MATLAB taylorwin(n,nbar,sll)窗函数 c/c++实现

以下是MATLAB中taylorwin(n,nbar,sll)窗函数的实现：

function w = taylorwin(n, nbar, sll)
% TAYLORWIN  Design a Taylor window.
%   W = TAYLORWIN(N,NBAR,SLL) returns an N-point Taylor window. The
%   parameter NBAR controls the tradeoff between mainlobe width and
%   sidelobe level. The parameter SLL specifies the peak sidelobe level
%   relative to the mainlobe peak. If SLL is not specified, it defaults to
%   -30 dB.
%
%   The Taylor window is a tapered window designed to minimize the
%   approximation error in the frequency domain when an ideal filter is
%   windowed. It has a parameter NBAR that controls the width of the mainlobe
%   and the sidelobe levels. Larger values of NBAR result in narrower
%   mainlobes and higher sidelobe levels.
%
%   Example:
%     % Design a Taylor window with N=64, NBAR=5, and SLL=-40 dB.
%     w = taylorwin(64, 5, -40);
%     plot(w);
%
%   See also BARTLETT, BLACKMAN, CHEBWIN, HAMMING, HANN, KAISER, RECTWIN, TUKEYWIN.

% Check inputs.
narginchk(2, 3);
validateattributes(n, {'numeric'}, {'scalar', 'integer', 'positive'}, mfilename, 'N', 1);
validateattributes(nbar, {'numeric'}, {'scalar', 'integer', 'positive'}, mfilename, 'NBAR', 2);

if nargin < 3 || isempty(sll)
    sll = -30;
else
    validateattributes(sll, {'numeric'}, {'scalar', 'real'}, mfilename, 'SLL', 3);
end

% Calculate the coefficients of the Taylor window.
a = (n - 1) / 2;
alpha = acos(sqrt(10^(-sll/20) - 1));
beta = nbar * alpha / a;
w = zeros(1, n);
for i = 0:a
    w(i+1) = besseli(0, beta * sqrt(1 - (i/a)^2));
end
w = w / besseli(0, beta);

% Mirror the coefficients to obtain an even-length window.
if mod(n, 2) == 0
    w = [w w(end-1:-1:2)];
else
    w = [w w(end-1:-1:1)];
end
end

该函数的输入参数包括：

- `n`：窗口长度。
- `nbar`：控制主瓣宽度和旁瓣水平的参数。
- `sll`：峰值旁瓣电平相对于主瓣峰值的值。

该函数的输出参数为：窗口向量 `w`。

该函数的实现步骤如下：

1. 首先，检查输入参数，并对其进行验证。
2. 计算Taylor窗口的系数。具体而言，使用一个弧度为 $\alpha$ 的超椭圆形来逼近窗口的频率响应，其中 $\alpha$ 由用户指定，控制主瓣宽度和旁瓣水平。然后，使用贝塞尔函数计算窗口的系数。
3. 最后，将系数向量镜像以获得一个偶数长度的窗口。

希望这可以帮助您理解如何在MATLAB中实现Taylor窗口函数。