function [ A, signal_t ] = generate_chirp_mtx(PRF, B, fs, D, gamma, sign_mid)
% Generates a chirp measurement matrix
%
% Usage: 
% [A, signal_t] = generate_chirp_mtx(PRF, B, fs, D, gamma, sign_mid)
%
% Inputs:
%   PRF:         Pulse Repetition Frequency
%   B:           Bandwidth
%   fs:          Sampling frequency
%   D:           Duty ratio
%   gamma:       Compression ratio
%   sign_mid:    if sign_mid is 0 means the initial frequency is 0,
%                if sign_mid is 1 means the initial frequency is -B/2,
%
% Outputs:
%   A:           Chirp measurement matrix
%   signal_t:    Transmitting signal


    % parameters
    if nargin < 5
        gamma = 0.5;
    end
    if nargin < 6
        sign_mid = 0;
    end
    Tr = 1 / PRF;
    Tp = Tr * D;
    K = B / Tp;
    
    % generate_signal
    N = Tr * fs;
    N_high = Tp * fs;
    N_mtx = round(N / gamma);
    
    signal_t  = zeros(1, N);
    for i = 1: N_high
        tp = i * (1 / fs) - sign_mid * N_high / fs / 2;
        signal_t(1, i) = exp(1j * 2 * pi * 0.5 * K * tp .^ 2);
    end

    signal_t_2fs  = zeros(1, N_mtx);
    for i = 1: round(N_high / gamma)
        tp = (i+1) * (1 / fs / 2) - sign_mid * N_high / fs / 2;
        signal_t_2fs(1, i) = exp(1j * pi * K * tp .^ 2);
    end
    
    % generate chirp matrix
    A = generate_matrix_by_signal2fs(transpose(signal_t_2fs));

end


%% sub-functions
% generate chirp matrix when gamma=0.5
function [ mtx ] = generate_matrix_by_signal2fs(signal)

    mtx = [];
    l = round(length(signal) / 2);
    temp1 = signal(1:2:end);
    temp2 = circshift(signal(2:2:end), 1);
    if length(temp2) ~= length(temp1)
        temp2 = [temp2; 0];
    end
    
    for i = 1:l
        t1 = circshift(temp1, i-1);
        t2 = circshift(temp2, i-1);
        if i - 1 > 0
            t1(1:i - 1,1) = 0;
        end
        if i - 1 > 0
            t2(1:i - 1,1) = 0;
        end
        mtx = [mtx,t1,t2];
    end
    
end