function r = rayleigh(doppler,rate,N,M)      fs = 2 * doppler ;      LCM = lcm(fs,rate) ;      
      kInt = LCM / fs ;      kDec = LCM / rate ;      df = fs / N ;       f = -doppler + df : df : doppler - df ;      S = sqrt(1.5 ./ (pi * doppler * sqrt(1 - (f / doppler).^2))) ;      sNeg = 2*S(1)-S(2) ;      S = [ sNeg S ] ;       I = randn(1,N/2-1) + j * randn(1,N/2-1) ;       Q = randn(1,N/2-1) + j * randn(1,N/2-1) ;       I = [ randn conj(I(N/2-1:-1:1)) randn I ] ;       Q = [ randn conj(Q(N/2-1:-1:1)) randn Q ] ;      filt_I = S .* I ;      filt_Q = S .* Q ;      filt_I = [ filt_I(N/2+1:N) filt_I(1:N/2) ] ;       filt_Q = [ filt_Q(N/2+1:N) filt_Q(1:N/2) ] ;       x = ifft(filt_I) ;      y = ifft(filt_Q) ;      x = real(x) ;      y = real(y) ;      r = x + j * y ;      nr = max(9,ceil(M*kDec/kInt)) ;      r = r(1:nr) ;      r = interp(r,kInt) ;      r = decimate(r,kDec) ;      r = r(1:M) ;      r = r / sqrt(mean(r .* conj(r))) ;