent study, the slopes of this wedge-shaped band were increased to 115 dBA/octave (quite steep for analog filtering), scores remained quite high at 77% (Warren, Riener, Bashford, and Brubaker, 1995).

To measure the relative contributions of passbands and transition bands in determining the intelligibility of narrowband speech, a series of experiments was conducted using FIR (finite impulse response) digital filtering to produce nearly vertical slopes without the passband distortions accompanying high-order analog filtering. In the first of these studies, Warren and Bashford (1999) separated the passband from the flanking 100 dBA/octave transition bands of everyday sentences centered at 1.5 kHz. This was done using 2000-order FIR filtering that produced filter slopes averaging approximately 1000 dBA/octave. It was found that the high pass and low-pass slopes separated by a 1/3-octave gap had an average intelligibility more than three times that of the excised passband that had occupied the gap. Subsequent experiments substituted word lists for the everyday sentences; intelligibilities were reduced as would be expected, but the ratio of transition-band scores to passband scores was equivalent to that obtained with sentences (Bashford, Warren, and Lenz, 2000). Another study also employed the 1/3-octave everyday sentences centered at 1.5 kHz with transition bands of 100 dBA/octave, and truncated the filter skirts at a series of increasing distances from the cutoff frequency using 2000-order FIR filtering. It was found that statistically significant contributions from these transition bands could be made for frequencies attenuated by 30 dBA, so that the nominal 1/3-octave band had a much larger effective bandwidth (i.e., the range of frequencies contributing to intelligibility) that extended to almost one octave (Warren, Bashford, and Lenz, 2000). While these experiments using 2000-order FIR filtering demonstrated the major role played by transition bands in determining intelligibilities of filtered speech, none of these experiments employed filter slopes steep enough to remove all contributions from transition bands, and so permit measurement of passband intelligibilities.

In order to determine the transition-band slopes necessary to ensure that passband contributions were not conflated with transition-band contributions, Warren, Bashford, and Lenz (2004) systematically increased transition-band slopes of a 1/3-octave band of everyday sentences centered at 1.5 kHz by starting at 150 dBA/octave, and continuing until further increases no longer reduced intelligibility. It was found that transition bands of 4800 dBA/octave for both high-pass and low-pass slopes (produced by FIR orders that exceeded 7000 for each slope) were needed to eliminate significant transition-band contributions and reach asymptotic scores. Even with both high-pass and low-pass transition bands as steep as 1200 dBA/octave, frequencies lying outside the passband still contributed over 30% of the 1/3-octave band’s intelligibility. In keeping with this information, 8000-order FIR filtering was used throughout the present study (except for1 that employed 20 000-order FIR filtering).

Experiment 1 obtained intelligibility judgments for six 1-octave rectangular passbands that covered the range of frequencies from 0.25 to 8 kHz. To determine the effect of amplitude upon intelligibility, separate groups of listeners were employed for each of four levels, 80, 70, 60, and 50 dB. On the basis of the results obtained in this experiment, 60 dB was selected as the optimal level to be employed in each of the subsequent experiments. Experiment 2 determined the intelligibility scores for the five adjacent pairings of the six 1-octave bands; Experiments 3a and 3b taken together obtained the scores for each of the 10 possible nonadjacent pairings.

II. METHOD

A. Subjects

The 212 listeners employed in Experiments 1, 2, 3a, and 3b (plus an additional 30 listeners used to obtain the data presented in1) were students at the University of Wisconsin-Milwaukee who received payment for their participation in the study. All were native English speakers who reported having no hearing problems and were screened to ensure that they had normal bilateral hearing as defined by pure tone thresholds of 20 dBA HL or better at octave frequencies from 250 to 8000 Hz.

B. Stimulus processing

The speech stimuli were sentences drawn from the “low-predictability” (LP) sublist of the revised Speech Perception In Noise (SPIN) test (Bilger, Nuetzel, Rabinowitz, and Rzeczkowski, 1984). These sentences are from five to eight words in length, and each ends with a monosyllabic noun serving as the keyword for scoring of intelligibility. In these LP sentences, the identity of the keyword is not predictable from sentence context (e.g., “The boy might consider the trap.”). The digitally recorded sentences (44.1 kHz sampling, 16-bit quantization) were produced by a male speaker having an average voicing frequency of about 100 Hz and having no obvious regional accent.

A total of 180 of the 200 LP SPIN sentences were used as experimental stimuli, and an additional five sentences were used as practice stimuli. Prior to filtering, the sentences were transduced by a Sennheiser HD 250 Linear II headphone and their slow-rms peak levels were matched to within 0.2 dB using a flat-plate coupler in conjunction with a Brüel and Kjaer model 2230 digital sound-level meter set at A-scale weighting (as were all level measurements reported).

All filtering to produce six 1-octave bands centered at 0.25, 0.5, 1, 2, 4, and 8 kHz was done using the fir1 function in MATLAB 5.2.1 running on a Macintosh G4 computer. As discussed in Sec. I, high-order FIR filtering was necessary to avoid confounding the contributions made by the passbands with those made by filter skirts. Slopes of 3.2 dBA/Hz, produced by two successive passes through 4000-order FIR filtering, ensured that filter slopes did not contribute to the intelligibility of any of the 1-octave bands. 1 The use of two successive stages for the 8000-order filtering reduced all frequencies within the stopbands to levels below threshold. Figure 1 shows the effectively vertical slopes of the long-term averaged spectrum for the midfrequency 2 kHz band superimposed upon that of broadband speech.

FIG. 1.

FIG. 1

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Long-term average spectrum of 180 LP SPIN sentences, subjected to two successive stages of 4000-order FIR filtering that produced a 1-octave rectangular band centered at 2-kHz. This plot for the filtered band is superimposed and coincides with the spectrum of the parent broadband stimulus. The plots were generated offline via discrete Fourier transform (DFT) with linear averaging of spectra using a 64 000-point (0.7 Hz resolution) Blackman window across the entire set of digitally recorded stimuli. Metric Halo Laboratories, Inc. produced the DFT software.

After filtering, the speech stimuli were again adjusted in level so that the slow-rms peaks of all of the sentences were matched to within 0.2 dBA SPL. The mixing of bandpass signals was done using Sound Designer II software running on a Macintosh G3 computer.

C. General procedure

A repeated measures design was used in each experiment. Before receiving each stimulus condition in an experiment, listeners were familiarized with the effects of filtering by listening to the set of five practice stimuli. These were first presented broadband, and then filtered in the same manner as the test stimuli. The test sentences in each experiment were grouped into sets, and these sets were presented in a balanced pseudorandom order, so that each center frequency was applied an equal number of times in each serial position to each sentence set across listeners.

After audiometric screening, subjects were tested singly while seated with the experimenter in an audiometric chamber. The stimuli were delivered diotically through Sennheiser HD250 Linear II headphones, with each of the speech bands, whether heard singly or in combination, presented at a fixed slow-rms peak level. The levels of the bands were varied from 50 to 80 dBA SPL for separate groups of listeners in Experiment 1, and each of the individual bands was delivered at 60 dBA when paired in Experiments 2, 3a, and 3b. Subjects were told to repeat the final word of each sentence as accurately as they could, and to guess if unsure. The keywords reported accurately were recorded by the experimenter. Testing occurred in a single session lasting approximately 30 minutes.

III. EXPERIMENTS

A. Experiment 1: Intelligibilities of the six 1-octave bands spanning the important frequencies of the speech spectrum at levels of 50, 60, 70, and 80 dBA

Four separate groups of 30 subjects each received 180 keywords (six sets of 30 keywords) at peak-rms levels of either 50, 60, 70 or 80 dBA. The six sets of sentences presented at each level were reduced to 1-octave bands having center frequencies of 0.25, 0.5, 1, 2, 4, and 8 kHz. Based upon the results obtained in Experiment 1, 60 dBA was used in Experiments 2, 3a, and 3b.

B. Experiment 2: Intelligibilities of adjacent pairs of 1-octave bands

The 30 subjects each received 180 keywords (5 sets of 36 keywords). Each set consisted of one of the five contiguous pairings of the 1-octave bands. These pairs were 0.25 +0.5 kHz, 0.5+1 kHz, 1+2 kHz, 2+4 kHz, and 4+8 kHz.

C. Experiment 3: Intelligibilities of paired nonadjacent 1-octave bands

Experiment 3a

Pairs separated by spectral gaps of one octave. The 32 subjects each received 180 keywords (4 sets of 45 keywords). Each set consisted of one of the following four pairs of the nonadjacent 1-octave bands: 0.25+1 kHz, 0.5+2 kHz, 1+4 kHz, and 2+8 kHz.

Experiment 3b

Pairs separated by spectral gaps of two, three, and four octaves. The 30 subjects each received 180 keywords (six sets of 30 words each). These sets consisted of the three pairs of 1-octave bands separated by two octaves (0.25+2 kHz, 0.5+4 kHz, and 1+8 kHz), the two pairs separated by three octaves (0.25+4 kHz, 0.5+8 kHz), and the single pair separated by four octaves (0.25+8 kHz). Experiments 2, 3a, and 3b taken together represent all of the 15 possible pairwise combinations of the six 1-octave bands in Experiment 1.

IV. RESULTS

A. Experiment 1

Figure 2 shows the average intelligibility scores (defined as the percent correct repetition of keywords) and standard errors for the six 1-octave bands at each presentation level. It can be seen that except for the 0.25 kHz band (having scores less than 1%), the highest intelligibility was obtained when the speech bands were presented at the two lowest levels of 60 and 50 dBA SPL. It also can be seen that intelligibility was highest for the 2 kHz band, and that the scores for the higher and lower bands decreased with the extent of their separation from the 2 kHz band. The data were subjected to a two-factor (speech level X center frequency) mixed analysis of variance, which yielded significant main effects of presentation level [F(3,116)=19.4, p<0.0001] and speech band center frequency [F(5,580)=523.9, p<0.0001], and a significant interaction of those factors [(F5,580)=4.9, p<0.0001]. Simple-effects comparisons yielded significant effects of presentation level at each speech band center frequency [F(3,116)≥3.5, p<0.02] or better], and subsequent Tukey HSD tests (Hays, 1988) revealed (p<0.05) that the effect of presentation level was due primarily to lower performance in the 80 dBA condition at all center frequencies except 250 Hz. For that speech band the 50 dBA level produced higher intelligibility than all other levels. The effect of center frequency also was subjected to simple-effects tests, which were significant at all presentation levels [F(5,145)≥116.7, p<0.0001]. Subsequent Tukey HSD tests indicated (p<0.05) that intelligibility at each presentation level was highest for the 2 kHz band, next highest for the 1 kHz band, lower for the 0.5 and 4 kHz bands (which did not differ significantly at any presentation level), and lowest for the 0.25 and 8 kHz bands.

FIG. 2.

FIG. 2

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Experiment 1: Mean percent intelligibility scores and standard errors as measured for the six 1-octave rectangular passbands presented at four different intensity levels to separate groups of listeners (N=30 at each level).

B. Experiment 2

The average percent intelligibility scores and standard errors for the five adjacent pairs of 1-octave bands (0.25+0.5,0.5+1,1+2,2+4,4+8 kHz) are shown in Table I, along with the scores for the nondjacent band conditions to be discussed below. The data for the adjacent bands were subjected to a repeated measures analysis of variance, which yielded a significant effect of band composition [F(4,116)=459.5, p<0.0001]. Subsequent Tukey HSD tests indicated (p<0.05) that intelligibility was highest for the 1+2 kHz pair, next highest and equivalent for the 0.5+1 kHz pair and 2+4 kHz pairs, and lowest for the 0.25+0.5 kHz and 4+8 kHz pairs, which did not differ significantly.

TABLE I.

Intelligibilities of individual rectangular 1-octave passbands spanning the speech spectrum and their synergistic or redundant interactions when paired. The matrix summarizes the results obtained in Experiments 1, 2, 3a, and 3b for bands presented at 60 dBA. The dark diagonal boxes show the intelligibility scores and standard errors for the six 1-octave rectangular passbands when heard alone. The boxes to the left of the diagonal show the dual-band intelligibility scores and standard errors (in parentheses) for all 15 possible pairings of the six bands. The boxes to the right of the diagonal show the percentage difference (Δ%) between the dual-band scores and the predicted scores based on the scores of the two component bands when heard alone, +Δ% values indicate synergy, −Δ% values (none found) would indicate redundancy (for further details see text). Note that the matrix exhibits reflection (or mirror) symmetry, so that if folded over on the major diagonal, the dual-band intelligibilities and their Δ% values are superimposed.

.25 kHz .5 kHz 1 kHz 2 kHz 4 kHz 8 kHz
Dual-Band intelligibility & (SE) 8 kHz 9.2%
(1.0)		 40.7%
(2.5)		 68.1%
(2.2)		 71.2%
(2.3)		 23.5%
(1.3)		 6.8%
(1.7)		 Dual Band Synergy
4 kHz 17.9%
(1.3)		 66.8%
(1.5)		 82.8%
(1.5)		 75.6%
(2.3)		 16.8%
(1.5)		 Δ+5%
2 kHz 65.6%
(2.4)		 89.9%
(1.0)		 90.0%
(1.1)		 54.8%
(3.3)		 Δ+21% Δ+23%
1 kHz 50.8%
(1.4)		 71.3%
(1.3)		 38.8%
(2.5)		 Δ+24% Δ+69% Δ+59%
.5 kHz 18.5%
(1.3)		 16.8%
(1.5)		 Δ+45% Δ+44% Δ+122% Δ+81%
.25 kHz 0.0%
(0.0)		 Δ+10% Δ+31% Δ+20% Δ+1% Δ+35%
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C. Experiments 3a and 3b

The data for the pairs of speech bands separated by a 1-octave spectral gap were subjected to a repeated measures analysis of variance, which yielded a significant effect of band composition [F(3,93)=165.3, p<0.0001]. Subsequent Tukey HSD tests indicated that all pairs differed significantly (p<0.05). The data for the band pairs separated by more than a 1-octave spectral gap were subjected to a similar analysis, which also yielded a significant effect of band composition [F(5,145)=226.3, p<0.0001]. Subsequent Tukey HSD tests indicated (p<0.05) that intelligibility was highest, and equivalent, for the 0.25+2 kHz, 0.5+4 kHz, and 1+8 kHz pairs. The next highest intelligibility was obtained for the 0.5+8 kHz pair, and the lowest performance was obtained for the 0.25+4 kHz and 0.25+8 kHz pairs, which did not differ significantly.

Table I shows the average intelligibility scores and standard errors for all 10 nonadjacent pairs of 1-octave bands presented in Experiment 3. Since the table also shows the scores for the five adjacent pairs of bands presented in Experiment 2, all possible pairings of the octave bands are represented in a single matrix. These values all appear on the left-hand side of the black boxes lying along the table’s diagonal. These black boxes contain the intelligibility scores and standard errors for each of the six 1-octave bands presented individually in Experiment 1. The boxes on the right-hand side of the main diagonal show the extent of synergy or redundancy produced when the individual bands are paired. The synergy/redundancy values were calculated based on the assumption that the error probability given by (1-proportion correct) for one band (P1) and for the other (P2) were independent and multiplicative. The “expected” dual-band score (SE) is then 100(1-P1xP2). The obtained dual-band score (SO) is shown on the left-hand side of the table’s major diagonal. The ratio SO/SE indicates whether the dual bands exhibit synergy or redundancy, with values greater than unity signifying synergy, and less than unity signifying redundancy. The extent of synergy or redundancy is shown to the right of the diagonal as Δ%=100[(SO/SE)−1], with positive values indicating synergy, and negative values indicating redundancy. It can be seen that none of the dual bands exhibit redundancy, and that all of the 15 dual-band combinations show synergy.

V. SUMMARY AND DISCUSSION

The effectiveness of speech as a means of communication depends upon the great redundancy provided by multiple dynamic cues, coupled with opportunistic strategies adopted by the listener. This can result in appreciable intelligibility even when some of the broadband information is severely distorted or missing. Some cues occur simultaneously across the entire spectrum (see Rosen and Fourcin, 1986); these include the presence or absence of voicing (e.g.,/v/ vs /f/), the duration of noise bursts before the onset of voicing (e.g., /d/ vs /t/), and the duration of articulatory closure and pauses. There are also frequency-specific cues, (1) the peaks in spectral envelopes corresponding to the three most important formants each have limited spectral ranges, and each can sweep across critical bands, with the individual formants following different trajectories (see Peterson and Barney, 1952); (2) cross-frequency integration of patterns of low-frequency amplitude fluctuation can provide significant information (see Cole and Scott, 1974; Shannon et al., 1995; Healy and Warren, 2003); (3) phase locking of auditory-nerve fibers can provide local timing and fine-structure information for the three principal vowel formants F1, F2, and F3 (Sachs and Young, 1979, 1980). As will be discussed, the current study provides information concerning the effectiveness of these cues when bands are heard singly and paired.

Experiment 1 was conducted to determine the optimal amplitudes for this study. Six 1-octave bands were presented at four different levels, 50, 60, 70, and 80 dBA. As shown in Fig. 2, scores were generally highest for the 60 dBA level, and scores declined somewhat at 70 dBA, indicating saturation of neural firing rate, and decreased still further at the 80 dBA level. Based on these results, the individual bands were presented at slow-peak levels of 60 dBA in all of the subsequent experiments.

The decrease in intelligibility starting at the high-to-moderate level of 70 dBA is in agreement with the observation reported by Bashford, Warren, and Lenz (2005) that the intelligibility of a rectangular speech band starts to decline at 65 dBA corresponding to the spectrum level it had in broad-band speech at 80 dBA. Although broadband speech intelligibility can remain nearly perfect at levels exceeding 90 dBA, bandpass speech excised without a change in its spectrum level exhibits the effects of neural saturation, apparently due to the lack of lateral suppression normally evoked by flanking components of the bandpass speech. Evidence supporting the role of lateral suppression was provided by a series of experiments employing flanking stochastic noise.

Table I contains all of the experimental data concerning dual-band intelligibility obtained in Experiments 2, 3a, and 3b with individual bands at a level of 60 dBA, as well as the single band data obtained at that level from Experiment 1. In Experiment 1, the octave band centered on 2 kHz had the highest intelligibility. This band has the advantage of lying within the transit range of two formants, the upper range of F2 and the lower range of F3 (see Peterson and Barney, 1952). It can be seen that intelligibility decreases monotonically as the separation of the lower and higher octave bands from the 2 kHz band increases.

The finding, shown in Table I, that all of the 15 dual bands exhibit synergy is not in agreement with earlier studies using pairs of band-limited speech. But in each of the previous studies, contributions of the passbands and transition bands were conflated. Experiments by Pollack (1948), Licklider (1959), Kryter (1960), Grant and Braida (1991), Steeneken and Houtgast (1999), and Müsch and Buus (2001a, 2001b) taken together, found that dual-band scores exhibited redundancy when bands were adjacent, and synergy when bands had sufficient separation. Grant and Braida suggested that when the bands were adjacent, there would be overlapping of transition bands, so that some of the information present in the individual bands would become redundant. When the bands were separated by spectral gaps, there would be “new” information, the extent of which depended upon the degree of separation.

Müsch and Buus (2001a, see also 2001b) stated that a “particularly impressive example of synergistic interaction was reported by Warren et al. (1995).” The study they referred to employed two widely separated 1/20-octave speech bands having slopes of approximately 100 dBA/octave. The band centered at 370 Hz had an intelligibility score of 0.9% and the band centered at 6 kHz had a score of 10.4%; when heard together, the intelligibility score was 27.8%. This measured score for the paired bands was considerably greater than the predicted score (11.2%) calculated by Müsch and Buus, based upon the same multiplication of error rates of the individual bands used in the present study. When expressed as Δ% (as in Table I), the extent of synergy was Δ+148%. Müsch and Buus argued that their Statistical Decision Theory (SDT) model could predict the extent of “synergistic interaction between frequency bands measured by Warren et al.”

The extent of synergy for the individual pairs shown in Table I depends upon a complex interaction of cues to phonetic and lexical identity. Some cues, such as the presence or absence of voicing, occur simultaneously across the spectrum, thus confirming but not adding new information to that available in each band. However, formants provide complex dynamic frequency-specific information; the sweeps of a formant across one of the 1-octave bands and the sweeps of the same or a different formant in the other band would be expected to interact in complex and (at present) unpredictable ways.

VI. CONCLUSION

The results obtained in the present study indicate that direct measurement of passband intelligibilities using rectangular bands could provide data for testing and perhaps modifying the estimates of passband intelligibilities based upon the AI/SII procedure. Comparison of the two procedures would be facilitated by obtaining direct intelligibility measurements for the same speech stimuli and passbands that had been employed for estimates based upon the SII.

ACKNOWLEDGMENT

This work was supported by NIH Grant No. DC00208 from the National Institute on Deafness and Other Communication Disorders.

Footnotes

PACS number(s): 43.71.Es, 43.71.Gv, 43.71.An [RLD]

1

In order to verify that the slopes in Experiment 1 were steep enough to eliminate out-of-band contributions for all 1-octave speech bands, the order of FIR filtering was increased from 8000 to 20 000. A separate group of 30 subjects was tested using the identical procedure employed at the 60 dBA level used in Experiment 1, except for the higher filter order that increased the slopes from 3.2 dBA/Hz to 8 dBA/Hz. Expressed in the more conventional terms of dBA/octave (rounded to two significant digits), the shallowest slope in Experiment 1 (the high-pass slope of the 0.25 kHz band) was 280 dBA/octave, and the low-pass slope of that band was 1100 dBA/octave. When the slopes were increased, the corresponding slopes for the 0.25 kHz band expressed as dBA/octave became 700 and 2700 respectively. For the five other 1-octave bands, the high-pass and low-pass bands were each doubled in dBA/octave for every increase of one octave. With careful listening by four laboratory personnel, no ringing (i.e., sound preceding the onset and following the offset of the sentences) could be heard for any of the six 1-octave bands presented in Experiment 1. However, clear ringing could be heard for the higher order filtering at center frequencies of 0.5, 1, and 2 kHz (there was no audible ringing for the other three bands). The percent intelligibilities for the six 1-octave bands follows with scores for the 3.2 dBA/Hz conditions preceding, and the 8 dBA/Hz conditions following the solidus: 0.25 kHz, 0.0/0.2; 0.5 kHz, 16.8/14.3; 1 kHz, 38.8/36.2; 2 kHz, 54.8/48.0; 4 kHz, 16.8/17.3; 8 kHz, 6.8/5.9. Increasing the slopes had no statistically significant effect upon any of the 1-octave passbands spanning the speech spectrum. It appears that 8000-order FIR filtering was sufficient to eliminate significant contributions from transition bands for each of the six 1-octave bands spanning the speech spectrum.

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