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Description  |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to a method for pitch recognition, in particular for
musical instruments which are excited by plucking or striking, in the case
of which method the interval between zero crossings of a signal waveform
of an audio signal is used as a measure for the period length for the
audio signal.
Although, in the time period when synthetic audio or tone production
started, reference was made to keyboard musical instruments in which each
key was assigned a clearly defined tone, efforts have for some time also
been directed at using other musical instruments for synthetic tone or
sound production. An exemplary application of this is a guitar, in which a
tensioned string is caused to oscillate by plucking or striking, either
directly using the fingers or using a plectrum. Different pitches can be
produced, as is known, in the case of a guitar by varying the effective
oscillation length of the string. Although the oscillation of the string
in the case of a classic, acoustic guitar was made directly audible by the
resonance of the guitar body, in the case of synthetic tone production it
is necessary to determine the oscillation frequency of the excited string.
Once the pitch has been determined, a corresponding signal can be produced
and further processed. The problem arises not only in the case of guitars,
but also in the case of other string instruments which are plucked or
struck, for example a harp, bass, zither or the like. Pitch recognition
may occasionally be of interest even in the case of drums. In principle,
such methods can, however, also be used for all other audio signals, for
example the human voice, which can be further processed in a so-called
"voice follower". However, for simplicity, the following description is
provided on the basis of pitch recognition in the case of a guitar.
2. Description of Related Art
U.S. Pat. No. 5,014,589 describes such a method for pitch recognition, in
which the zero crossings of the audio signal are determined. The interval
between two zero crossings in the same direction is considered as a
measure for the period length. The inverse value of the period length
corresponds to the frequency. The problem in such pitch recognition is
that, in addition to the zero crossings which determine the period length,
zero crossings of the audio signal which are caused, for example, by
harmonics can also occur within one period. In the case of the known
method, it is therefore necessary to determine not only the points in time
of the zero crossings but also the amplitude maxima of the signal
waveform. A type of envelope curve is produced in this case, which is also
called an "envelope follower". In consequence, additional criteria are
obtained in order to assess whether a zero crossing does or does not
represent the boundary of a period. A pitch signal is produced when two
successive period lengths do not differ by more than a specific amount.
The signal processing in such methods is increasingly carried out
digitally. In the case of the known method, considerable computation power
is necessary. If one keeps sight of the fact that this computation power
must be kept available not only for one string but for a plurality of
strings, it quickly becomes clear that an economical solution cannot be
practically implemented with the processors available at the moment.
SUMMARY OF THE INVENTION
The invention is thus based on the object of achieving reliable pitch
recognition in a simple manner.
This object is achieved in the case of a method of the type mentioned
initially by the magnitude of the gradient of the signal waveform in each
case being determined in the region of its zero crossing, and by the
magnitude of the gradient being used as an assessment criterion for the
selection of the zero crossings to be evaluated.
The required computation power can be drastically reduced, to be precise to
less than a tenth as a rule, compared to the method which is known from
U.S. Pat. No. 5,014,589. Specifically, the audio signal, which is present
in digitalized form from samples, need be evaluated only in the region of
its zero crossings. The zero crossings can easily be determined by
comparison of the polarity of two successive samples. All the other
samples can be left out of the evaluation. A few values in the region of
the zero crossings can be considered in addition, if required, in order to
improve the accuracy. The gradient of the zero crossings can likewise be
determined relatively easily. If one presupposes a constant sampling
frequency, it is in principle sufficient to determine the interval between
the two samples before and after the zero crossing. It is now possible to
define that the signal waveform of the audio signal is at its steepest at
the zero crossings which bound one period. Therefore, all that need be
considered is the steepest zero crossings of the same polarity. The
interval between these zero crossings is then the period length. The
information which is necessary to assess the question as to whether a zero
crossing is or is not significant for the period length is thus obtained
directly from the signal waveform at the zero crossing. It is thus
possible to reduce the necessary computation power very considerably
because only those samples which are located at the zero crossing or in
its immediate vicinity need be included at all in the calculation. The use
of the zero crossings in which the signal waveform is at its steepest,
that is to say has the greatest gradient, furthermore has the advantage
that the influences of disturbances are at their lowest here. If, in the
simplest case, such a disturbance is regarded as an offset (shift in the
signal waveform by a constant value in the positive or negative
direction), a shift in the point at which the signal waveform crosses the
zero axis in the case of a zero crossing with a flat signal waveform
results which is larger than if a zero crossing with a steep signal
waveform were considered. The accuracy of pitch recognition is thus
improved by the limitation to such zero crossings.
Since the information about the audio signal waveform is no longer
required, apart from a relatively narrow band around the zero crossings,
it is also possible to manage with relative coarse resolution, that is to
say a low sampling rate. The human ear has relatively fine resolution in
its own frequency bands. The pitch information should thus be achieved
with an accuracy of approximately 1 cent, that is to say 1/100th of a
half-tone. In the case of a guitar, whose frequency range extends from
about 80 Hz to 1 kHz, a sampling rate of 1.7 MHz would be necessary for
this purpose. The computation complexity for this would be enormous. Using
the method according to the invention, it is possible to manage with a far
smaller number of samples. In this case, sampling rates of about 10 kHz
are adequate.
In order to assess the gradient value which will be used for evaluation, a
maximum value of the gradient is preferably determined, a decay function
is produced on the basis of this maximum value, and only those zero
crossings whose gradient magnitude exceeds the value of the decay function
at this point in time are subjected to further processing. On the one
hand, the decay function filters out all the zero crossings whose gradient
is too small. In addition, no computation power is required for these zero
crossings during the further processing. The exclusion of zero crossings
which are not significant thus occurs relatively early. In addition, in
contrast to a fixed threshold value, the decay function has the advantage
that account is taken of the dynamic range of a real musical instrument.
The gradient is also governed, inter alia, by the volume with which the
instrument is played. Furthermore "spikes" can occur in the gradient at
the moment when a string is struck, which spikes are in principle not
significant. The decay function ensures that, despite matching to the
dynamic range of the instrument, exclusion of those zero crossings which
have an excessively low gradient is possible, but on the other hand also
ensures that the spikes mentioned above do not block the method in the
long term.
It is in this case particularly preferred for the values of the decay
function to be reduced only when a zero crossing occurs. This saves
computation power, but on the other hand also ensures that the decay
function is reduced step by step.
It is also preferred for the values of the decay function to be multiplied
by a constant factor on every reduction. This results in an exponential
decay behavior being achieved, which initially leads to a relatively
drastic reduction and later to a moderate reduction. Spikes are therefore
eliminated more quickly.
The remaining gradient values are preferably subjected at least a second
time, in the same way, to the comparison with a decaying function. An
improved evaluation capability is obtained in this way. As a result of the
natural non-uniform nature of an audio signal, in particular in the region
of its start when produced by striking, it is possible for a relatively
large scatter to occur in the gradient values. If the threshold value is
too high, significant zero crossings are not recognized although they
should be recognized. If the signal has a large number of zero crossings,
the decay function quickly decays to an excessively small value, so that a
zero crossing is incorrectly classified as significant as result of a
comparison of the gradient with the decay function. The second (or
further) "filtering" on the one hand excludes those values which are still
incorrect or unnecessary, but on the other hand reliably retains all the
significant values. As a rule, one second comparison is sufficient in
order actually to determine the steepest zero crossings, which are used
for the determination of the period length.
The gradient at the zero crossing is preferably interpolated from a
plurality of gradient values of the audio signal in the vicinity of the
zero crossing. While one gradient determination from two values is
sufficient when the basis is an essentially linear signal waveform in the
region of the zero crossing, errors result in the case of this simple
gradient determination if the signal waveform in this region has a
relatively high degree of curvature. In this case, improved accuracy can
be achieved by using further samples from the vicinity of the zero
crossing.
A zero crossing is advantageously rejected as being insignificant if its
gradient does not achieve a predetermined proportion of the magnitude of
the gradient of a subsequent zero crossing. In this way, spikes, that is
to say values which do not fit the normal signal waveform, can also be
eliminated easily and quickly.
The point in time of a significant zero crossing is preferably determined
by interpolation. However, such an interpolation is necessary only when a
significant zero crossing has actually been found. Computation power is
thus required only when a useful result can actually be expected.
Successive time intervals between zero crossings are advantageously
compared with one another, and a pitch is determined only in the event of
discrepancies below a predetermined limit. This is advantageous in
particular if the pitches and the associated period lengths are stored in
a table. As long as the period length does not change, the pitch also does
not change. It is thus unnecessary to start a new computation or search
operation in order to determine information, since the information is
already present. This also saves considerable computation time.
In a particularly preferred refinement, a fixed sampling frequency is used
for the audio signal and an initial value for the pitch is produced only
at the end of time interval having a predetermined constant length, by
averaging over the determined pitch values in the time interval. Such a
time interval can have, for example, a length of 8 to 15 ms. A fixed
sampling frequency leads to more samples per period in the case of deeper
tones and to fewer samples per period in the case of higher tones. The
relative accuracy for pitch determination in the case of higher tones
would thus accordingly and intrinsically be reduced. This disadvantage is
compensated for by the averaging in the fixed time interval. The relative
accuracy in the case of one individual period is admittedly somewhat
lower. However, the fact that a greater number of periods are accommodated
in a fixed time interval in the case of higher tones results in the
averaging once again giving a better approximation to the actual pitch.
It is in this case particularly advantageous for the initial value to be
passed on via an interface only when it differs by more than a
predetermined amount from the last initial value passed on. Such an
interface can be, for example, a "musical instrument digital interface"
(MIDI). Such an interface is also still in widespread use for other forms
of signal transmission. By limiting the transmitted data to changes, the
interface is kept free.
The audio signal is preferably low-pass-filtered before the pitch
recognition. Such low-pass filtering should be carried out very
cautiously, for example using a two-pole IIR filter, in order to avoid
filtering out too much information. As a guidance figure, one can assume
that not more than ten zero crossings should be present per period after
filtering.
Zero crossings are advantageously evaluated both in the positive direction
and in the negative direction. Admittedly, more computation power is
required for this than in the case of the limitation to one polarity. On
the other hand, additional information is obtained, which contributes to
an improvement in the accuracy.
It is particularly preferred in this case for a zero crossing not to be
evaluated if its gradient is less than half the gradient of the preceding
zero crossing of opposite polarity. In this case, use of this zero
crossing to determine the period length is dispensed with. However, since,
on the other hand, the period length is available via the interval between
the zero crossings of the other polarity, this information loss can be
coped with.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention is described in the following text with reference to a
preferred exemplary embodiment in conjunction with the drawing, in which:
FIG. 1 shows a typical audio signal waveform with zero crossings,
FIG. 2 shows a schematic illustration of method steps for pitch
recognition,
FIG. 3 shows a detail from a signal waveform in the vicinity of a zero
point, and
FIG. 4 shows a block diagram of a tone pitch recognition apparatus
according to the invention.
DESCRIPTION OF PREFERRED EMBODIMENTS
FIG. 1 shows the waveform of a typical audio signal in which a plurality of
zero crossings are present in each period T. The illustrated signal has
already passed through low-pass filtering, a simple, two-pole IIR filter
having been used. This filter removes disturbing harmonics. Such a signal
is digitalized for further processing, that is to say amplitude values A0,
A1, A2, A3 . . . are determined at various points in time P0, P1, P2, P3,
. . . (FIG. 3) and are converted into a digital value. The values can be
stored in a shift register or FIFO buffer in order to keep a stock of more
than two values.
The zero crossings of the signal waveform illustrated in FIG. 1 can easily
be determined by comparing two successive samples with one another. If
both have the same polarity, for example in the case of the value pairs
A0, A1 and A2, A3, then there is no zero crossing between them. Such
values can be left out if one ignores exceptions in the immediate vicinity
of such a zero crossing. The period length P results from the interval
between two such zero crossings, that is to say X21P--X11P or X22P--Xl2P
or X21N--X11N or X22N--X12N. Although all the options for period length
determination are possible, the most accurate result is obtained if the
value pairs X21P, X11P or X21N, X11N are used because the signal waveform
has the greatest gradient at the zero crossing at these points. A
disturbance has the least effect here, that is to say the offset of the
zero crossing becomes smaller, the steeper the signal waveform is at the
zero crossing.
A relatively simple method is used for determination of the steepest zero
crossings, and is explained in the following text with reference to FIG.
2.
FIG. 2a shows a typical signal waveform having a plurality of zero
crossings per period. The magnitude of the gradient of the signal waveform
at each zero crossing is also shown. FIG. 2b shows the positive gradient
values. The gradient values were in this case simply determined by
subtraction between the two samples in each case adjacent to the
respective zero crossing. Since the sampling rate in the present case is
constant at 10 kHz, the difference is sufficient to be able to make a
statement about the gradient.
It is possible to see just by comparison between FIGS. 2a and 2b that a
large amount of information is no longer required for further evaluation.
Thus, no computation power is any longer required for this amount of
information either.
FIG. 2c shows the gradient values from FIG. 2b. In addition, the values of
a decay function are illustrated by dashed lines, this decay function
being formed as follows:
Let D be the value of the gradient, ENV1 the value of the decay function
and F1 a constant decay factor, for example 11/16.
At the first zero crossing, ENV1 is set to the value D.
At the next zero crossing, the decay function is changed:
ENV1=F1.times.ENV1
If, now:
D>ENV1
then
ENV1=D
is set.
This case is shown for the second zero crossing. If D<ENV1, then this is a
zero crossing having a small gradient, which can be regarded to be
non-significant. This point is removed from the further evaluation.
As can be seen from FIG. 2d, only the first, second, fifth, sixth, ninth,
tenth etc. zero crossings still remain after this first filtering. All the
other zero crossings have already been eliminated.
In the same manner, the remaining zero crossings can be subjected to
further filtering (FIG. 2e), ENV2 being the values of the second decay
function and F2 the decay factor:
ENV2=F2.times.ENV2
This zero crossing is evaluated further only if D>ENV2. If this is not the
case, the corresponding zero crossing is rejected as not being
significant.
It can be seen in FIG. 2f that only the steepest zero crossings are left
after this filtering. The interval between these zero crossings is the
period length T which, in turn, is a measure of the pitch.
In order to improve the accuracy, further points can be used in the
vicinity of the zero crossing, for example no longer just the two adjacent
points P1, P2 but also the points P0 and P3 before them and after them.
If the following notation is used:
D10=A1-A0
D21=A2-A1
D32=A3-A2
dx=A2/(A2-A1) (Distance between the zero crossing and the point P2)
then the gradient D becomes:
D=(D21+dx.times.D10+(1-dx).times.D32)/2
If one wishes to avoid a floating point operation, such an interpolation
can also be carried out using an integer operation if 16-times
"oversampling" is simulated. The division by two can also be avoided if
one is not interested in the absolute gradient but only in the ratio
between the individual gradient values. In this case, one can set:
dx=(A2<<4)/(A2-A1)
D=(dx.times.(A2-A0)+(16-dx).times.(A3-A1)
The symbol "<<" in this case means a "shift left" operation in the binary
domain. The illustrated shift by four bits to the left thus results in
multiplication by 16. In this case, the point in time of the zero crossing
becomes
T=(IX<<4).times.dx,
where IX is the sampling index of the point P2. The difference between two
successive zero crossing points in time determined in this way then
produces the period length.
If the difference between two successive period lengths is now less then a
predetermined value, for example 40 to 60 cents, then it can be assumed
that the determined period length actually corresponds to the period
length of the oscillation. In this case, the period length is formed by
the arithmetic mean of the two successive period lengths, in order to
eliminate small inaccuracies as well.
A further error correction possibility is created by also comparing
successive values with one another backwards. For example, a sequence of
gradient values 50, 35, 27 is sensible. This corresponds to a rapidly
decaying signal. In contrast, a sequence of 50, 35, 48 is relatively
improbable. In this case, the second value (35) would not fit in with the
signal. The associated zero crossing should thus be removed. This can be
implemented relatively easily by comparing the preceding value with a
predetermined proportion of the current value. If F3 is a constant value
<1, for example 3/4, the zero crossing associated with the gradient D
(n-1) is eliminated if
F3.times.D(n)>D(n-1)
The absolute accuracy of the described method is .+-.1/32 T, where T is the
sampling period. The relative accuracy is governed by the frequency. It is
greater for low frequencies and is thus sufficient to produce a signal
with the initially mentioned inaccuracy of 1 cent (1/100th half tone).
However, the relative error increases at higher frequencies, so that there
is a risk here of incorrect pitch information being produced. This error
is overcome by no longer producing a pitch signal at the end of each
period, but at the end of a predetermined "time slot" with a constant
length of, for example, 8 to 15 ms. Faster provision of the pitch
information is unnecessary anyway, because the subsequent processing takes
a corresponding period of time. Fewer periods are obtained at low
frequencies in such a time slot, but they have been determined with high
relative accuracy, or a large number of periods are obtained in the case
of high pitches, which have been determined with lower relative accuracy.
If the period lengths in the respective time slot are now averaged, the
inaccuracies can be overcome again to such an extent that they are no
longer found to be unpleasant by the human ear.
The period length and thus the pitch information are obtained both from
zero crossings with a positive gradient and from zero crossings with a
negative gradient. The situation occasionally arises where the magnitudes
of these gradients differ very greatly from one another. If one amount is
more than twice as great as the other, the zero crossing having the
smaller gradient is not considered.
It is also possible to define a minimum gradient which must be present in
order that a zero crossing is intended to be evaluated at all during the
pitch determination. This minimum gradient can also be changed dynamically
by using half the maximum gradient of the preceding time slot as the
minimum gradient for the next time slot.
FIG. 4 shows a schematic diagram of a tone pitch recognition apparatus
according to the invention. A waveform signal received from the pickup of
a string instrument, such as a guitar, is fed as an audio input signal to
A/D-converter 1, where it is sampled at a constant sampling rate and
converted into a digital signal. The digital output signal is filtered in
low-pass filter 2 in order to remove disturbing harmonics. The output of
low-pass filter 2, which may be represented by waveform as shown in FIG.
2A, is then input to a computation unit 3 consisting of a zero crossing
detector 3a and a steepness calculator 3b where it is subject to zero
crossing detection in zero crossing detector 3a. The zero crossing
detector determines the timings of the zero crossings according to one of
the methods described above. The steepness calculator 3b calculates for
each zero crossing a steepness value indicating the steepness of the
waveform in each zero crossing. Several methods of how to calculate the
steepness have been disclosed above. The most simple way to calculate the
steepness is to calculate the absolute value of the difference of two
sampling values in the immediate neighbourhood of a respective zero
crossing.
The zero crossing detector 3a and the steepness calculator 3b reduce the
amount of data received from low-pass filter 2 drastically. The output of
the computation unit 3 consists of a sequence of pairs of data, the first
data of each pair indicating the timing position of the zero crossing, the
second data of each pair indicating the steepness of the waveform in the
point of the respective zero crossing.
In order to eliminate those zero crossings having a relatively low
steepness the output of the computation unit 3 is subject to discriminator
4. This discriminator 4 eliminates all those zero crossings whose
steepness is below a certain threshold. The threshold ENV1 is generated by
generator 5 according to the method described above. Shortly stated the
threshold ENV1 is reduced by a constant factor F1 at each zero crossing
and it is raised to assume the steepness value of the zero crossing,
provided that the steepness value is higher than the previous threshold.
Thus the discriminator 4 eliminates all zero crossings having a relatively
low steepness so that the amount of data is reduced to the data as
exemplified in FIG. 2D. A second filtering of this kind by discriminator 6
and generator 7 finally leads to a set of data as exemplified by FIG. 2F.
The remaining zero crossings at the output of discriminator 6, which are
shown in FIG. 2F correspond to the basic zero crossings which define the
period length of the musical tone. The calculator 8 determines the time
interval between at least two of the remaining zero crossings and
calculates its inverse value, which corresponds directly to the basic
frequency of the musical tone, whose waveform is to be analyzed. The
frequency signal can be easily converted into a tone pitch signal which is
output by calculator 8.
Having thus described the principles of the invention together with several
illustrative embodiments thereof, it is to be understood that although
specific terms are employed, they are used in a generic and descriptive
sense, and not for purposes of limitation, the scope of the invention
being set forth in the following claims:
* * * * *
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