function n = rebound(x,N)
%n = rebound(x,N)
%   Finds noise margins of e.g. a clock signal
%   due to ringing on the inside of the signal.
%   The inside is important because this ringing 
%   may cause false triggering of logic device.
% Inputs:
%   'x' the periodic signal of at least 1.5 cycles.
%   'N' the period of 'x' in samples.
% Output:
%   'n' the vector containing the location in 'x'
%       of the peak(s) of ringing in the first 
%       half-cycle.  The size of 'n' is the number
%       of inflection points minus 2 present in the half
%       cycle.
% Example: (5 inflection points, length(n)=2)
%    t = [0.5:0.01:2];
%    a = 1-0.8*sin(t*5)-0.1*sin(3*t*5)-0.25*cos(5*t*5);
%    n = rebound(a,126);
%    plot(t,a,'b',t(n),a(n),'r*'); grid on;
%
% Now includes needed "findpeak.m" function in M-file.
% Last edited by Colin Joye, 7/20/03
x1 = x/max(abs(x)); % normalize.
xm = x-mean([max(x1) min(x1)]); % remove offset.
xm = xm/max(abs(xm)); % normalize.
xd = abs(diff(xm)); 
nh = findpeak(xd,ceil(N/2));
if length(nh)<2 | max(nh)>length(xd),
   nh=[1 2];
end
xN = xd(nh(1):nh(2)); % one cycle.
ff = diff(xN)>0;
nx = find(diff(ff)>0);
n  = nx(2:2:(end-1)) + nh(1);


%---------------------------
function k = findpeak(x,w)
%k = findpeak(x,w) finds local periodic maxima
%    in signal 'x' by finding the location of the
%    peak every 'w' samples.
%  Input:
%    'x' the signal vector.
%    'w' is the window width in samples.
%        length(x) must greater than or equal to 'w'
%  Outputs:
%    'k' the locations in vector 'x' of local maxima. 
%
% Last edited by Colin Joye, 6/19/2002
n=0;f=0;
k=find(max(x(1:w))==x(1:w));
k=k(1);
while (w+n)<=length(x),
  n=n+w;
  r=(1+n):(w+n);
  if r(end)>length(x),
     r=(1+n):length(x);
  end
  if length(r)>0,
    f=n+find(max(x(r))==x(r));
    k=[k f(1)];
  end
end
% ----- End findpeak.m ---------- 


% ----- End rebound.m ----------