# Maple program for the parameterization of a
# length N scaling filter in terms of angles.

with(linalg):           # load linear algebra package

N := 8;			# filter length
K := (N-2)/2;		# number of angles (N = 2K+2)
R := t -> matrix(2,2, [cos(t), sin(t), -sin(t), cos(t)]);
Lambda := matrix(2,2,[1, 0, 0, 1/z]);

Hp := R(t0):		# construct polyphase matrix
i := 'i':
for i from 1 to K do
        Hp := evalm(R(t.i) &* Lambda &* Hp):
od:
H00 := expand(Hp[1,1]):	# extract H00 and H01
H01 := expand(Hp[1,2]):	# expand polynomials

# display coefficients as functions of angles
lprint(t.K = Pi/4 - sum('t.i','i'=0..(K-1)));
i := 'i':
n := 1:
for i from 0 to K do
	lprint(h[n] = coeff(H00,z,-i));
	n := n + 1:
        lprint(h[n] = coeff(H01,z,-i));
	n := n + 1:
od: