dfrft.m

阵列信号处理中常用的LS算法,用于估计目标的方位角等位置参数.

function Xp=dfrft(x, p, M, Ts)
% the realization of the FRFT's fast algorithm by Soo-Chang Pei
% x : the input sequence and its length is 2*N+1
% p : the frft's order
% M : 2*M+1 is the length of the output Xp and M>=N
% Ts : the sampling time interval

p = mod(p,4);
if p == 0
    Xp = x;
end
L = length(x);
if p == 2
    k = L : -1 : 1
    Xp = x(k);
end

alpha = p*pi/2;
Ap = sqrt((-sin(alpha )+j*cos(alpha))/(2*M+1));
Us = 2*pi*abs(sin(alpha))/(Ts*(2*M+1));
N = (L-1)/2;
t = Ts*(-N:N);
u = Us*(-M:M);
chirp_t = exp(j/2*cot(alpha)*t.^2);
chirp_u = exp(j/2*cot(alpha)*u.^2);
if sin(alpha)>0
    Xp = Ap*chirp_u.*fftshift(fft(x.*chirp_t));
else
    Xp = Ap*chirp_u.*fftshift(ifft(x.*chirp_t))*L;
end