Thanks for recent reply. I am not a PRO in signal processing and appreciate those careful comments. First, this project is for understanding FFT and to get a practical view of what convolution is, in common language(!).
For a complete module, an accurate set of 9 adjacent musical notes can be generated/sensed (synchronously) using integer clock dividers of 17 or nearby. Those being: divide by (22, 21, 20, 19, 18, 17, 16, 15 and 14). In this first module, it is 8800 hz divided by 22 (and then divided by 2) for detecting 200 hz (I believe near 'G' note) as the lowest in the run of detection points. Engineering often calls for knowing what kind of sensitivity 'band' is in operation (using a rectangular sample window of 114 microseconds duration).
The notes corresponding are: G, G#, A, A#, B, C, C#, D, and D# at (200hz, 210hz, 220hz, 232hz, 244hz, 259hz, 275 hz, 293hz, and 314hz).
Now,for the CD4017 sequential outputs, channel T-20 for example, has a Modulo-20 counter: lets assume the channel T20 counter is in 'LOCK' mode (lock with the audio input). This simply means the counter Q0 output clocking state has the best phase for detection, (and thus the sample/hold circuit uses Q0 as a gate trigger.) The 20 counts represent a full circle of analog phase (360 degrees), so a superimposed 'SINE WAVE' actually stretches along with 5 counts for every 90 degrees of waveform.
Thus the expected sine function is 90 degrees phase-shifted, starting at minus 5 counts, (that is count 15 for the 220 hz channel T20), going to the SINE peak at count=0 (phase = 90 degrees) and then going thru 180 degrees of phase, at count=5. The shifted SINE function ends (360 degrees) at count=15.
Readers should start to see: the counter plays a simple dual role, both in synchronous input actions and in synchronous output actions. Pulses at Q15 and at Q5 are brought out, representing 'zero-crossing' times (zero and 180 degrees).
It is a textbook matter from there, to generate an appropriate analog SINE wave: first, the Q5 and Q15 outputs connect to clock a flip-flop (CD4013). Now you have a square wave, 50/50 duty cycle. Referring to the work of Forrest M. Mimms III , page 80 shows a function generator circuit. (see Mini-Notebook Series Volume I). A square wave is converted to triangular, then filtered to make an approximate SINE wave output.
It is perhaps helpful to push the 'pulse stream' for earlier output, using Q4 and Q14, as there are analog delays in converting towards analog SINE output. (Maybe does not matter, tho).
Now, for the T16 channel (a multiple of 4) each 90 degrees of analog phase travel is represented by 4 counts, and so the pulse outputs will be Q4 and Q12, neatly. However, what about T19, or T17 ? WELL... never stopped me before: Channel 19 simply 'pretends' to be approximately an even divisor: Thus the pulse outputs, for channel 19, are placed at Q5 and Q15, and resulting waveform is not entirely symmetrical, at about 55/45 duty cyle.
Astute readers might note: it is not trivial to 'chain' together two CD-4017 decade counter, as both IC's will have 'live' outputs. One method uses a 'RANGE' high / low flip-flop to switch out Q0 from the 'high' counter IC (and suppress counting). That way a RESET can clear both counter IC's and clear the 'RANGE' flip-flop.
The modulo-20 counters can simply roll-over, to zero. The others (MOD19, 18, 17, 16, 15, and 14) use the classic method, by connecting 'last count+1' to the IC RESET.
ERRATIA: I will discuss in another post, thanks for your time!