小波变换行变换verilog

以下是一个基于行变换的小波变换的Verilog代码示例：

module wavelet_transform(input clk, input rst, input signed [7:0] in_data [0:7], output signed [7:0] out_data [0:7]);

parameter N = 8; // 数据点个数
parameter LOG_N = 3; // 数据点个数的对数

// 小波变换矩阵和逆矩阵
reg signed [7:0] wavelet_matrix [0:N-1][0:N-1];
reg signed [7:0] inverse_wavelet_matrix [0:N-1][0:N-1];

// 小波变换的核心部分
always @(posedge clk, posedge rst) begin
    if (rst) begin
        // 初始化小波变换矩阵和逆矩阵
        // 这里使用了 Daubechies-4 小波变换
        wavelet_matrix[0][0] = 0.482962913145; wavelet_matrix[0][1] = 0.836516303738; wavelet_matrix[0][2] = 0.224143868042; wavelet_matrix[0][3] = -0.129409522551; wavelet_matrix[0][4] = 0; wavelet_matrix[0][5] = 0; wavelet_matrix[0][6] = 0; wavelet_matrix[0][7] = 0;
        wavelet_matrix[1][0] = -0.129409522551; wavelet_matrix[1][1] = 0.224143868042; wavelet_matrix[1][2] = 0.836516303738; wavelet_matrix[1][3] = 0.482962913145; wavelet_matrix[1][4] = 0; wavelet_matrix[1][5] = 0; wavelet_matrix[1][6] = 0; wavelet_matrix[1][7] = 0;
        wavelet_matrix[2][0] = 0; wavelet_matrix[2][1] = 0; wavelet_matrix[2][2] = -0.482962913145; wavelet_matrix[2][3] = 0.836516303738; wavelet_matrix[2][4] = -0.224143868042; wavelet_matrix[2][5] = -0.129409522551; wavelet_matrix[2][6] = 0; wavelet_matrix[2][7] = 0;
        wavelet_matrix[3][0] = 0; wavelet_matrix[3][1] = 0; wavelet_matrix[3][2] = 0.129409522551; wavelet_matrix[3][3] = -0.224143868042; wavelet_matrix[3][4] = 0.836516303738; wavelet_matrix[3][5] = -0.482962913145; wavelet_matrix[3][6] = 0; wavelet_matrix[3][7] = 0;
        wavelet_matrix[4][0] = 0; wavelet_matrix[4][1] = 0; wavelet_matrix[4][2] = 0; wavelet_matrix[4][3] = 0; wavelet_matrix[4][4] = 0.482962913145; wavelet_matrix[4][5] = 0.836516303738; wavelet_matrix[4][6] = 0.224143868042; wavelet_matrix[4][7] = -0.129409522551;
        wavelet_matrix[5][0] = 0; wavelet_matrix[5][1] = 0; wavelet_matrix[5][2] = 0; wavelet_matrix[5][3] = 0; wavelet_matrix[5][4] = -0.129409522551; wavelet_matrix[5][5] = 0.224143868042; wavelet_matrix[5][6] = 0.836516303738; wavelet_matrix[5][7] = 0.482962913145;
        wavelet_matrix[6][0] = 0; wavelet_matrix[6][1] = 0; wavelet_matrix[6][2] = 0; wavelet_matrix[6][3] = 0; wavelet_matrix[6][4] = 0; wavelet_matrix[6][5] = 0; wavelet_matrix[6][6] = 0.482962913145; wavelet_matrix[6][7] = -0.836516303738;
        wavelet_matrix[7][0] = 0; wavelet_matrix[7][1] = 0; wavelet_matrix[7][2] = 0; wavelet_matrix[7][3] = 0; wavelet_matrix[7][4] = 0; wavelet_matrix[7][5] = 0; wavelet_matrix[7][6] = 0.129409522551; wavelet_matrix[7][7] = 0.224143868042;

        inverse_wavelet_matrix[0][0] = 0.482962913145; inverse_wavelet_matrix[0][1] = -0.836516303738; inverse_wavelet_matrix[0][2] = 0.224143868042; inverse_wavelet_matrix[0][3] = 0.129409522551; inverse_wavelet_matrix[0][4] = 0; inverse_wavelet_matrix[0][5] = 0; inverse_wavelet_matrix[0][6] = 0; inverse_wavelet_matrix[0][7] = 0;
        inverse_wavelet_matrix[1][0] = 0.129409522551; inverse_wavelet_matrix[1][1] = 0.224143868042; inverse_wavelet_matrix[1][2] = -0.836516303738; inverse_wavelet_matrix[1][3] = 0.482962913145; inverse_wavelet_matrix[1][4] = 0; inverse_wavelet_matrix[1][5] = 0; inverse_wavelet_matrix[1][6] = 0; inverse_wavelet_matrix[1][7] = 0;
        inverse_wavelet_matrix[2][0] = 0; inverse_wavelet_matrix[2][1] = 0; inverse_wavelet_matrix[2][2] = 0.482962913145; inverse_wavelet_matrix[2][3] = 0.836516303738; inverse_wavelet_matrix[2][4] = 0.224143868042; inverse_wavelet_matrix[2][5] = -0.129409522551; inverse_wavelet_matrix[2][6] = 0; inverse_wavelet_matrix[2][7] = 0;
        inverse_wavelet_matrix[3][0] = 0; inverse_wavelet_matrix[3][1] = 0; inverse_wavelet_matrix[3][2] = 0.129409522551; inverse_wavelet_matrix[3][3] = -0.224143868042; inverse_wavelet_matrix[3][4] = 0.836516303738; inverse_wavelet_matrix[3][5] = 0.482962913145; inverse_wavelet_matrix[3][6] = 0; inverse_wavelet_matrix[3][7] = 0;
        inverse_wavelet_matrix[4][0] = 0; inverse_wavelet_matrix[4][1] = 0; inverse_wavelet_matrix[4][2] = 0; inverse_wavelet_matrix[4][3] = 0; inverse_wavelet_matrix[4][4] = 0.482962913145; inverse_wavelet_matrix[4][5] = -0.836516303738; inverse_wavelet_matrix[4][6] = 0.224143868042; inverse_wavelet_matrix[4][7] = 0.129409522551;
        inverse_wavelet_matrix[5][0] = 0; inverse_wavelet_matrix[5][1] = 0; inverse_wavelet_matrix[5][2] = 0; inverse_wavelet_matrix[5][3] = 0; inverse_wavelet_matrix[5][4] = 0.129409522551; inverse_wavelet_matrix[5][5] = 0.224143868042; inverse_wavelet_matrix[5][6] = -0.836516303738; inverse_wavelet_matrix[5][7] = 0.482962913145;
        inverse_wavelet_matrix[6][0] = 0; inverse_wavelet_matrix[6][1] = 0; inverse_wavelet_matrix[6][2] = 0; inverse_wavelet_matrix[6][3] = 0; inverse_wavelet_matrix[6][4] = 0; inverse_wavelet_matrix[6][5] = 0; inverse_wavelet_matrix[6][6] = 0.482962913145; inverse_wavelet_matrix[6][7] = 0.836516303738;
        inverse_wavelet_matrix[7][0] = 0; inverse_wavelet_matrix[7][1] = 0; inverse_wavelet_matrix[7][2] = 0; inverse_wavelet_matrix[7][3] = 0; inverse_wavelet_matrix[7][4] = 0; inverse_wavelet_matrix[7][5] = 0; inverse_wavelet_matrix[7][6] = 0.129409522551; inverse_wavelet_matrix[7][7] = -0.224143868042;
    end else begin
        // 行变换
        for (int i = 0; i < N; i = i + 2) begin
            for (int j = 0; j < N; j = j + 1) begin
                out_data[i][j] = (in_data[i][j] * wavelet_matrix[0][0]) + (in_data[i+1][j] * wavelet_matrix[0][1]) + (in_data[i][j+1] * wavelet_matrix[0][2]) + (in_data[i+1][j+1] * wavelet_matrix[0][3]);
                out_data[i+1][j] = (in_data[i][j] * wavelet_matrix[1][0]) + (in_data[i+1][j] * wavelet_matrix[1][1]) + (in_data[i][j+1] * wavelet_matrix[1][2]) + (in_data[i+1][j+1] * wavelet_matrix[1][3]);
                out_data[i][j+1] = (in_data[i][j] * wavelet_matrix[2][0]) + (in_data[i+1][j] * wavelet_matrix[2][1]) + (in_data[i][j+1] * wavelet_matrix[2][2]) + (in_data[i+1][j+1] * wavelet_matrix[2][3]);
                out_data[i+1][j+1] = (in_data[i][j] * wavelet_matrix[3][0]) + (in_data[i+1][j] * wavelet_matrix[3][1]) + (in_data[i][j+1] * wavelet_matrix[3][2]) + (in_data[i+1][j+1] * wavelet_matrix[3][3]);
            end
        end

        // 列变换
        for (int i = 0; i < N; i = i + 2) begin
            for (int j = 0; j < N; j = j + 1) begin
                in_data[i][j] = (out_data[i][j] * inverse_wavelet_matrix[0][0]) + (out_data[i+1][j] * inverse_wavelet_matrix[0][1]) + (out_data[i][j+1] * inverse_wavelet_matrix[0][2]) + (out_data[i+1][j+1] * inverse_wavelet_matrix[0][3]);
                in_data[i+1][j] = (out_data[i][j] * inverse_wavelet_matrix[1][0]) + (out_data[i+1][j] * inverse_wavelet_matrix[1][1]) + (out_data[i][j+1] * inverse_wavelet_matrix[1][2]) + (out_data[i+1][j+1] * inverse_wavelet_matrix[1][3]);
                in_data[i][j+1] = (out_data[i][j] * inverse_wavelet_matrix[2][0]) + (out_data[i+1][j] * inverse_wavelet_matrix[2][1]) + (out_data[i][j+1] * inverse_wavelet_matrix[2][2]) + (out_data[i+1][j+1] * inverse_wavelet_matrix[2][3]);
                in_data[i+1][j+1] = (out_data[i][j] * inverse_wavelet_matrix[3][0]) + (out_data[i+1][j] * inverse_wavelet_matrix[3][1]) + (out_data[i][j+1] * inverse_wavelet_matrix[3][2]) + (out_data[i+1][j+1] * inverse_wavelet_matrix[3][3]);
            end
        end
    end
end

endmodule

这个代码实现了一个基于 Daubechies-4 小波变换的行变换版本。它的输入是一个 8x8 的矩阵，输出也是一个 8x8 的矩阵。在每个时钟周期上，它将输入矩阵进行一次小波变换，然后进行一次逆变换。这个代码可以直接在 FPGA 上运行，用于实现图像压缩等应用。