The audio files on this page are examples of compression using the
real-time energy spreading transform known as PONS. Many details are in US
patent number 5913186, 1999, "Discrete One Dimensional Signal Processing
Method and Apparatus Using Energy Spreading Coding" (Byrnes, Ramalho,
Ostheimer, Gertner).
The patent abstract is at the end of this page.
Recent improvements in the implementation were done by Prometheus Principal
Scientist Jerry Kautsky.
The purpose of this demonstration is for the reader to compare the
difference between uniformly rounding an audio signal to a small number of
bits per sample and doing the same thing on a signal transformed by the PONS
system. Similar results would be obtained if the same technique were applied to
any digital signal.
The energy spreading feature of PONS allows the PONS encoder to dispense
completely with time-varying bit allocation. This, plus the fact that the PONS
coder requires almost exclusively integer arithmetic, makes PONS extremely
fast and efficient.
In addition, the PONS coder is in-place, thereby minimizing computer storage
requirements during encoding and decoding. Finally, the PONS transform matrix
is symmetric, which further reduces the computation requirement.
The sample audio file which we have chosen to illustrate these features of
PONS is the beginning of the Tchaikovsky Piano Concerto. The 4-bit standard sample 1-bit standard sample are the results of uniformly quantizing the 16-bits per sample digitized version of
the original sample to 4 and 1 bits per sample respectively. i.e., to get 4-bit standard sample
from the 16-bits per sample digitized version of the original standard sample we simply discard
the bottom 12 bits of each sample. 16-bit standard sample is the full 16-bits per
sample digitized version of the original standard sample.
The files pons-xbit, where x = 1, 2, 4 or 6, are gotten by first
applying the PONS transform to the 16-bits per sample digitized version of
the original standard sample, which yields 16-bit coefficients. Then the bottom 16-x bits of each
coefficient are dropped and Huffman coding is applied to what remains.
Finally, the inverse PONS transform (which is the same as the forward
transform because the PONS matrix is symmetric) is applied to the result and
the PONS x-bit resampling file is created from this, yielding an approximation to the original
standard sample.
To play any of these .wav files simply double click on the name.
The reader will judge how good this approximation is, partially by comparing
PONS 1-bit resampling with 1-bit standard sample and PONS 4-bit resampling with
4-bit standard sample.
It should be mentioned that there are a few additional details to the PONS
coding and decoding, such as blocking the original signal and other
"bookkeeping", but these barely affect the processing, which is real-time and
in-place in both the compression and decompression stages. The basic
processing is illustrated in the flow diagram.
The sizes of the files that are created (in real-time) by applying the PONS
algorithm, which are the files that would need to be stored or transmitted
before the .wav files are constructed (again, in real-time), are:
tchai-pons-6bit.mat, 442906 bytes
tchai-pons-4bit.mat, 289749 bytes
tchai-pons-2bit.mat, 126590 bytes
tchai-pons-1bit.mat, 63693 bytes
Note, for example, that tchai-pons-1bit.wav requires a file to be stored or
transmitted that is less than 3.9% of the size of tchai.wav (1638188 bytes).
The corresponding statement is true for the other (more audibly pleasing)
choices of x (2, 4, 6), and would also hold for any other choices of x (from 3
to 16 in this case) as well as for any other audio signals that one chose to
process.
It is also worth mentioning that a simple but effective encryption step may
be added with virtually no effect upon the encoding or decoding speed or
complexity. This would be accomplished by permuting the elements of the
PONS basis. While such an encryption technique is well known to be relatively
insecure, in the real-time communications environment envisioned it should
prove to be completely adequate. Combined with the fact that the PONS
transform representation of a signal inherently resembles white noise, the
technology described herein should prove particularly advantageous in an
environment where secure, real-time, computationally simple communications
are required.
Patent abstract: PONS comprises a transform coder and decoder for discrete
time electrical signals, in particular acoustic signals. The PONS coder
utilizes an integer coefficient transform coder which is not frequency based,
which requires almost exclusively fast integer arithmetic, and which spreads
incoming signal energy nearly as evenly as possible among coefficients in the
transform domain. The PONS coder also has the property that the magnitudes of
transform domain coefficients vary by less than about an order of magnitude,
so that the PONS coder dispenses completely with time-varying bit allocation.
PONS uses only the quantization step to achieve significant compression.
Energy spreading also permits reasonably accurate signal reconstruction even
when significant numbers of transform coefficients are lost or corrupted.
PONS coding is the foundation of Cisco Systems' second generation 'Intelligent Proximity', which lets user PC, MacOS, Apple iOS and Android devices connect to Cisco telepresence systems.
