I assume "reflection coeffcient" is no different from an ordinary FIR coefficient.
Filter is y = x * t1 + x(n-1) * t2 + x(n-2) * t3+ x(n-3) * t4
then Y(z) = t1 + t2*z^-1 + t3*z^-2 + t4*z^-3 + ..
Now filter changes to
y1 = x * t1 + x(n-1) * 0 + x(n-2) * t2 + x(n-3) * 0 + x(n-4) * t3 + x(n-5) * 0 + x(n-6) * t4...
then Y1(z) = t1 + t2*z^-2 + t3*z^-4 + t4*z^-6 +...
great idea blux but is the reflection coefficient really not different from the FIR coefficients.
there is a formula relating them called "step up recursion"
If the reflection coefficient is zero, does this mean the coefficients will be zero