pyProject/test_STEPS.py

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import least_squares


class STEPS:
    """实现子信号技术参数估计算法(STEPS)"""

    def __init__(self, fs, N0):
        """
        初始化STEPS估计器
        :param fs: 采样频率
        :param N0: 原始信号长度
        """
        self.fs = fs
        self.N0 = N0
        # 子信号长度选择为原始信号的2/3（论文推荐的最优比例）
        self.N1 = int(2 * N0 / 3)
        self.N2 = self.N1
        # 子信号起始索引
        self.n1 = 0
        self.n2 = N0 - self.N2

        # 确保子信号长度有效
        if self.N1 <= 0 or self.N2 <= 0:
            raise ValueError("子信号长度必须为正数，请增加原始信号长度")

        # 预计算频率分辨率
        self.freq_res = fs / N0

    def extract_subsignals(self, x):
        """
        从原始信号中提取两个子信号
        :param x: 原始信号
        :return: 两个子信号x1和x2
        """
        if len(x) != self.N0:
            raise ValueError(f"输入信号长度必须为{N0}，实际为{len(x)}")

        x1 = x[self.n1: self.n1 + self.N1]
        x2 = x[self.n2: self.n2 + self.N2]
        return x1, x2

    def compute_dft(self, x):
        """计算信号的DFT并返回幅度和相位"""
        X = np.fft.fft(x)
        amp = np.abs(X)
        phase = np.angle(X)
        return amp, phase

    def find_peak_bin(self, amp):
        """找到DFT幅度谱中的峰值位置"""
        return np.argmax(amp)

    def phase_correction(self, phase, k, N):
        """
        相位校正，消除线性相位影响
        :param phase: 原始相位
        :param k: 峰值所在的频点
        :param N: 信号长度
        :return: 校正后的相位
        """
        return phase - 2 * np.pi * k * (N - 1) / (2 * N)

    def objective_function(self, delta1, k1, k2, c1, c2, phi1, phi2):
        """用于求解非线性方程的目标函数"""
        # 计算方程左边
        left_numerator = c1 * np.tan(phi2) - c2 * np.tan(phi1)
        left_denominator = c1 * c2 + np.tan(phi1) * np.tan(phi2)
        left = left_numerator / left_denominator

        # 计算方程右边
        term = np.pi * (k1 + delta1) / self.N1 * (2 * (self.n2 - self.n1) + self.N2 - self.N1)
        right = np.tan(term)

        # 返回误差
        return left - right

    def estimate_frequency(self, x1, x2):
        """
        估计信号频率
        :param x1, x2: 两个子信号
        :return: 估计的频率
        """
        # 计算子信号的DFT
        amp1, phase1 = self.compute_dft(x1)
        amp2, phase2 = self.compute_dft(x2)

        # 找到峰值位置
        k1 = self.find_peak_bin(amp1)
        k2 = self.find_peak_bin(amp2)

        # 相位校正
        phi1 = self.phase_correction(phase1[k1], k1, self.N1)
        phi2 = self.phase_correction(phase2[k2], k2, self.N2)

        # 计算c1和c2参数
        c1 = np.sin(np.pi * k1 / self.N1) / np.sin(np.pi * (k1 + 1) / self.N1)
        c2 = np.sin(np.pi * k2 / self.N2) / np.sin(np.pi * (k2 + 1) / self.N2)

        # 求解非线性方程找到delta1
        def func(delta):
            return self.objective_function(delta, k1, k2, c1, c2, phi1, phi2)

        # 使用最小二乘法求解
        result = least_squares(func, x0=0.5, bounds=(0, 1))
        delta1 = result.x[0]

        # 计算频率
        l0 = (self.N0 / self.N1) * (k1 + delta1)
        f0 = (l0 / self.N0) * self.fs

        return f0, k1, amp1[k1]

    def estimate_amplitude(self, k1, amp1_peak):
        """估计信号振幅"""
        # 计算振幅校正因子
        delta1 = (self.N1 / self.N0) * (self.fs / self.freq_res) - k1
        correction = np.abs(np.sin(np.pi * delta1) / (self.N1 * np.sin(np.pi * (k1 + delta1) / self.N1)))
        amplitude = amp1_peak * correction
        return amplitude

    def estimate_phase(self, f0, k1, amp1_peak):
        """估计信号初始相位"""
        delta1 = (self.N1 * f0 / self.fs) - k1
        phase = np.angle(amp1_peak) - np.pi * delta1 * (self.N1 - 1) / self.N1
        # 将相位归一化到[-π, π]范围
        return (phase + np.pi) % (2 * np.pi) - np.pi

    def estimate(self, x):
        """
        估计正弦信号的参数
        :param x: 输入信号
        :return: 频率、振幅和相位的估计值
        """
        # 提取子信号
        x1, x2 = self.extract_subsignals(x)

        # 估计频率
        f0, k1, amp1_peak = self.estimate_frequency(x1, x2)

        # 估计振幅
        amp = self.estimate_amplitude(k1, amp1_peak)

        # 估计相位
        phase = self.estimate_phase(f0, k1, amp1_peak)

        return f0, amp, phase


# 演示如何使用STEPS类
if __name__ == "__main__":
    # 生成测试信号
    fs = 1000  # 采样频率
    N0 = 1024  # 信号长度
    f_true = 75.3  # 真实频率
    amp_true = 2.5  # 真实振幅
    phase_true = np.pi / 3  # 真实相位
    snr_db = 40  # 信噪比(dB)

    # 生成时间向量
    t = np.arange(N0) / fs

    # 生成干净信号
    x_clean = amp_true * np.sin(2 * np.pi * f_true * t + phase_true)

    # 添加噪声
    snr = 10 ** (snr_db / 10)
    signal_power = np.sum(x_clean ** 2) / N0
    noise_power = signal_power / snr
    noise = np.sqrt(noise_power) * np.random.randn(N0)
    x = x_clean + noise

    # 创建STEPS估计器并进行参数估计
    steps = STEPS(fs, N0)
    f_est, amp_est, phase_est = steps.estimate(x)

    # 计算误差
    f_error = np.abs(f_est - f_true)
    amp_error = np.abs(amp_est - amp_true)
    phase_error = np.abs(phase_est - phase_true)

    # 显示结果
    print(f"真实频率: {f_true:.4f} Hz, 估计频率: {f_est:.4f} Hz, 误差: {f_error:.6f} Hz")
    print(f"真实振幅: {amp_true:.4f}, 估计振幅: {amp_est:.4f}, 误差: {amp_error:.6f}")
    print(f"真实相位: {phase_true:.4f} rad, 估计相位: {phase_est:.4f} rad, 误差: {phase_error:.6f} rad")

    # 绘制信号和频谱
    plt.figure(figsize=(12, 8))

    # 设置中文字体支持
    plt.rcParams["font.family"] = ["SimHei"]
    plt.rcParams["axes.unicode_minus"] = False  # 解决负号显示问题

    # 绘制时域信号
    plt.subplot(2, 1, 1)
    plt.plot(t, x_clean, label='干净信号')
    plt.plot(t, x, alpha=0.7, label='带噪声信号')
    plt.xlabel('时间 (s)')
    plt.ylabel('振幅')
    plt.title('时域信号')
    plt.legend()

    # 绘制频谱
    plt.subplot(2, 1, 2)
    freq = np.fft.fftfreq(N0, 1 / fs)
    x_fft = np.fft.fft(x)
    plt.plot(freq[:N0 // 2], 20 * np.log10(np.abs(x_fft[:N0 // 2])), label='信号频谱')
    plt.xlabel('频率 (Hz)')
    plt.ylabel('幅度 (dB)')
    plt.title('信号频谱')
    plt.xlim(0, 150)  # 限制频率范围以便观察
    plt.axvline(f_true, color='r', linestyle='--', label=f'真实频率: {f_true} Hz')
    plt.axvline(f_est, color='g', linestyle='--', label=f'估计频率: {f_est:.2f} Hz')
    plt.legend()

    plt.tight_layout()
    plt.show()