A) Effect of pitch on lower- and higher-order MFCC distributions

The effect of pitch differences between training and test data on the MFCC feature distribution is explored in a connected-digit recognition task to assess the impact of acoustic mismatch on recognition performance. The digits whose recognition models and features are most affected by the pitch mismatch are identified by determining the frequency of substitution, deletion, and insertion errors across different digit models from the ASR performances of “CHts1” on models trained with “ADtr”.

Explicit pitch normalization of each child test signal is performed with respect to the pitch distribution of the adult training data set using a maximum likelihood (ML) grid search approach. To carry out the ML grid search, the pitch of each child test signal is first transformed to seven different pitch values ranging from 70 to 250 Hz in steps of 30 Hz using the pitch synchronous time scaling method [Reference Cabral and Oliveira24]. This range of transformed pitch values was chosen based on the fact that the adult training data has a pitch distribution from 70 to 250 Hz. Given the various pitch-transformed versions within the specified range, the optimal value p̂, to which the pitch of each signal is to be transformed to, is estimated as:

(1) $${\hat p} = \arg \mathop {\max }\limits_p \Pr \lpar {X_i^p \vert \lambda, W_i} \rpar,$$

where $X_{i}^{p}$ is the feature for the ith utterance with pitch transformed to p, λ is the speech recognition model, and W _i is the transcription of the ith utterance. W _i is determined by initial recognition pass using original feature (i.e. without pitch transformation). The ML search is then performed over the original speech signal and its corresponding seven different pitch-transformed versions.

The recognition performances (in WER) obtained for CHts1 test set on models trained on ADtr using default 13-D base MFCC features with and without explicit pitch normalization of child speech and that using truncated 4-D base MFCC features are 11.37% WER, 9.64% WER, and 5.21% WER. For recognition, the base MFCC features are also appended with their corresponding first- and second-order derivatives. The frequency of substitution, deletion, and insertion errors in these ASR outputs are given in Table 5. It is shown that explicit pitch normalization results in substantial reduction in the number of substitution errors, deletion errors, and insertion errors. The deletion and insertion errors are mainly governed by the differences in speech rate in training and test data sets. Substitution errors are therefore used as the main criterion for evaluating performance. About 35% reduction is obtained in the substitution errors, which constitute 90% of total substitution errors in the original ASR system output on children's speech, while about 40% reduction is obtained in the substitution errors, which constitute 75% of total substitution errors in the original ASR system output on children's speech, after pitch normalization. The underlined numbers highlight examples from the top 10 highest occurring substitution errors (together constituting 67% of total substitution errors) in the original ASR system output obtained using default MFCC features, which were improved by more than 70% after pitch normalization. All substitution errors were verified, but due to space limitations analysis for only two of the underlined cases, which have the highest frequency in the original ASR system output, i.e. original digit “FIVE” recognized as “NINE” and original digit “OH” recognized as “TWO” is shown.

Table 5. Frequency of substitution, deletion, and insertion errors as resulting by evaluating the outputs of different ASR systems for “CHts1” on models trained on “ADtr”.

The ASR performances are computed on outputs of ASR systems making use of different set of features including: 13-D base MFCC features of children's original and explicitly pitch normalized test signals and 4-D base MFCC features of children's original test signals. For recognition, the base MFCC features are also appended with their corresponding first- and second-order derivatives. The bold numbers highlight examples from the top 10 highest occurring substitution errors (together constituting 67% of total substitution errors) in the original ASR system output obtained using default MFCC features, which were improved by more than 70% after using 4-D base MFCC features, while the underlined numbers highlight examples, which were improved by more than 70% after pitch normalization.

The higher-order coefficients C ₁₁ and C ₁₂ are extracted from the 13-D base MFCC feature vectors for 200 digit “FIVE” utterances and 200 digit “NINE” utterances from the original “ADtr” corpus. Similarly, the C ₁₁ and C ₁₂ coefficients are also extracted for 200 digit “FIVE” utterances from the original “CHts1” and 200 digit “FIVE” utterances from the explicitly pitch-normalized “CHts1” corpus. The distributions of the C ₁₁ and C ₁₂ coefficients extracted from MFCC features of digit “FIVE” utterances from original “ADtr” are shown in yellow, from original “CHts1” in blue, from explicitly pitch normalized “CHts1” in magenta and of digit “NINE” utterances from original “ADtr” are shown in black in Fig. 1. For ease of comparison, distributions of the C ₁₁ and C ₁₂ coefficients extracted for all these four different data sets are shown in both subplots of Fig. 1. The multivariate Gaussian distributions estimated using the means and variances of the corresponding coefficients and weighted by the corresponding mixture weights for each mixture in each state of the digit “FIVE” and digit “NINE” recognition models trained on “ADtr” are then computed and are also shown in gray scale in Fig. 1. These distributions are similarly obtained for the lower-order coefficients C ₁ and C ₂ for the same digit utterances and recognition models, which are shown in Fig. 2 using same color coding as given in Fig. 1.

Fig. 1. Scatter plots showing distributions of C ₁₁ and C ₁₂ coefficients of digit “FIVE” utterances from (a) original “CHts1” (in blue) along with Gaussian distributions (in gray scale) of those coefficients in digit “NINE” models trained with “ADtr”, and (b) explicitly pitch normalized “CHts1” (in magenta) along with Gaussian distributions (in gray scale) of those coefficients in digit “FIVE” models trained with “ADtr”. The spread of the C ₁₁–C ₁₂ distribution for digit “FIVE” utterances from “CHts1” test set is significantly reduced and is better mapped for digit “FIVE” models after explicit pitch normalization of the test set.

Fig. 2. Scatter plots showing distributions of C ₁ and C ₂ coefficients of digit “FIVE” utterances from (a) original “CHts1” (in blue) along with Gaussian distributions (in gray scale) of those coefficients in digit “NINE” models trained with “ADtr”, and (b) explicitly pitch normalized “CHts1” (in magenta) along with Gaussian distributions (in gray scale) of those coefficients in digit “FIVE” models trained with “ADtr”. No significant change is observed in the distribution of lower-order C ₁ and C ₂ coefficients for digit “FIVE” utterances from “CHts1” test set after pitch normalization.

Scatterplots given in black and yellow show the examples of perfect matching of distributions of MFCCs of adult utterances for each of the two digits with the Gaussian distributions for the corresponding MFCCs of the respective digit models shown in gray scale. As shown in Fig. 1, the spread of the C ₁₁–C ₁₂ distribution for digit “FIVE” utterances from the “CHts1” test set (given in blue) is significantly reduced after explicit pitch normalization of the test set (given in magenta), which explains the reduction in variance of those coefficients observed in [Reference Sinha and Ghai15]. The C ₁₁–C ₁₂ distribution for digit “FIVE” utterances from the “CHts1” test set is better mapped for digit “FIVE” after explicit pitch normalization of the test set. On the other hand, no significant change is observed in the distribution for the lower-order C ₁ and C ₂ coefficients after pitch normalization, as evident in Fig. 2.

Similar observations hold for the C ₁₁–C ₁₂ and C ₁–C ₂ distributions of digit “OH” and digit “TWO” utterances and recognition models shown in Figs 3 and 4, respectively. These observations indicate that variations in the pitch of the signals predominantly affect the higher-order MFCCs, which typically carry less linguistically relevant information. Differences in pitch between training and test speech lead to pattern mismatch between the higher-order MFCCs, resulting in poor ASR performance under mismatched conditions.

Fig. 3. Scatter plots showing distributions of C₁₁ and C₁₂ coefficients of digit “OH” utterances from (a) original “CHts1” (in blue) along with Gaussian distributions (in gray scale) of those coefficients in digit “TWO” models trained with “ADtr”, and (b) explicitly pitch normalized “CHts1” (in magenta) along with Gaussian distributions (in gray scale) of those coefficients in digit “OH” models trained with “ADtr”. The spread of the C ₁₁–C ₁₂ distribution for digit “OH” utterances from “CHts1” test set is significantly reduced and is better mapped for digit “OH” models after explicit pitch normalization of the test set.

Fig. 4. Scatter plots showing distributions of C ₁ and C ₂ coefficients of digit “OH” utterances from (a) original “CHts1” (in blue) along with Gaussian distributions (in gray scale) of those coefficients in digit “TWO” models trained with “ADtr”, and (b) explicitly pitch normalized “CHts1” (in magenta) along with Gaussian distributions (in gray scale) of those coefficients in digit “OH” models trained with “ADtr”. No significant change is observed in the distribution of lower-order C ₁ and C ₂ coefficients for digit “OH” utterances from “CHts1” test set after pitch normalization.

B) Effect of higher-order MFCCs on Mel spectrum

To better comprehend the impact of higher-order MFCCs on the MFCC feature representation, the spectra corresponding to MFCC features of different feature lengths are illustrated. The plots of the smooth spectra corresponding to various truncated base feature lengths including C ₀ for the stable portion of vowel /iy/ with average pitch value 300 Hz along with its linear discrete Fourier transform (DFT) spectrum are shown in Fig. 5. The frequency of the first two pitch harmonics in the linear DFT spectrum in Fig. 5(b) exactly matches that of the two harmonics in the lower-frequency region of the smoothed. Mel spectrum in Fig. 5(a) in case of default MFCC base feature length.

Fig. 5. Plots of (a) smoothed spectra corresponding to the base MFCC features of different dimensions along with corresponding. (b) Linear DFT spectrum for a frame of vowel /iy/ having the average pitch value of 300 Hz.

Truncation in quefrency domain is equivalent to convolving the spectral envelope of the MFCC filterbank with the spectrum of the truncation window in frequency domain. As the degree of truncation increases, the bandwidth of the truncation window spectrum increases resulting in greater smoothening of the pitch harmonics and the spectral peaks (formants) in the spectrum. Therefore, with increasing cepstral feature truncation, the two harmonics in the lower-frequency region of the smoothed Mel spectrum in Fig. 5(a) are getting smoothed out.

Thus, excluding higher-order MFCCs for speech recognition under mismatched conditions is hypothesized to reduce the gross acoustic mismatch between training and test data by minimizing the effect of pitch differences, VTL differences (one of the foremost source of acoustic mismatch between adult and child speech [Reference Ghai and Sinha25]) and any other sources of speaker-specific acoustic mismatch which induce rapidly varying changes in spectra.

A) Effect of MFCC feature truncation on ASR performance

In order to study the extent of acoustic mismatch captured by higher-order MFCCs, the effect of exclusion of the higher-order coefficients from the MFCC feature vector is tested by truncating the MFCC base features for the children's test data from 13 (C ₀-C ₁₂) down to 3 (C ₀-C ₂) in steps of 1. For recognition, the various truncated MFCC base features are augmented with their corresponding first- and second-order derivatives. The resulting feature set is then decoded using ASR models of the same dimensionality extracted from the baseline 39-D models. The recognition performance for “CHts1” for different dimensions of the truncated test features on corresponding models trained on “ADtr” with matching feature dimensions are given in Table 6. The table also shows the pitch group-wise breakup of performances corresponding to each of the truncations. The recognition performance for “CHts1” improves consistently with feature truncation. The best relative improvement of about 54% is obtained over the baseline for “CHts1” with 4-D base MFCC features. The age group-wise breakup of this best recognition performance obtained for “CHts1” using 4-D base MFCC features is given in Table 7.

Table 6. Performance of “CHts1” on models trained with “ADtr” for various truncations of the base MFCC features along with its pitch group-wise breakup.

The truncated base MFCC features are also appended with their corresponding first- and second-order derivatives for recognition. The quantity in bracket gives the number of utterances corresponding to that pitch group. The bold numbers highlight the best performances obtained for each pitch group by increasing the truncation of the base MFCC feature beyond the default length of 13 up to 3.

Table 7. Age group-wise breakup of the best recognition performance obtained for “CHts1” on models trained with “ADtr” using 4-D base MFCC features.

The truncated base MFCC features are also appended with their corresponding first- and second-order derivatives for recognition. The quantity in bracket gives the number of utterances corresponding to that age group.

This improvement in ASR performance with feature truncation beyond the default feature length is an outcome of consistent reduction in all three categories of recognition errors as given in Table 5. The bold numbers in Table 5 highlight examples from the top 10 highest occurring substitution errors (together constituting 67% of total substitution errors) in the original ASR system output on children's speech obtained using default MFCC features, which are improved by more than 70% after using 4-D base MFCC features.

To validate the improvement in performance with increasing MFCC feature truncation on a continuous speech recognition task, the recognition performance for “PFts” is evaluated on the corresponding models trained on “CAMtr” with matching feature dimensions, as given in Table 8. When the higher-order MFCCs are excluded from the feature vector, improvement is obtained in recognition performance on a continuous speech recognition task as well. The best relative improvement of about 38% is obtained over the baseline for “PFts” with 6-D base MFCC features. The age group-wise breakup of this best recognition performance obtained for “PFts” using 6-D base MFCC features, given in Table 9, shows consistent improvements across all age groups.

Table 8. Performance of “PFts” on models trained with “CAMtr” for various truncations of the base MFCC features along with its pitch group-wise breakup.

The truncated base MFCC features are also appended with their corresponding first- and second-order derivatives for recognition. The quantity in bracket gives the number of utterances corresponding to that pitch group. The bold numbers highlight the best performances obtained for each pitch group by increasing the truncation of the base MFCC feature beyond the default length of 13 up to 3. The numbers indicate that greater truncation is chosen for signals of higher pitch group.

Table 9. Age group-wise breakup of the best recognition performance obtained for “PFts” on models trained with “CAMtr” using 6-D base MFCC features.

The truncated base MFCC features are also appended with their corresponding first- and second-order derivatives for recognition. The quantity in bracket gives the number of utterances corresponding to that age group.

These results verify our hypothesis that a large degree of degradation in ASR performance on children's speech under the mismatched conditions is mainly caused by the acoustically mismatched information present in the higher-order coefficients of the MFCC feature vector.

B) Relation between MFCC feature truncation and acoustic mismatch

Although truncating MFCC base features beyond the default length of 13 helps in reducing the gross acoustic mismatch between the child test set and the models trained on adult speech, for each test signal the degree of acoustic mismatch with respect to the models would be different. Therefore, we investigate the correspondence between MFCC feature length and degree of acoustic mismatch in speech recognition.

Due to reduction in the dimensionality of feature vectors, the likelihoods of test features increase monotonically with increasing truncation. Thus, the ML criterion cannot be simply used to determine the appropriate truncation for a test feature without using appropriate penalties. Since we have hypothesized that increased MFCC feature truncation reduces the acoustic mismatch mainly due to pitch differences and differences in formant frequencies, we explore the appropriate MFCC base feature truncations for the test signals based on their average pitch values and their optimal VTLN warp factors on default MFCC features.

The speech signals of child test sets are divided into different groups based on their average pitch values. The pitch group-wise performances of “CHts1” and “PFts” for different dimensions of the truncated test features on corresponding models trained on adult speech with matching feature dimensions are also given in Tables 6 and 8. On both tasks, the best ASR performances correspond to the same MFCC base feature truncation for different pitch groups. Therefore, pitch cannot be used for determining the appropriate MFCC feature truncation for a signal. Although the acoustic mismatch due to pitch differences is also addressed by increased MFCC feature truncation, it is not large enough to quantify the gross acoustic mismatch of the signals with respect to the models.

Among the various other sources of acoustic mismatch, the VTL differences are the foremost source of mismatch. VTLN provides an easy quantification of the acoustic mismatch in terms of the frequency warp factor. To investigate appropriate MFCC base feature truncations for children test signals, we now explore optimal VTLN warp factors. The VTLN warp factors for all speech signals of both child test sets are estimated on an utterance-by-utterance basis with respect to the corresponding 39-D baseline models trained on adult speech by carrying out a ML grid search among 13 frequency warp factors (α) ranging from 0.88–1.12 in steps of 0.02 as described in [Reference Lee and Rose26]. This range of VTLN warp factors is chosen in order to study the relation between degree of MFCC feature truncation and acoustic mismatch (as quantified by VTLN warp factors) in speech recognition of child speech on models trained on adult speech with the default feature and recognition model settings that are typically used for recognition of adult speech under matched conditions. Piece-wise linear frequency warping of the filterbank, as supported in the HTK Toolkit [Reference Young21], is used. The optimal warp factor α̂, is estimated as:

(2) $${\hat \alpha} = \arg \mathop {\max }\limits_\alpha \Pr \lpar {X_i^\alpha \vert \lambda ,W_i } \rpar,$$

where $X_{i}^{\alpha}$ is the frequency warped feature for the ith utterance. λ is the speech recognition model, and W _i is the transcription of the ith utterance. W _i is determined by the initial recognition pass. Both test sets are then divided into different groups based on their optimal VTLN warp factors.

The VTLN warp factor-wise recognition performances of “PFts” are given in Table 10. There are not sufficient numbers of signals corresponding to each of the values of the VTLN warp factor in the child test sets. The recognition performances for “CAMts” are therefore also evaluated on models trained on “CAMtr” as given in Table 11.

Table 10. Performance of “PFts” on models trained on “CAMtr” for various truncations of the base MFCC features along with their VTLN warp factor-wise breakup.

The truncated base MFCC features are also appended with their corresponding first- and second-order derivatives for recognition. The quantity in bracket gives the number of utterances corresponding to that VTLN warp factor. The bold numbers highlight the best performances obtained for each group of signals corresponding to different VTLN warp factors by increasing the base MFCC feature truncation beyond default. The numbers indicate that greater truncation is chosen for signals having greater VTL differences.

Table 11. Performance of “CAMts” on models trained on “CAMtr” for various MFCC base feature truncations along with their VTLN warp factor-wise breakup.

The truncated test features also include their first- and second-order derivatives. The quantity in bracket gives the number of utterances corresponding to that VTLN warp factor. The bold numbers highlight the best performances obtained for each group of signals corresponding to different VTLN warp factors by increasing the base MFCC feature truncation beyond default. The numbers indicate slight improvement over baseline with increased MFCC feature truncation only up to MFCC base feature length of 12 due to smaller degree of gross acoustic mismatch between the test and training data set.

While the ASR performance improves consistently with increased MFCC feature truncation for “PFts”, there is a slight improvement over baseline with increased MFCC feature truncation up to the MFCC base feature length of 12 for “CAMts”. The reduced feature truncation and small improvement for “CAMts” is attributed to the smaller degree of gross acoustic mismatch for adult test set with respect to the models trained on adult speech unlike the data set “PFts”. However, for both child and adult test data sets, different truncations of MFCC base features are required for signals with different degrees of VTL differences. Greater truncation is chosen for signals having greater VTL differences. Child speech has greater acoustic mismatch with respect to ASR models trained on adult speech. As a result, larger improvements are obtained in speech recognition performance on children's speech, while no significant change is obtained for adults' speech using increased MFCC feature truncation.

Thus, increasing MFCC feature truncation helps to improve ASR performance under mismatched conditions by efficiently reducing significant gross acoustic mismatch between the test signals and the training set.

C) Proposed algorithm for adaptive MFCC feature truncation for ASR

We have already found that the appropriate MFCC base feature truncation increases as the degree of acoustic mismatch increases between the test speech and the speech recognition models. Under matched and mismatched conditions, however, on the whole, less MFCC feature truncation is required for matched test speech, while greater truncation is required for mismatched test data. In order to automate the procedure of determining the appropriate MFCC feature truncation for a test signal, the test speech must first be categorized as matched or mismatched.

The frequency spectrum of child speech may require compression by a frequency warp factor of as low as 0.88 relative to adult speech. On the other hand, the frequency spectrum of adult speech would often need expansion by a frequency warp factor of as high as 1.12 relative to child speech. Thus, to categorize the test signal as belonging to a child speaker or an adult speaker, we compare the log likelihood for the test signal using the default MFCC feature set and the feature sets corresponding to different VTLN warp factors.

On models trained on adult speech, if the likelihood is greater for the feature set corresponding to VTLN warp factor of 0.88 than that corresponding to the default MFCC features, the test signal is categorized as belonging to a child speaker. However, on models trained on child speech, the test signal is categorized as adult speech if its likelihood is greater for the feature set corresponding to VTLN warp factor of 1.12 than that corresponding to the default MFCC features. For the sake of generality, based on the ASR performances obtained for adult and child speech corresponding to different VTLN warp factors using different MFCC feature lengths, we propose a piece-wise linear model for the relationship between MFCC base feature truncation for both adult and child test signals and their acoustic mismatch, as assessed by their VTLN warp factor (α̂), depicted in Fig. 6.

Fig. 6. Graph showing the relation proposed between appropriate length of MFCC base feature and VTLN warp factor for both adult and child test signals.

Once the test signal is categorized as belonging to adult or child, the appropriate MFCC base feature length is determined using the optimal VTLN warp factor (α̂). The flow diagram of the algorithm proposed for models trained on adult speech or child speech is shown in Fig. 7.

Fig. 7. Flow diagram of the proposed algorithm to determine the appropriate MFCC base feature length for test signal on models trained on adult speech (solid lines) or models trained on child speech (in dashed lines).

The recognition performances for all test sets using the proposed algorithm are given in Table 12. The numbers given in brackets give the relative improvements obtained using the proposed algorithm over the corresponding baseline. Relative improvements of 38% (on a connected-digit recognition task) and 36% (on a continuous speech recognition task) are obtained for child test sets over baseline that are close to the best performance improvements of 54% (on a connected-digit recognition task) and 38% (on a continuous speech recognition task) obtained using the same MFCC base feature length for all test signals. However, when tested on the adult test set, no significant improvement in performance is obtained compared with baseline on the models trained on adult speech. In fact, the performance of adult test sets on matched models show slight degradation using the proposed algorithm as indicated with negative numbers in brackets for two cases in Table 12.

Table 12. Performances of test sets on recognition models trained with different training data sets using MFCC features derived using the proposed algorithm referred to as “Proposed” for both connected-digit and continuous speech recognition task.

The numbers given in brackets give the relative improvements obtained using the proposed algorithm over their corresponding baselines.

However, their performance degradation, attributed to smaller degree of gross acoustic mismatch between adult training data and adult test data, is insignificant relative to the degree of improvement that is obtained in the recognition performance for child test sets. Further, when tested on models trained on child speech, the proposed algorithm gives consistent improvements for both mismatched adult test set and matched child test set on both digit and continuous speech recognition tasks. Relative improvements of 49 and 31% are obtained over baseline in ASR performances on children's speech. When the adult test set is evaluated using models trained on child speech, relative improvements of 35 and 10% are obtained over baseline on the digit and continuous speech recognition tasks. However, greater improvements are obtained for children's speech than for adults' speech on models trained on child speech. Also, for ASR of adults' speech, the improvements obtained are less than that for ASR of children's speech under mismatched conditions. This is because the variances for the observation densities of the phone models are greater for the poor models trained on child speech than for the models trained on adult speech [Reference Lee, Potamianos and Narayanan2,Reference Gerosa, Giuliani and Brugnara8]. This means that the Gaussian densities are more scattered and thus less separable in the acoustic feature space for models trained on child speech.

Thus, the proposed algorithm is effective in reducing the acoustic mismatch between child speech and adult speech, without using any prior knowledge about the speaker of the test utterance, and with the additional advantage of reduced MFCC feature dimensions. Relative improvements obtained using the proposed algorithm in all ASR performances under acoustically mismatched conditions are close to the best performances obtained with constant fixed feature truncation for all test signals. However, these significant improvements in the recognition performances using the proposed algorithm are obtained with an increase in the execution time by a factor of 10 with respect to the default HMM-based ASR algorithm.

D) Combining proposed algorithm with VTLN and/or CMLLR

VTLN and CMLLR are the two effective techniques in the literature that are used to reduce acoustic mismatch between adult speech and child speech [Reference Gerosa, Giuliani and Brugnara8,Reference Giuliani, Gerosa and Brugnara11]. Our proposed algorithm for adaptive MFCC feature truncation also addresses acoustic mismatch and has given significant improvements in performance. It would be interesting to explore whether the improvement obtained by our proposed algorithm is additive to that obtained by VTLN and/or CMLLR or not.

In these experiments, VTLN is performed on an utterance-by-utterance basis on the test speech data. An ML grid search procedure is used to carry out VTLN with frequency warp factors ranging from 0.88 to 1.12 in steps of 0.02 as described in Section IV-B. CMLLR is a feature adaptation technique that estimates a set of linear transformations for the features. The effect of these transformations is to modify the feature vector so as to increase its likelihood with respect to the given model. The transformation matrix used to give a new estimate of the adapted observation ô is given by:

(3) $${\hat o}=Ao+b,$$

where o is an n × 1 observation vector, A represents an n × n transformation matrix, and b represents an n × 1 bias vector. The ML estimates of the affine transformations for adaptation of the features are obtained using the EM algorithm on adaptation data.

The recognition performances for “PFts” on models trained on “CAMtr” using the default MFCC features and the features derived using the proposed adaptive MFCC feature truncation algorithm both with and without VTLN are given in Table 13. Another 15% relative improvement is obtained over the performance obtained using VTLN on default MFCC features by carrying out VTLN with MFCC features derived using the proposed adaptive truncation algorithm. However, the relative improvement with VTLN is reduced by 15% when the MFCC features derived using the proposed algorithm are used. The ASR performances for “PFts” on models trained on “CAMtr” using CMLLR on the default MFCC features and the features derived using the proposed adaptive truncation algorithm both with and without VTLN are also given in Table 13.

Table 13. Performances of different test sets using the default MFCC features referred to as “Default” and MFCC features derived using the proposed algorithm referred to as “Proposed” both with and without VTLN and/or CMLLR on recognition models trained with different training data sets for continuous speech recognition task. Relative gain in ASR performance obtained with CMLLR over the respective baseline is also given.

The bold numbers highlight the best performances obtained for each test set on recognition models trained on different training data sets using the proposed algorithm in conjunction with VTLN and CMLLR.

CMLLR is performed for computing speaker-specific transformations as supported in the HTK Toolkit [Reference Young21]. A relative gain of 40% is obtained in the recognition performance using CMLLR on MFCC features derived using the proposed algorithm over the performance obtained by using CMLLR on the default. MFCC features. In relation to the recognition performances obtained by combined VTLN and CMLLR, a relative improvement of 13% is obtained using the proposed algorithm over that obtained using the default MFCC features.

The additional improvements obtained for “PFts” using the proposed algorithm over those obtained from VTLN and/or CMLLR under mismatched conditions are further validated for recognition of “PFts” and “CAMts” on models trained using “PFtr” as given in Table 13. A similar trend to that obtained for “PFtr” on models trained on “CAMtr” is observed in performance improvements for both “PFts” and “CAMts” on models trained on “PFtr”. Relative gains of 15% for VTLN, 26% for CMLLR, and 16% for VTLN with CMLLR are obtained in the ASR performance over baseline for “PFts” using MFCC features derived using the proposed algorithm. Relative gains of 6% for VTLN, 23% for CMLLR, and 7% for VTLN with CMLLR are obtained in the recognition performance over baseline for “CAMts” using MFCC features derived using the proposed algorithm.

Thus, the improvement obtained using the proposed adaptive MFCC feature truncation algorithm is additive to those obtained with VTLN and/or CMLLR. This is because the proposed algorithm is not constrained to use linear transformations. By reducing the feature dimension for both training and test sets at the same time, SAT is implicitly incorporated in the proposed algorithm and thus does not require the models to be explicitly adapted and retrained.