function [ykhat,n]=make_ykhat(wk,nd,phi1);
%%%  This function makes the 512-pt ykhat[n] pulse required by Exercise 6.5 
%%%  in Computer Explorations in Signals & Systems by Buck/Daniel/Singer
%%%
%%%  This function uses the same notation as Problem 5.57 in the textbook
%%%  by Oppenheim/Schafer/Buck.  That is, nd and phi1 are the quantities
%%%  defined in part b of that problem.  
%%%
%%%  Function call:  [ykhat,n]=make_ykhat(wk,nd,phi1);
%%%  
%%%  Output is ykhat=x[n-nd]cos(wk*n-phi1)
%%%
%%%  Variables:     
%%%      wk = pulse center frequency (rad/sec)
%%%      nd = restricted to integer
%%%    phi1 = phase shift
%%%   ykhat = output pulse vector
%%%       n = vector of time indices
%%%
%%%  Note:  this function will have wrap-around problems if nd approaches
%%%         512 points, which is the overall length of the pulse
%%%         (including zero-padding).  
%%%

p=[hamming(75); zeros(437,1)];
n=(0:511)';

xkshift=circshift(p,nd);                % use circshift to shift envelope
ykhat=xkshift.*cos(wk*n-phi1);

return