(d) Conventional method with p =
(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
of order p = 100
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
of Section 5
fragment of orchestral music
- Piano: a
3.7-s-long isolated low-pitched piano
a 14.3-s-long segment of Finnish pop
- Singing: a 20-s-long excerpt of
singing a capella
1: corrupted signal
2: restored via
conventional method with p = 1000
3: restored via
conventional method with p = 100
4: restored via
proposed method with p = 50 (for both full band and sub-band
on the links to listen or download the sound samples.
Comments on the PAQM (Perceptual Audio Quality Measure)
Perceptual Audio Quality
Measure (PAQM)  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
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 . However, such mapping not only tends to be application
dependent, but also would require extensive listening tests to assure a
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.
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.
 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.
Last Modified: 03 Nov. 2004
© Paulo Esquef