🚀 go-pugleaf

In the book `Digital Signal Processing', R.A. Roberts and C.T. Mullis have
presented an algorithm for calculating the output roundoff noise of digital
filters using a factored form of the signal flow graph. The algorithm 
essentially does the following:
	
	1. obtain primitive SFG which gives the variable classes
	2. obtain transition matrices
	3. merge the last matrix G0 with its neighbour
	4. compute the K and W matrices using the ABCD matrices
	5. compute the Ki's and Wi's corresponding to the transition matrices
	6. compute the noise gain contribution from each factor as the sum of 
	   the Ki*Wi for each non trivial row
	7. sum the noise contributions from all the factors to get the total
	   noise gain.

The trouble is that the corresponding K and W matrices are not the same
dimensions unless shifted by one relative to each other. The other problem
is that in D.M. Henrot's Ph.D. dissertation, a similar algorithm is presented.
The algorithm goes through steps 1 and 2 above. In step 3, G0 is not merged.
Step 4 is the same. The calculation of the Ki's is the same. The calculation
procedure of the Wi's is different; in particular the initialization is not the
same. Henrot scales the factors and computes the total noise gain as the sum of
all the Wi traces. The two algorithms give very different results.

I am looking to reconcile the two algorithms or to figure out the correct one
to use. It seems to me that Henrot's algorithm would be correct if he picked
out, from the factors, only those rows with non-trivial multiplier 
coefficients.

I am looking to hear from anyone who has had occassion to use either one of the
algorithms and in what perspective they view the whole process of computing the
noise in this manner.

Please reply using the e-mail address below:

		kace@enel.ucalgary.ca

Ray Kacelenga (Ph.D. candidate).