Pitch extractor apparatus and the like

A method of (and apparatus for) extracting the fundamental pitch period of a complex electrical signal V.sub.2 (t), that includes the serial steps of deriving a time varying reference signal V.sub.ref (t) from the complex electrical signal V.sub.2 (t), which reference signal V.sub.ref (t) adapts continuously (i.e., each cycle of the complex electrical signal) to peak amplitude excursions of the complex electrical signal V.sub.2 (t); sensing ascending values of the signal V.sub.2 (t) to a first point at which the maximum magnitude of the signal V.sub.2 (t) of one polarity is reached and reversal of direction thereof occurs; storing the first substantially instantaneous difference in magnitude between the complex electrical signal V.sub.2 (t) and the time varying reference V.sub.ref (t) at the point of maximum magnitude of the signal V.sub.2 (t); thereafter sensing a point at which the magnitude of the signal V.sub.2 (t) minus the first substantially instantaneous difference equals zero; thereafter sensing ascending values of the signal V.sub.2 (t) to a further point at which a maximum magnitude of the signal V.sub.2 (t) of opposite polarity to the one polarity is reached and reversal of direction thereof occurs; then storing the value of the signal V.sub.2 (t) at the further point and sensing ascending value of the signal V.sub.2 (t) to a still further point at which the substantially instantaneous value of the signal V.sub.2 (t) exceeds the stored value of the reference signal V.sub.ref (t), the pitch period being the time span between successive occurrences of the still further point.

The present invention relates to apparatus to extract the fundamental pitch 
period of a complex periodic elctrical signal and, in preferred form, to 
extract also a mesurement of the peak amplitude of the complex electrical 
signal during each pitch period. 
To place the invention in context, attention is called to U.S. Pat. Nos. 
4,108,035 (Alonso), 4,178,822 (Alonso), 4,279,185 (Alonso) and 4,345,500 
(Alonso et al), all of which disclose aspects of digital music 
synthesizers. 
Although the invention is broader in scope, it is described in greatest 
detail in the context of an electronic guitar, but the concepts can be 
employed using other string or other instruments and those concepts have 
value in other than acoustic devices. In a typical application pitch and 
amplitude of musical note from a single string of a guitar is analyzed and 
from these are extracted pitch of the fundamental of the note and 
amplitude (i.e., a signal indicative of the level of energy of the note by 
virtue of the strength at which the string was plucked and which would be 
sound level from a conventional acoustic guitar). In this specification 
the term "note" is used in its usual sense to denote a pure musical tone 
of definite pitch, i.e., C, D, E, F, G, A and B. 
As described in greater detail later, the output of the extractor is fed as 
input to a digital synthesizer of the type, for example, described in the 
above-identified patents and more particularly in an application for 
Letters Patent Ser. No. 572,625, filed Jan. 24, 1984, Alonso et al, (now 
U.S. Pat. No. 4,554,855) which discloses a multi-channel synthesizer. The 
synthesizer can use the pitch information as a basis for generating, say, 
the sound of a pipe organ, the amplitude information being used to control 
loudness of a particular note. In fact, the typical system uses isolated 
inputs from each string of a six-string guitar to provide an output. 
For the purpose of this discussion, a complex electric signal is one which 
may contain not only a fundamental periodic component, but also a 
multitude of harmonic or nonharmonic components, the amplitudes and phases 
of which need not bear a constant relationship to the amplitude and phase 
of the fundamental periodic component. The invention provides a way to 
measure both the fundamental pitch period and the amplitude of each of a 
plurality of such complex electrical signals transduced individually from 
the vibrating strings of the electronic guitar. The digitally encoded 
measurements of pitch and amplitude from these transduced signals can be 
subsequently conveyed to a computer or otherwise automated electronic 
complex wave synthesis device in order to produce musical sounds other 
than the original, yet exhibiting pitch and amplitude variations 
controlled by the pitch and amplitude characteristics of the guitar 
strings themselves. However, the concepts disclosed herein are robust 
enough to be applied to other electrical signals from other musical 
instruments or devices, not necessarily musical, the utility of which 
would benefit from application of the methods described herein. 
Later there is a brief overview of both the problems inherent in extracting 
a measure of the fundamental pitch period from a complex electrical signal 
and the limitations and complexities of traditional approaches to this 
problem. What is shown is that the present invention is both unique and 
robust in its method of operation and is an improvement in the 
state-of-the-art. Furthermore, the direct conversion of pitch measurement 
to a digital code permits a higher pitch period resolution and stability 
of measurement than can be achieved by pitch-to-voltage conversion methods 
which are prone to drift, require an aboslutely calibrated voltage to 
pitch reference, and would require an additional step of analog-to-digital 
conversion before use on a computer system. 
Accordingly it is an objective of the present invention to provide 
apparatus to extract the fundamental pitch period of a complex periodic 
electrical signal. 
Another object is to provide apparatus that can also extract peak amplitude 
of the signal for the particular pitch period. 
Still another objective is to provide apparatus which can interface with an 
acoustic synthesizer and provide input to the synthesizer which generates 
music on the basis of the pitch and amplitude information. 
These and still further objectives are addressed hereinafter. 
The foregoing objectives are achieved, generally, in a method (and 
apparatus) for extracting the fundamental pitch period of a compelx 
electrical signal V.sub.2 (t), that comprises the serial steps of deriving 
a time varying reference signal V.sub.ref (t) from the complex electrical 
signal V.sub.2 (t), which reference signal V.sub.ref (t) adapts 
continuously (i.e., each cycle of the fundamental) to peak amplitude 
excursions of the complex electrical signal V.sub.2 (t); sensing ascending 
values of the signal V.sub.2 (t) to a first point at which the maximum 
magnitude of the signal V.sub.2 (t) of one polarity is reached and 
reversal of direction thereof occurs; storing the first substantially 
instantaneous difference in magnitude between the complex electronic 
signal V.sub.2 (t) and the time varying reference V.sub.ref (t) at said 
first point; sensing a point at which the magnitude of the signal V.sub.2 
(t) minus said first substantially instantaneous difference equals zero; 
sensing ascending values of the signal V.sub.2 (t) to a further point at 
which a maximum magnitude of the signal V.sub.2 (t) of opposite polarity 
to said one polarity is reached and reversal of direction thereof occurs; 
then storing the value of the signal V.sub.2 (t) at said further point; 
and sensing ascending value of the signal V.sub.2 (t) to a still further 
point at which the substantially instantaneous value signal V.sub.2 (t) 
exceeds the stored value of the signal V.sub.2 (t) at said further point 
by an amount equal to the substantially instantaneous value of the time 
varying reference signal V.sub.ref (t), said pitch period being the time 
span between successive occurrences of said still further point.

Turning now to FIG. 1, there is shown at 101 a system embodying a guitar 
102, pitch and amplitude extractor apparatus 103 and a synthesizer 104. As 
is shown in FIG. 1, there are six signals out from the guitar to the pitch 
and amplitude apparatus 103, one from each string. Each string is 
acoustically isolated from every other string. The output of the apparatus 
103 at 2 is a digital pulse train 105 for each of the six strings, formed 
of pulses whose amplitude is V.sub.p and whose spacing, as later 
discussed, represents a measure of the fundamental pitch of the particular 
string (i.e., there are six pulse trains 105). There are also six outputs 
at 3 representing the samples peak amplitudes V.sub.4 of the six strings. 
In what follows to simplify the explanation emphasis is placed on an 
explanation with respect to a single string, but it will be understood 
that the explanation applies to the other strings and can be applied to 
other string or other instruments as well. Furthermore, while the 
discussion covers a system with outputs at both 2 and 3 representing pitch 
and amplitude, respectively, yet either can be employed in the synthesizer 
without the other. What is done here is to provide a mechanism to permit 
the guitar (or other instrument) to interface with a synthesizer to 
produce an acoustic output from the synthesizer that is controlled by the 
guitar but is not guitar (or not usually guitar) sounds. In what now 
follows, to place the invention in context, there are some observations by 
the present inventor of characteristics needed to extract pitch 
information; this is followed by a brief discussion of proposals by 
others; then a detailed explanation of the present invention follows. 
In FIG. 2A and more particularly in FIG. 2B, the envelope of a typical 
guitar output waveshape is shown rising rapidly to a maximum and decaying 
thereafter--at first rapidly and non-monotonically, then very gradually. 
The dynamic range is on the order of 50 dB. At the onset of string 
vibration (see FIG. 2C(a)), the region labeled a in FIG. 2A is greatly 
enlarged; there is a transient burst of both pitched and unpitched signal, 
a portion of which is pick noise. It is also likely that the vibration 
characteristics of the guitar string during and shortly following this 
phase are non-linear. Following the initial transient (FIGS. 2C(a)) the 
transduced wave still contains considerable harmonic content exhibited by 
multiple local maxima/minima (FIG. 2C(b), 2C(c), 2C(d)), multiple 
zero-crossings, and generally asymmetry with respect to its own mean 
value. The lower case letters a, b, c and d in FIG. 2A represent the 
instants of time of the representations in FIGS. 2C(a), 2C(b), 2C(c) and 
2C(d), respectively. As the vibration of the string damps out (FIG. 
2C(d)), the signal contains a diminishing harmonic content and is of 
considerably smaller amplitude. In the limit the signal approaches a pure 
fundamental wave. The exact harmonic and decay characteristics of a given 
note are dependent on such diverse factors as picking force, physical and 
mechanical characteristics of both the guitar and guitar strings, and 
location of the fretboard at which note is played. 
Several conclusions may be drawn from FIG. 2 which have general 
implications for any method proposed for extracting the fundamental pitch 
period from such a complex electrical signal: (1) methods based solely on 
zero-crossing detection without drastic preconditioning of the signal are 
clearly inadequate and will yield erroneous measurements (likewise, 
acceptable methods must be immune to the occurrence of multiple adjacent 
local maxima/minima); (2) accurate detection of pitch period requires a 
method employing a form of continuous adaptation to either spectral and/or 
amplitude features of the complex signal (such adaptation should take 
place on a period-by-period basis to provide tracking of short duration 
spectral or amplitude changes); (3) the detection method must accommodate 
at least two octave ranges of fundamental pitch period (the usable range 
of a guitar string) and must reliably extract pitch in the presence of a 
50 dB range of a signal amplitude; and (4) a suitable pitch extraction 
method must exhibit negligible detection delay and yield a measurement 
within one period of the complex signal fundamental. 
With regard to conventional methods, there now follows a discussion of 
pitch period extraction methods which rely primarily on zero-crossing 
detection preceeded by a high degree of spectral lowpass filtering to 
suppress as much as possible all harmonics above the lowest fundamental 
frequency of interest. The rationale of these methods is that 
zero-crossing detection is a reliable pitch period measurement technique 
if only the fundamental component of the original signal remains after 
such filtering. Furthermore, a pulse train derived by such a method and 
having the fundamental as its repetition rate can then be converted by one 
of many frequency-to-voltage conversion mechanisms into a voltage 
proportional to pitch period. Of course, such a system requires an 
absolutely calibrated reference function which relates output voltage to 
input frequency. 
If the prerequisite lowpass filtering is to be performed by a fixed filter, 
the typical filter for this purpose must be at least 4th order, and must 
be well into lowpass rolloff at the frequency to which the open guitar 
string is normally tuned. The ultimate attenuation rate of such a filter 
is 24 dB/octave of frequency. Thus, over the two octave pitch range of a 
guitar string, the transduced signal may undergo as much as 48 dB (256 to 
1) attenuation before pitch extraction can be effected. However, the 
dynamic range requirement of an additionally 50 dB (300 to 1) of amplitude 
variation must additionally accommodated if pitch tracking is to be 
obtained over the entire duration of a picked note allowed to decay 
without muting. A dynamic range requirement of 98 dB is unacceptably 
stringent; thus high pre-amplification followed by compression or limiting 
is typically employed to reduce the dynamic range requirement of the pitch 
detector and to prevent overloading of the detector by input pitches near 
the open string fundamental. If some form of automatic gain control is 
attempted, the dynamic control characteristics must be carefully chosen so 
as not to alter the original signal waveform. Finally, it is apparent that 
if multiple zero-crossings in the input waveform are amplified and clipped 
to the same level as the maxima of the waveform, the resulting signal may 
exhibit a harmonic power density greater than that of the original input 
signal, which makes subsequent suppressions of these components even more 
difficult. 
One method employed to circumvent some of these difficulties uses input 
amplitude compression followed by a filter dynamically controlled such 
that its cutoff frequency and attenuation characteristics are made 
commensurate with the harmonic suppression requirements for a specific 
note played on a specific guitar string. The method makes use of the 
observation that as notes are played successively higher on the guitar 
fretboard, their waveforms exhibit successively less harmonic content, 
presumably because the shorter string length permits few modes of 
vibration. The filter cutoff frequency is dynamically positioned by 
voltage obtained from the final pitch-to-voltage converter in the system. 
There are several problems with that method not the least of which is that 
its rationale works for the guitar but little else- In the specific case 
of the guitar, an absolute voltage reference corresponding to a specific 
pitch is necessary to estimate the fret at which the note was played 
(which also pre-supposes normal tuning of the instrument). Until the 
filter control loop has settled, the filter cutoff frequency will change 
during the measurement response to a transient pitch condition. To prevent 
this behavior, such systems are typically overdamped which introduces a 
slower than desirable response time to pitch fluctuations in the input 
signal. Finally, the filters and their responses must differ for each 
string, hence complicating the design and calibration of such a system. 
The present invention utilizes no automatic gain control, no compression or 
limiting, no dynamic filtering, and requires minimal pre-conditioning to 
achieve accurate pitch detection. Furthermore, no absolute references are 
utilized, as all measurements are made on a basis relative to the signal 
being processed. The invention adapts continuously to both the amplitude 
and the waveform of the complex signal, thus accommodating both 
time-varying spectral content and amplitude. The method has been designed 
to be specifically immune to multiple zero-crossings of the signal within 
a pitch period. The method also exhibits excellent immunity to multiple 
local maxima/minima of the wave cycle. 
A suitably pre-amplified complex electrical signal V.sub.1 (t) in FIG. 3 
(which is one signal of the six signals at 7 in FIG. 1) is provided as 
input to a preconditioning filter 4 the purpose of which is to suppress to 
a known degree the harmonic frequencies above the lowest fundamental of 
the guitar string and provide a complex electrical signal output V.sub.2 
(t). The filter 4 in practice is a simple two-pole lowpass filter with 
cutoff frequencies of 0.8fo and 1.25fo, where fo is the lowest open guitar 
string fundamental. It will be noted that over a two octave fundamental 
range the maximum attenuation is approximately 24 dB. The pre-conditioned 
output signal V.sub.2 (t) is simultaneously applied to two paths 5 and 6, 
one being to a peak envelope detector 8 the other being to a pitch 
extractor 9. The peak envelope detector 8 is a peak detector exhibiting a 
fast attack and exponentially decaying release, the decay being controlled 
by a time constant T, whose magnitude is chosen to be short enough to 
permit the decay response to follow typically encountered downward 
amplitude variations of the guitar string. The output labeled 10 of the 
peak detector is a signal V.sub.3 (t) and is reconnected as an input to an 
attenuator 11 having an attenuation (typically V.sub.ref (t) is 0.8 to 0.9 
V.sub.3 (t)) to derive a time-varying reference signal V.sub.ref (t) at 12 
from the complex electrical signal V.sub.2 (t), which reference signal 
V.sub.ref (t) adapts continuously (i.e., from period to period of the 
fundamental) to peak amplitude excursions of the complex electrical signal 
V.sub.2 (t). The output signal V.sub.3 (t) of the peak detector 8 is also 
applied to a sample-hold device 13 whose output at 3 is a constant 
amplitude sample voltage V.sub. 4 which is updated each new extracted 
pitch period. (The voltage V.sub.4 is a piece-wise constant representative 
of the signal V.sub.3 (t).) FIG. 4 shows the signals V.sub.2 (t), V.sub.3 
(t), V.sub.4, and V.sub.ref (t). It will be noted (1) that the V.sub.ref 
(t) adapts continually to the peak magnitude variations of the signal 
V.sub.2 (t) and (2) that zero-crossings have no effect whatever on the 
voltage signal V.sub.ref (t). 
Turning to FIG. 5 a capacitor C' has a voltage drop .DELTA.V across its 
terminals; the voltage drop .DELTA.V is the stored potential difference 
(polarity convention as shown) at any instant as a result of prior charge 
transfers. One side of the capacitor C' is connected through a resistance 
R to the preconditioned signal V.sub.2 (t). The purpose of the resistance 
R is (1) to isolate the driving source V.sub.2 (t) from the capacitance of 
C' and (2) to prevent transient conditions of the signal V.sub.sw (t) on 
the other side of the capacitance C' from reaching V.sub.2 (t). The other 
side of the capacitance C', by virtue of circuit operation, is (1) 
connected by a switch S1 to zero volts (ground) or (2) connected by a 
switch S2 to the potential V.sub.ref (t) or (3) left unconnected to any 
source potential and only to an impedance so large it is an effective open 
circuit. 
Two voltage comparison devices or comparators C1 and C2, exhibiting very 
large input impedance, each sense the potential V.sub.sw (t), and output 
signals Vc1 and Vc2 as a result of comparisons of V.sub.sw (t) versus 
their reference potentials zero and V.sub.ref (t), respectively. The 
comparator C1, by its output Vc1, also controls the state of the switch 
S1. The comparator C2, by its output Vc2, controls the state of the switch 
S2. While both S1 and S2 may be simultaneously open, their closures are 
mutually exclusive. Outputs Vc1 and Vc2 are conveyed to a trigger device 
15, the output of which is a series of short pulses, the spacing of which 
is the desired fundamental pitch period of V.sub.2 (t). Also, it will be 
noted that with the polarity convention of .DELTA.V as shown, V.sub.sw 
(t)=V.sub.2 (t)-.DELTA.V. The comparison devices have the properties and 
logic now discussed. 
Comparator 1: When V.sub.sw (t) crosses zero volts in a negative going 
direction, Vc1 switches to zero volts and the switch S1 is closed. When 
V.sub.sw (t) reverses direction, Vc1 switches to -VLIM, and the switch S1 
opens. Comparator 2: when V.sub.sw (t) crosses V.sub.ref (t) (which is 
derived from V.sub.2 (t), as above noted) in a positive going direction, 
Vc2 switches to V.sub.ref (t), and the switch S2 closes. When V.sub.sw (t) 
reverses direction, Vc2 switches to +VLIM, and the switch S2 opens. The 
potentials of +VLIM and -VLIM are the respective limiting positive and 
negative output excursions of the comparison device circuitry. The trigger 
device 15 can change its internal state only when either of the following 
conditions occur: (States can only occur alternately. 
(*1) If Vc2 exceeds V.sub.ref (t) while Vc1=-VLIM, then a short duration 
pulse of amplitude +V.sub.p issues at the conductor 2 (i.e., one of the 
pulses 105A . . . ) and the output at 2 returns to 0. 
(*2) If Vc1=0 while Vc2=+VLIM, then the voltage on the conductor 2 remains 
=0 but the trigger device 15 is enabled to produce a pulse (+V.sub.p) when 
condition *1 above reoccurs. Each time state transition (*1) above occurs 
the trigger device 15 issues a short pulse V.sub.p of approximately one 
microsecond duration. 
In the example to follow, it will be shown that the output pitch pulses of 
amplitude V.sub.p can occur only once per fundamental pitch period. Thus, 
the interpulse time interval, as encoded by any of several known digital 
counting techniques or devices in the synthesizer 104 in FIG. 1, is a 
direct measure of the fundamental pitch period of the complex electrical 
signal. A suitably delayed replica of these "pitch" pulses is used to 
operate the sampling device 13 so as to acquire a new value of peak 
envelope magnitude V.sub.4 each new pitch period. The delay of the 
sampling pulse is necessary to ensure sampling V.sub.3 (t) just after the 
new peak value has been acquired by the peak detector. 
Before proceeding further it must be noted that the system is an adaptive 
time-varying system. Thus, to explain its operation over a single period 
of the input signal one must admit the initial conditions from a previous 
time period, specifically the stored potential .DELTA.V on capacitor C', 
the value of which will generally vary with time from one period to the 
next. 
Referring to both FIG. 6 and the arrangement of FIG. 5, the explanation 
begins at point A of FIG. 6; the initial condition on the capacitor C' is 
.DELTA.V=-V.sup.-.sub.2max, the potential corresponding to the maximal 
negative peak excursion of voltage V.sub.2 (t) during the prior pitch 
interval. Also at point A, the switches S1 and S2 are open, Vc2=+VLIM, 
Vc1=-VLIM and there is a 0-volt ouptut at 2 in FIGS. 3 and 5. Use will 
also be made of the relation V.sub.sw (t) =V.sub.2 (t) -.DELTA.V. 
Beginning at point A with the voltage V.sub.2 (t) increasing in a positive 
direction, a value of voltage V.sub.2 (t) will be reached, say, at a point 
B, such that the voltage V.sub.sw (t) will exceed the voltage V.sub.ref 
(t). This occurs when V.sub.sw (t)=V.sub.ref (t)=V.sub.2 (t)-.DELTA.V or 
when V.sub.2 (t)=V.sub.ref (t)-V.sup.-.sub.2max. At point B, the output 
Vc2 of comparator Vc2 of comparator 2 switches to V.sub.ref (t) and the 
switch S2 closes thus holding V.sub.sw (t)=V.sub.ref (t). The trigger 
device 15 makes a state transition and issues a short pulse of amplitude 
V.sub.p at its output 2 in FIG. 4. It will be noted that until V.sub.2 (t) 
(also V.sub.sw (t)) reverses direction, V.sub.sw (t) will increase with 
V.sub.ref (t) during the peak detector update of the voltage V.sub.ref 
(t). When the voltage V.sub.2 (t) reaches its maximum and reverses 
direction at point C, Vc2 switches to +VLIM and S2 opens leaving on the 
capacitance C' a stored potential difference .DELTA.V=V.sup.+.sub.2max 
-V.sub.ref (t). At some time later, V.sub.2 (t) will have decreased to a 
value such that V.sub.sw (t)=0 (point D). This occurs when V.sub.2 (t) 
=.DELTA.V or when V.sub.2 (t)=V.sup.+.sub.2max -V.sub.ref (t), which 
indicates that V.sub.2 (t) has diminished from its own maximum positive 
excursion by an amount equal to V.sub.ref (t). This occurs prior to but 
close to V.sub.2 (t) crossing zero because V.sub.ref (t) is a large 
fraction (typically 0.9, but it can be about 0.8 to 0.9) of 
V.sup.+.sub.2max. This is the condition for comparator C1 to switch Vc1 to 
zero volts, and for the switch S1 to close thus forcing V.sub.sw (t)=0 
while V.sub.2 (t) continues in a negative direction. This is also a 
necessary internal condition (trigger state *2; see above) for the trigger 
device 15 to enable itself to issue a pulse output, but not sufficient to 
generate such a pulse. The multiple zero-crossings at points E and F have 
no effect on the trigger output. Each time V.sub.sw (t) crosses zero in a 
negative going direction, the capacitance C' charges to a potential 
.DELTA.V=-V.sup.-.sub.2max which is held every time the voltage V.sub.2 
(t) reverses direction from a negative peak excursion. 
A trigger pulse output at 2 can only occur if after crossing zero in a 
negative direction, V.sub.sw (t) exceeds V.sub.ref (t) in a positive going 
direction. This will occur when V.sub.sw (t)=V.sub.2 
(t)-.DELTA.V=V.sub.ref (t) or when V.sub.2 (t)=-V.sup.-.sub.2max 
+V.sub.ref (t). This states that to cause another trigger output pitch 
pulse at 2, the voltage V.sub.2 (t) must not only cross zero once in a 
negative direction but must also make a positive excursion equal to 
V.sub.ref (t) above its own negative maximal excursion (point G ). It will 
be noted that V.sub.ref (t) has decayed with time to a value slightly 
lower than that which is acquired at point C but not substantially 
different from that which it has at the point B. The final transition of 
the pitch extractor cycle (and the start of the next period) is denoted by 
point H which is where the example began and where the next pitch pulse of 
amplitude V.sub.p is. The time span between points B and H is the pitch 
period of the signal V.sub.2 (t). 
To recapitulate briefly some of the foregoing, the time varying reference 
signal V.sub.ref (t), as shown in FIG. 3, is derived from the complex 
electrical signal V.sub.2 (t) through the peak envelope detector 8 whose 
output V.sub.3 (t) fed through the attenuator 11 to provide the signal 
V.sub.ref (t) at 12 as input to the pitch extractor 9; hence the signal 
V.sub.ref (t) adapts or adjusts continuously, i.e. once each period of the 
fundamental, to amplitude excursions of the signal V.sub.2 (t). The 
sensing mechanism by which the signal V.sub.2 (t) is sensed includes the 
comparators C1 and C2 which interact with the switches S1 and S2 to sense 
values of the signal V.sub.sw (t) in terms of its relationship to 
V.sub.ref (t). In the sensing cycle before discussed, a first point on the 
siganl waveform V.sub.2 (t) in FIG. 6 is reached at which the maximum 
magnitude of the signal V.sub.2 (t) of one polarity (i.e., the point C of 
+ polarity) occurs; at that juncture the capacitance C' stores the 
substantially instantaneous difference in magnitude between the complex 
electrical signal V.sub.2 (t) (at the point C) and the time varying 
reference signal V.sub.ref (t). The sensing mechanism thereafter senses a 
point (i.e., the point D) at which the magnitude of the signal V.sub.2 (t) 
minus the before-mentioned substantially instantaneous difference equals 
zero (i.e., the point D in FIG. 6). The sensing mechanism then senses 
ascending values of the signal V.sub.2 (t) to a further point G at which 
the maximum magnitude of the signal V.sub.2 (t) of opposite polarity 
(i.e., --polarity in FIG. 6) to the polarity at point C is reached and 
reversal of direction occurs. The value of the signal V.sub.2 (t) at the 
point G is then stored on the capacitance C. The sensing mechanism then 
senses ascending values of the signal V.sub.2 (t) (from the point G) to a 
still further point H at which the substantially instantaneous value of 
the signal V.sub.2 (t) exceeds the stored value of the signal V.sub.2 (t) 
at the further point G by an amount equal to the substantially 
instantaneous value of the time-varying reference signal V.sub.ref (t). 
The pitch period of the signal V.sub.2 (t) is the span between successive 
occurrences of the still further point, that is, the pitch period is the 
time span between the points B and H in FIG. 6 and is given as output by 
the time-spaced short pulses of the pulse train 105. 
To clarify the operation of the device on a continually time varying basis, 
it should be realized that for a constant input signal the points B and H 
occur at identical points on the wave signal, that is the signal V.sub.2 
(t). More important is that changes in amplitude of the signal V.sub.2 (t) 
occur slowly with respect to the cycle duration. In the case of the guitar 
signal, the pitch extractor is able to make adaptive changes by updating 
V.sub.ref (t) each new cycle. Although the exact points at which pulses 
are output on the waveform may gradually shift with harmonic content, the 
time interval between pitch pulses is equal to the fundamental pitch 
period. It should be noted also that the pitch pulses of magnitude V.sub.p 
are of very short duration with respect to the pitch period itself. For 
example, a pulse duration of one microsecond used for pitch periods of one 
millisecond (minimum) to tens of milliseconds (maximum) yields a very 
small uncertainty of period measurement due to finite pitch pulse width. 
The device 103 is described above with reference to a guitar, but the 
concepts have use with other instruments (e.g., violin, cello, flute) as 
well. 
Further modifications of the invention herein disclosed will occur to 
persons skilled in the art and all such modifications are deemed to be 
within the scope of the invention as defined by the appended claims.