File: Tracksplit.txt

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||  NOTE: This document describes the track location algorithms found in
||  versions 1.0 - 1.3 of GramoFile. The new algorithm found in version 1.4
||  and up is described in the file Tracksplit2.txt. 







                          Track Splitting in GramoFile

                 A successful approach to a problem of old times



                                           By J. A. Bezemer
                                           J.A.Bezemer@ITS.TUDelft.NL
                                           Last update: 07/07/1998

                                           GramoFile website:
                                           http://cardit.et.tudelft.nl/~card06


INTRODUCTION

Only a few years ago, gramophone records were the most popular way of
distributing music. These days, their place has been taken entirely by
Compact Discs. Some of the most popular records have been digitally
remastered, and CDs with music from the `good old times' have been
pressed. After the introduction of CD-Recordables and CD Recorders for use
with Personal Computers, some people started making CDs from their own
records. It is desirable to have tracks on the CD just as they were on the
original gramophone record. This can be done by sampling each individual
track of the record to a seperate audio file on the harddisk of the PC,
and then use a piece of CD writing software that can make separate tracks
of a row of audio files. This way, the sampling process is laborious and
requires constant attention.

In this document, a process is described that automates the separation of
tracks. An entire side of a record is sampled to one big audio file, and
an intelligent piece of software automatically detects where tracks begin
and end. This process has been implemented in the GramoFile program, that
is also capable of applying anti-tick signal processing to audio files.
The routines of that program will be mentioned a few times in this
document.


REDUCTION OF DATA

The size of a CD-quality audio file (.wav format) that represents sampled
audio of a gramophone record, is about 200 megabytes. This is far more
data than is needed to compute track starts and ends. Therefore, a large
scale reduction of the data is possible. It is also necessary, because
processing several hunderd megabytes of data will take far too long to be
useful, even on the fastest computers available.

One way to characterize tracks with respect to inter-track silence, is the
fact that the signal power (or volume) is higher. The signal power may be
computed with the root-mean-square (RMS) expression

                                __________________________
                               /       i=0
                          _   /   1    ---             2
    y[t] = RMS(x[t]) =     | /   ---   )     ( x[t+i] )
                           |/     N    ---
                           /           N-1


with N the `length' of the RMS operation.

When calculating the RMS of an audio signal for tracksplitting purposes, a
good choise for the length is one tenth second. Then there are enough
samples to compute an accurate RMS (4410 when using CD-quality sampling),
there are sufficient (typ. >30) RMS-points within an inter-track silence,
and the total number of RMS points is limited enough to fit completely in
a computer's memory (typ. <100 kB).

If stereo signals are used, there may be some soft signal at one channel,
while there is only silence on the other channel. Therefore, it is
advisable to compute the RMS of both channels separately, and then store
the maximum of the two values in a RMS list (array).

Figure 1 dipalys an example sequence of RMS data.


                                            |     |
             |     ||                   ||  ||  |||             ||  |  ||
       |  | || |||||||                 ||||||||||||||           ||| ||||||
      ||||| ||||||||||||              |||||||||||||||||         ||||||||||
      ||||||||||||||||||              |||||||||||||||||        |||||||||||
      |||||||||||||||||||            ||||||||||||||||||       ||||||||||||
     |||||||||||||||||||||          ||||||||||||||||||||      |||||||||||||
     |||||||||||||||||||||||     |||||||||||||||||||||||     ||||||||||||||
 |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

  ^                           ^                           ^                 ^
 silence                   silence                     silence         silence

  Figure 1. Example sequence of RMS data. Tracks are recognized
  immediately as they have a much larger RMS value than silence. 



BEAUTIFYING THE RMS DATA

The RMS data is rather `raw', and contains a number of `ticks'. To
beautify the data a little, a median filter can be used. This filter, that
is described in detail in the file Signproc.txt, has the property that it
filters out short disturbances. After median filtering with a length of 3,
the RMS data looks much more `neat'.


DETERMINING THE SILENCE THRESHOLD

When the median-filtered RMS data is studied more closely, it becomes
clear that during the inter-track silence, there is no silence at all. To
the contrary, the average signal power (that's the RMS) is relatively
high. That is because a gramophone record has little disturbances
everywhere, like ticks or the relatively rough surface the needle rests
upon.

However, there still is a clearly defined separation bewteen the various
tracks, at least to humans that look at the median filtered RMS data. 
Inter-track silence is characterized as such by a prolonged period of a
very low RMS value. The questions that need to be answered are therfore
how long the interval must be, and what the `very low RMS value' is. The
former may be answered immediately, as practically all records have 5, but
certainly more that 3, seconds of silence between tracks. The latter is
more complex, for it will be different for all records. Thus, a method
needs to be developed for the automatic deduction of the correct `silence
threshold' of the RMS value. 

A very interesting observation can be made if the RMS data is sorted by
value. This is depicted in figure 2.


                                                                             |
                                                                            ||
                                                                          ||||
                                                                        ||||||
                                                                    ||||||||||
                                                ||||||||||||||||||||||||||||||
                            ||||||||||||||||||||||||||||||||||||||||||||||||||
               |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
             |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
 |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

      ^                                        ^
 collected silence                           music

  Figure 2. Example of RMS data that is sorted by value.


It is clear, that all silence values are moved to the left of graph, and
all music values to the right. When we walk through the graph from left to
right, first we encounter a lot of silence. When the silence is over, the
music starts. And an interesting phenomenon occurs just there, namely that
there is a very quick transition from the silence level to the soft-music
level. Theoretically, this was to be expected, since even soft music must
be well above a certain power level, to maintain a reasonable
signal-to-noise ratio. The values that occur between silence level and
soft-music level arise from fade-in and fade-out effects. 

The middle of this sharp level-transition is easily detectable by
computing the differential for each position, as in

    diff(x[t]) = x[t+5] - x[t-5]

The `differential-length' of 11 is taken that large to enhance the desired
effect. In figure 3, an example of the differential is displayed. 


                                                                             |
                                                                            ||
              |                                                            |||
              |                                                          |||||
             |||                                                     |||||||||
             |||||                                                ||||||||||||
             ||||||   ||     ||  ||||               |||||    |||||||||||||||||
            |||||||||||||| ||||||||||||||||  |||||||||||||||||||||||||||||||||
 ||       ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
 |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

              ^
           maximum

  Figure 3. Example of differentials of the sorted RMS data.


Where the differential reaches its maximum (to be more precise, the
maximum of the first part), the slope of the sorted RMS data is maximal.
As pointed out above, this point doesn't really belong to either silence
or music. And, as could be expected, it turns out that this value is
perfectly useable as silence threshold.

Note that this threshold is decuded completely from the signal itself, and
its inherent (theoretically plausible) properties. No user-interaction is
either necessary or possible.


BETTER ESTIMATION OF STARTS AND ENDS

The first detection of inter-track silence takes place by walking through
the median filtered RMS data, searching for locations where the RMS value
is below the silence threshold for a period of minimally, say, 30
tenth-seconds. This way, the silences begin and end on the places where
the silence threshold is crossed. Usually, these positions are not quite
correct, as the fade-ins and fade-outs are not handled correctly. 

Thus problem may be addressed by finding another (lower) threshold, that
excludes fade-ins and fade-outs from the inter-track silence. Generally,
these new thresholds are different for each individual inter-track silence
on the record. So, another way of deducing the new threshold must be
developed.

A quite straightforward way of doing this, is to compute the mean of all
RMS values in the silence, and setting the threshold a few percent above
this mean. To find a correct mean, a few (e.g. 5) points at the beginning
and end of the `coarse' silence are excluded, to prevent the fade-ins and
fade-outs from pulling the mean too high. In praxis, a threshold of 8%
above the (local) mean (1,08 times the local mean) is generally found to
be acceptable.

The median-filtered RMS data is now scanned from the previously detected
start of the silence forward and from the end backward to the first and
last points the RMS drops below the new threshold. These new points are
incremented, respectively decremented, again by a fixed number of points
(e.g. 3) to account for all possible circumstances.

Note that this method requires one user-specifiable parameter, namely the
percentage of the threshold above the local mean. However, the mentioned
value of 8% should be correct for most cases. 


THE LIST OF TRACKS

If the silences are detected, there is no problem in building a list of
track starts and ends. For music is there where no silence is. But there
may be `fake' tracks at the beginning and end of the big audio file, so an
extra selection may be appied, for example discarding all tracks that are
shorter than 5 seconds.


IMPLEMENTATION IN GRAMOFILE

The method for splitting tracks as described above, has been implemented
in the GramoFile program. It is accessible with the `Determine track
separation points' in the main menu. After the selection of the audio file
that is to be splitted, a screen appears with several adjustable
parameters. The first parameter is the length (in samples) of the volume
blocks. With CD quality sampling, there are 44100 samples per second, so
one tenth second is 4410 samples. Then there is the local silence
threshold (in percent), minimal length of inter-track silence and tracks
themselves, and the number of blocks that should be added to tracks after
the fine-detection. All these parameters are described above.

Because the computation of the RMS values (signal power / volume
information) takes rather long, there is an option to save/load the RMS
data in/from a .rms file (.rms appended to the audio file name, like
side_1.wav.rms). If the .rms file does not exist, or if it is made with
another block-length as requested, it is (re-)generated. This may take
quite a while, dependant on the speed of the computer used. If the .rms
file is present and useable, it will be used right away, so the time
consuming recalculation is avoided. In that case, the audio (.wav) file
is not accessed. 

Finally, there is an option `Generate graph files'. When this option is
turned on, a few files will be created, namely: 
 - .med  : graph of the median filtered RMS data, like figure 1
 - .sor  : graph of the sorted median filtered RMS data, like figure 2
 - .dif  : graph of the differential of the sorted data, like figure 3
 - .drms : RMS filtered version of the .dif file

GramoFile actually uses a RMS filtered version of the differential to
detect the maximum slope in the sorted data.

When track detection is done, a .tracks file will be written. This file
will be used by the Signal Processing to create separate audio files for
each track mentioned in the .tracks file. The .tracks file is a .ini-style
plaintext file, and may be edited. Currently, only the Track??start end
Track??end values are used (and the Number_of_tracks of course); the
others are mainly for your own reference. The various graph files provide
much information that can be used to verify or correct the times mentioned
in the .tracks file.


RESULTS AND CONCLUSION

With the GramoFile program, several gramophone records have been recorded,
and have had their tracks split. The results were very satisfying. That is
mainly because practically all required parameters are deduced from the
audio signal itself. Some more tests will be performed, in order to
guarantee the correctness of the algorithm in most circumstances.

On the GramoFile website, http://cardit.et.tudelft.nl/~card06, a few
examples of the various graph files are published.

If you encounter a situation in which the track splitting doesn't function
properly, you can contact me about it. Please include gzip'd versions of
both the .rms and .tracks files you have problems with, and describe your
problem as clearly and completely as possible. Also, corrections,
additions, suggestions and compliments are heartily welcomed. Contact
information is in the general `README' file.