function [C, B, A, rM] = dir2fs_r(h, r);

	% DIRECT-form to Frequency Sampling form conversion

	% ----------------------------------------------------------

	% [C, B, A, rM] = dir2fs_r(h, r)

	%  C = Row vector containing gains for parallel sections

	%  B = matrix containing numerator coefficients arranged in rows

	%  A = matrix containing denominator coefficients arranged in rows

	%  h = impulse response vector of an FIR filter

	% rM = r^M factor needed in the feedforward loop

    %  r = radius of the circle over which samples are taken (r<1)

	M = length(h); H = fft(h, M);

	magH = abs(H); phaH = angle(H)';

	% check even or odd M

	if (M == 2*floor(M/2))

		L = M/2-1;          % M is even

		%A1 = [1, -1, 0; 1, 1, 0];

		A1 = [1, -r, 0; 1, r, 0];

		C1 = [real(H(1)), real(H(L+2))];

	else

		L = (M-1)/2;        % M is odd

		%A1 = [1, -1, 0];

		A1 = [1, -r, 0];

		C1 = [real(H(1))];

	end

	k = [1:L]';

    % initialize B and A arrays

    B = zeros(L, 2); A = ones(L, 3);

    % compute denominator coefficients

    A(1:L, 2) = -2*r*cos(2*pi*k/M);

    A(1:L, 3) = r*r;

    A = [A;A1];

    % compute numerator coefficients

    B(1:L,1) = cos(phaH(2:L+1));

    B(1:L,2) = -r*cos(phaH(2:L+1) - (2*pi*k/M));

    % compute gain coefficients

    C = [2*magH(2:L+1), C1]';

    rM = r^M;

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

%%            Output Info about this m-file

fprintf('\n***********************************************************\n');

fprintf('        <DSP using MATLAB> Problem 6.20 \n\n');

banner();

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

%format long;

format short;

fprintf('\n FIR filter DIRECT-form:     \n');

h = [1, 2, 3, 2, 1]/9; 

b = h

a = 1.0

fprintf('\nConvert DIRECT-form to PARALLEL-form :     \n');

[C, Bp, Ap] = dir2par(b, a)

if size(C)==0

  C = 0;

end

fprintf('\nConvert DIRECT-form to CASCADE-form :     \n');

[b0, Bc, Ac] = dir2cas(b, a) 

fprintf('\nConvert TF-form to SOS-form :     \n');

[sos, g] = tf2sos(b, a)

% ----------------------------------------------------------

% NOTE: linear-phase can not use LATTICE-form

% ----------------------------------------------------------

fprintf('\nConvert DIRECT-form to All-Zero LATTICE-form :     \n');

[Klc] = dir2latc(b) 

fprintf('\nConvert DIRECT-form to FREQUENCY-SAMPLE-form 1 :     \n');

[Cfs, Bfs, Afs] = dir2fs(b) 

fprintf('\nConvert DIRECT-form to FREQUENCY-SAMPLE-form 2 :     \n');

r = 0.9;

[Cfs_r, Bfs_r, Afs_r, rM] = dir2fs_r(b, r) 

% -----------------------------------------

%     START check

% -----------------------------------------

n = [0:7];

delta = impseq(0, 0, 7)

%format long

format  short

hcas = casfiltr(b0, Bc, Ac, delta)

hltc = latcfilt(Klc, delta)

%hladr = ladrfilt(Klr, Clr, delta)

hdir = filter(b, a, delta)

% -------------------------------------------

%       END check

% -------------------------------------------