An Efficient Model-Based Method for Reconstruction of Audio Signals Across Long Gaps

Paulo A. A. Esquef and Luiz W. P. Biscainho

Companion web page of the homonym  paper submitted to the IEEE Transactions on Speech and Audio Processing

Examples of Section 3

Original Piano Tone
(d) Conventional method with p = 1000
(c) Fulband plus post-processing stage, both with  AR models of order p = 50
(b) Fullband stage of the proposed method with p = 50
(a) Conventional method with AR model of order p = 100

Examples of Section 4

(d) Proposed interpolator: fulband plus post-processing stage, both with  p = 50
(c) (LSAR-E): LSAR with constant energy excitation with p = 100
(b) (LSAR+SIN): LSAR plus sinusoidal basis representation: p = 60 (AR part) + 40 sinusoids
(a) (LSAR): Standard LSAR-based interpolator with model order p = 100

Examples of Section 5

Test Signals

  1. Classical: a 13-s-long fragment of orchestral music
  2. Piano: a 3.7-s-long isolated low-pitched piano tone
  3. Pop: a 14.3-s-long  segment of Finnish pop music
  4. Singing: a 20-s-long excerpt of singing a capella 


  1. Case 1: corrupted signal
  2. Case 2: restored  via conventional  method with p = 1000
  3. Case 3: restored  via conventional  method with p = 100
  4. Case 4: restored  via proposed  method with p = 50 (for both full band and sub-band interpolation)
Click on the links to listen or download the sound samples.

Signal Type PAQM x (-32)

Case 2
Case 3
Case 4

Comments on the PAQM (Perceptual Audio Quality Measure)

The Perceptual Audio Quality Measure (PAQM) [1] is an objective measure that has been originally devised to assess the quality of lossy-coded audio signals. It has been demonstrated to correlate strongly with human judgment regarding the subjective quality of both wideband audio and band-limited speech signals.

The basic principle behind the PAQM is to compare the inner ear representations of a reference signal and a processed version of it. Based on the differences observed in these representations a cognitive model generates an index of overall dissimilarity between the two signals. This index, the PAQM, can reflect the loss of valuable information as well as the introduction of spurious artifacts in the processed signal.

The transformation of the input signals into their inner ear representations involves several signal processing manipulations that take into account psychoacoustic phenomena. Nonetheless, it must be emphasized that the PAQM values shown in the simulations reported here are merely an objective dissimilarity index. Mapping the PAQM into a subjective grading system such as the mean opinion score (MOS) can be carried out [1]. However, such mapping not only tends to be application dependent, but also would require extensive listening tests to assure a high correlation between the PAQM and MOS values.
The way it is computed, the lower the value of PAQM, the more similar to the reference the processed signal is. A PAQM = 0 implies a processed signal perceptually identical to the reference. However, drawing conclusions on the subjective quality of a reconstructed signal based solely on its PAQM is not straightforward.

In the absence of a mapping into a subjective quality grading system, the PAQM assumes a speculative role regarding the subjective assessment of the results. Nevertheless, it is plausible to expect that PAQM values close to each other are likely to reflect signals with similar perceptual quality. In this context, comparing the PAQMs of a set of processed signals, such as the degraded and distinct satisfactorily restored signals, can be useful. They allow an approximate inference on the quality of other restored versions from their corresponding PAQMs.

Note that the measured  values of PAQM shown in the table above were arbitrarily scaled by a factor of -32. This resource was taken to adjust the dynamic range of the PAQM results to coincide with that of the subjective gradings, which vary approximately from -4 (corrupted) to 0 (reference), presented in Section V of the paper.

Bonus Examples

The examples below are related to the effects of changing order of the prototype filter on the interpolation performance. Test-signal piano is employed in this simulation. 

  1. Case 4 (Daubechies-8)
  2. Case 4 (Daubechies-16)
  3. Case 4 (Daubechies-32)


[1]  J. G. Beerends, “Audio Quality Determination Based on Perceptual Measurement Techniques,” in Applications of Digital
Signal Processing to Audio and Acoustics, M. Kahrs and K. Brandenburg, Eds., chapter 1, pp. 1–38. Kluwer Academic
Publishers, Boston, USA, 1998.

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Last Modified: 03 Nov. 2004
© Paulo Esquef