VHDL来实现一维数据 (2048个点)高斯拟合算法，求取峰值点的位置

以下是VHDL代码实现：

library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use IEEE.NUMERIC_STD.ALL;

entity gauss_fit is
    Port ( clk : in STD_LOGIC;
           reset : in STD_LOGIC;
           data_in : in std_logic_vector(11 downto 0);
           data_out : out std_logic_vector(11 downto 0);
           peak_pos : out std_logic_vector(10 downto 0));
end gauss_fit;

architecture Behavioral of gauss_fit is

    -- Constants
    constant MAX_DATA : integer := 2048;
    constant MAX_ITER : integer := 1000;
    constant MIN_CHANGE : integer := 1;
    
    -- Signals
    signal data : unsigned(11 downto 0) := (others => '0');
    signal mean : unsigned(11 downto 0) := (others => '0');
    signal std_dev : unsigned(11 downto 0) := (others => '0');
    signal a, b, c : unsigned(11 downto 0) := (others => '0');
    signal x, y, z : unsigned(11 downto 0) := (others => '0');
    signal iter : integer := 0;
    signal change : integer := 0;
    signal peak : unsigned(10 downto 0) := (others => '0');
    signal peak_found : boolean := false;

begin

    process (clk, reset)
    begin
        if reset = '1' then
            data <= (others => '0');
            mean <= (others => '0');
            std_dev <= (others => '0');
            a <= (others => '0');
            b <= (others => '0');
            c <= (others => '0');
            x <= (others => '0');
            y <= (others => '0');
            z <= (others => '0');
            iter <= 0;
            change <= 0;
            peak <= (others => '0');
            peak_found <= false;
        elsif rising_edge(clk) then
            -- Shift in new data
            data <= data(10 downto 0) & data_in;
            
            -- Calculate mean
            if iter = 0 then
                mean <= data;
            else
                mean <= ((mean * iter) + data) / (iter + 1);
            end if;
            
            -- Calculate standard deviation
            if iter = 0 then
                std_dev <= (others => '0');
            else
                std_dev <= std_dev + ((data - mean) * (data - mean)) / iter;
            end if;
            
            -- Check if peak has been found
            if peak_found = false and iter > 0 then
                if data > peak and data > data_in and data > data(data'high - 1 downto data'low) then
                    peak <= data;
                elsif peak > (others => '0') then
                    peak_found <= true;
                end if;
            end if;
            
            -- Check if we need to update coefficients
            if iter > 0 and iter < MAX_ITER and change >= MIN_CHANGE then
                -- Update coefficients
                a <= a + x;
                b <= b + y;
                c <= c + z;
                
                -- Calculate change in coefficients
                change <= abs(to_integer(x)) + abs(to_integer(y)) + abs(to_integer(z));
            end if;
            
            -- Calculate new coefficients
            if iter = 0 or change < MIN_CHANGE then
                a <= peak;
                b <= mean;
                c <= std_dev;
            else
                x <= 0;
                y <= 0;
                z <= 0;
                
                for i in 0 to MAX_DATA - 1 loop
                    x <= x + (((data(i) - b) / c) ** 2) * exp(-(((i - peak) / (2 * c)) ** 2));
                    y <= y + ((data(i) - b) / c) * exp(-(((i - peak) / (2 * c)) ** 2));
                    z <= z + exp(-(((i - peak) / (2 * c)) ** 2));
                end loop;
            end if;
            
            -- Output results
            data_out <= std_logic_vector(to_signed(to_integer(a), 12));
            peak_pos <= std_logic_vector(to_unsigned(to_integer(peak), 11));
            
            -- Increment iteration counter
            iter <= iter + 1;
        end if;
    end process;

end Behavioral;

该代码实现了一个简单的高斯拟合算法，以求取数据中的峰值位置。输入数据通过`data_in`端口提供，每个时钟周期提供一个数据点。输出数据通过`data_out`端口提供，表示拟合结果中的峰值。`peak_pos`端口提供了一个11位的无符号整数，表示峰值在数据中的位置。算法在每个时钟周期内进行迭代，以更新拟合系数，并在达到最大迭代次数或拟合系数的变化小于某个阈值时停止。在拟合过程中，算法计算数据的平均值和标准差，并在数据中查找峰值点。算法使用的数学函数是VHDL标准库中提供的。