function [Achirp,AchirpOut,H,scale] = fracF_init(a)
%#codegen
%
% fracF_init
%
% Precompute FrFT coefficients for DPW processing.
%
% INPUT:
%   a  - FrFT order (single)
%
% OUTPUTS:
%   Achirp     [1024 x 1]
%   AchirpOut  [512  x 1]
%   H          [2048 x 1]
%   scale      scalar

N    = 1024;

pi_s = single(pi);

phi = a * (pi_s/2);

tan_half_phi = tan(phi/2);
sin_phi      = sin(phi);
cos_phi      = cos(phi);

csc_phi = 1/sin_phi;
cot_phi = cos_phi/sin_phi;

twoDelta = 2*sqrt(single(N)/2);

%% Chirp A

n = single((-N/2:N/2-1).') / twoDelta;

Achirp = exp(-1j*pi_s*(n.^2)*tan_half_phi);

%% Chirp B

m = single((-N:N-1).') / twoDelta;

Bchirp = exp(1j*pi_s*csc_phi*(m.^2));

%% FFT of Chirp B

H = fft(Bchirp);

%% Output chirp

AchirpOut = Achirp(1:2:end);

%% Scale factor

scale = sqrt(1 - 1j*cot_phi) / twoDelta;

%% Force single precision complex

Achirp    = complex(single(real(Achirp)), ...
                    single(imag(Achirp)));

AchirpOut = complex(single(real(AchirpOut)), ...
                    single(imag(AchirpOut)));

H         = complex(single(real(H)), ...
                    single(imag(H)));

scale     = complex(single(real(scale)), ...
                    single(imag(scale)));

end