frequency tracking

[Scott Bernardi]

I was just looking at another method of isolating the fundamental in pitch
to voltage converters in Bernie Hutchins Electronotes - I believe it was EN
134 and EN 138. It uses a Hilbert Transformer, which can be approximated by
a 90 degree Phase Delay Network. The shifted and unshifted signals are both
squared (signal going into both inputs of a multiplier), then summed. The
effect is that energy from the sidebands are reflected into the
fundamental, thus strengthening the fundamental and weakening the
harmonics, but in a frequency independent way. 


+----------+      
|          |0  +-----+      +-------+
|          +---+ x^2 +------+       |
|  90 deg  |   +-----+      |       |
|   PDN    |                |  (+)  +----->
|          |90 +-----+      |       |
|          +---+ x^2 +------+       |
+----------+   +-----+      +-------+


The theory of operation was a bit hairy, but the circuitry was actually
quite simple - four opamps to makle a 90 deg PDN, a couple multipliers
(Bernie used OTA multipliers), and an opamp for the summer.
Bernie had a Cornell grad student do the circuitry and measurements for his
Master's Thesis. They were using lab oscillators to simulate "musical"
signals with strong higher harmonics (and therefore "extra" zero
crossings). But the results did weaken the harmonics enough to remove the
spurious zero crossings, resulting in a signal suitable for converting into
a pulse train with a simple comparator.
My Electronotes subscription ended at Vol. 13 and I never saw whether he
developed the idea into a practical pitch follower. Has anybody else had
some experience with the idea? It's on my "things to try someday" list.


At 08:06 AM 6/9/98 +0200, you wrote:

>> this isn't for any particular project (yet), just a point of interest for 
>All pitch2volt converters I have seen so far convert the incomming
>signal into a pulse train. The "magic" is to isolate the fundamental
>which may be very weak for some instruments. 
>There are two basic methods:
>
>a) Time Domain
>There is for example a moog patent (ibm patent server)
>that decribes how to use an arrangement of  peak detectors in order to
>isolate the fundamental in the hope that the waveform maximum and minimum
will indicate
>the fundamental frequency (which may work with rather soft sounding
>input, but certainly not with, say a guitar signal as input).
>
>b) Frequency Domain
>Another one by Bode which proposes  a multiple bandpass filter bank
>with amplitude measurement and square wave converter for each channel,
>so that the lowest channel (fundamental) will suppress all higher
>channel output, which seems to me quite reasonable. And moreover it
>allows for buzz/hiss detection know by vocoders, ie. you can hope to
>detect noise at the input in order to shut down the audio output of the
>whole system (because in this cause the frequency measurement will be
>bogus) or to sample and hold the last meaningfull result. (by the way,
>the EMS5000 vocoder has a pitch extractor and beeing a vocoder, the
>filter bank is allready there... , so it is very likely that the
>EMS5000 uses this spectral measurement method, could somebody confirm
>?)
>
>m.c.
>
>------------------------------------------------------------------------
>m.c. has made it finally:  3 CDs out now; 72 min. minimum; "1"
>(1994-1995),"2" (95-96),"three" (96-97); experimental stuff; mostly
>Eimert/Stockhausen style; but also modern popular style
>
>
>
>
--------------------------------------
Scott Bernardi
voice: 415-538-0439 (note new number)
fax:   415-904-8375
scott.bernardi at fritz.com