Explain this DSP Notation

Question

I'm trying to implement this extenstion of the strobe algorithm using twisted Karplus-Strong cards, but I don’t understand the notation that was used there, Maybe it will take years of study, but maybe it’s not, maybe you can tell me.

I think the equations below are in the frequency domain or something like that. Starting with the first equation, H _p (z), filter the bottom filter of the direction filter of choice. For one direction you use p = 0, for the other - 0.9. This reduces to 1 in the first case, or 0.1 / (1 - 0.9 z ^-1 ) in the second.

alt text http://www.dsprelated.com/josimages/pasp/img902.png

Now I feel that this could mean, in terms of coding, something with respect to:

H_p(float* input, int time) {
  if (downpick) {
    return input[time];
  } else {
    return some_function_of(input[t], input[t-1]);
  }
}

Can someone tell me? Or is it useless and do I really need the whole DSP background to implement this? Once I was a mathematician ... but this is not my domain.

Answer 1

Thus, z ^-1 means a single delay.

Take H _p = (1-p) / (1-pz ^-1 ).

If we follow the convention "x" for input and "y" for output, the transfer function is H = y / x (= output / input)

then we get y / x = (1-p) / (1-pz ^-1 )

or (1-p) x = (1-pz ^-1 ) y

(1-p) x [n] = y [n] - py [n-1]

: y [n] = py [n-1] + (1-p) x [n]

C

y += (1-p)*(x-y);

- , , "y" . :

y_delayed_1 = y;
y = p*y_delayed_1 + (1-p)*x;

, , , H _{& Beta;}= 1-z ^{- 1} 1-z ^-2. ( N?)

, , .

H = H0 * (1 + az ^-1 + bz ^-2 + cz ^-3...)/(1+ RZ ¹ + SZ ^-2 + TZ ^-3...)

, , H = y/x, ,

H0 * (1 + az ^-1 + bz ^-2 + cz ^-3...) * x = (1+ rz ^-1 + sz ^-2 + tz ^-3...) * y

"y" , "y" .

( a, b, c ..) , , .