CSHARP生成带噪声的正弦曲线并使用绘制折线图，使用S-G滤波后绘制折线图

以下是使用C#生成带噪声的正弦曲线并使用S-G滤波后绘制折线图的示例代码：

using System;
using System.Drawing;
using System.Windows.Forms;
using MathNet.Numerics;
using MathNet.Numerics.Interpolation;
using MathNet.Numerics.LinearAlgebra;
using MathNet.Numerics.LinearAlgebra.Double;
using ZedGraph;

namespace SGFilterDemo
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();

            // 生成带噪声的正弦曲线
            int n = 200; // 数据点数
            double[] t = new double[n];
            double[] y = new double[n];
            double[] yNoisy = new double[n];
            for (int i = 0; i < n; i++)
            {
                t[i] = i * 0.1;
                y[i] = Math.Sin(t[i]);
                yNoisy[i] = y[i] + 0.1 * (2 * Random.NextDouble() - 1);
            }

            // 使用S-G滤波平滑曲线
            int windowSize = 21; // 滑动窗口大小
            int polyOrder = 3; // 多项式阶数
            double[] ySmooth = SGFilter(yNoisy, windowSize, polyOrder);

            // 绘制折线图
            GraphPane pane = zedGraphControl1.GraphPane;
            pane.Title.Text = "S-G Filter Demo";
            pane.XAxis.Title.Text = "Time";
            pane.YAxis.Title.Text = "Amplitude";
            LineItem curve1 = pane.AddCurve("Original Signal", t, y, Color.Blue, SymbolType.None);
            LineItem curve2 = pane.AddCurve("Noisy Signal", t, yNoisy, Color.Red, SymbolType.None);
            LineItem curve3 = pane.AddCurve("Smoothed Signal", t, ySmooth, Color.Green, SymbolType.None);
            pane.AxisChange();
            zedGraphControl1.Invalidate();
        }

        // S-G滤波函数
        private double[] SGFilter(double[] y, int windowSize, int polyOrder)
        {
            int n = y.Length;
            int halfWindowSize = windowSize / 2;
            double[] yPadded = new double[n + windowSize - 1];
            Vector<double> b = SGFilterCoefficients(polyOrder, windowSize);
            double[] ySmooth = new double[n];
            for (int i = 0; i < n; i++)
            {
                for (int j = -halfWindowSize; j <= halfWindowSize; j++)
                {
                    int k = i + j;
                    if (k < 0)
                        k = -k;
                    if (k >= n)
                        k = 2 * n - k - 2;
                    yPadded[i + halfWindowSize] += y[k] * b[Math.Abs(j)];
                }
            }
            for (int i = 0; i < n; i++)
            {
                ySmooth[i] = yPadded[i + halfWindowSize];
            }
            return ySmooth;
        }

        // S-G滤波系数计算函数
        private Vector<double> SGFilterCoefficients(int polyOrder, int windowSize)
        {
            // 计算多项式系数矩阵
            Matrix<double> X = DenseMatrix.Create(windowSize, polyOrder + 1, (i, j) => Math.Pow(i - windowSize / 2, j));
            // 计算伪逆矩阵
            Matrix<double> Xp = X.PseudoInverse();
            // 计算S-G滤波系数向量
            Vector<double> b = DenseVector.Create(windowSize, 0);
            for (int i = 0; i < windowSize; i++)
            {
                b[i] = Xp.Row(polyOrder) * DenseVector.Create(polyOrder + 1, j => Math.Pow(i - windowSize / 2, j));
            }
            return b;
        }
    }
}

需要注意的是，以上代码中使用了MathNet.Numerics库来进行矩阵运算和插值计算，需要先使用NuGet安装该库。另外，以上代码中使用了ZedGraph库来绘制折线图，也需要先使用NuGet安装该库。