adesign wrote on Jul 26th, 2007, 8:40pm:If quantization noise is E(z), the noise transfer function is L(z) and output after the quantizer is V(z) then equation (1) must be
V(z) = F(z).U(z) + L(z).E(z)
This equation does not apply to the linearized model I´m assuming (please see attached figure). This model is actually the same one that is usually assumed as you'll see below: A SD modulator
output signal is usually expressed - by means of a linear modeled - as a function of two different transfer function transfer functions: one affecting only the signal (STF) and the other one only affecting the noise (NTF)
However, expression (1) y[z]=F[z] x U[z] + L[z] x V[z] is just describing the
quantizer input as a function of the input U[z] and V[z]. (recall L[z] is the
loop filter transfer function and NOT the NTF. It is on the loop filter that we apply the delay≠0 for realizability).
If you replace y[z] in equation (1) with equation (3) - which is valid by definition of linearized quantization error - you get:
V[z]=F[z]/(1-L[z]) × U[z] + 1/(1-L[z]) × E[z].
Therefore STF [z] = F[z]/(1-L[z]) and NTF[z] = 1/(1-L[z]) = H[z] (5)
Another direct proof for the condition is just taking (5) and setting L[∞]=0 → H[∞]=1 or h(0)=1.