import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

import numpy as np

def wgn(signal, snr=0):
    signal_power = np.mean(signal ** 2)
    noise_power = signal_power / (10 ** (snr / 10))
    noise = np.random.normal(0, np.sqrt(noise_power), len(signal))
    return noise


def hilbert(signal, num_hilbert=11):
    n = np.arange(-num_hilbert // 2, num_hilbert // 2 + 1)
    hilbert_transformer = np.where(n % 2 != 0, 2j / (np.pi * n), 0)
    hilbert_transformer[num_hilbert // 2] = 1

    return np.convolve(signal, hilbert_transformer, mode='same')


def pulse_compress(signal_src, signal_ref):
    # 计算所需的FFT长度
    fft_len = 2 * len(signal_src) - 1
    fft_len = int(2 ** np.ceil(np.log2(fft_len)))

    # 对参考信号进行共轭翻转
    signal_ref = np.conj(np.flip(signal_ref))

    # 对信号进行Hamming窗加权
    window = np.hamming(len(signal_ref))
    signal_ref *= window

    # 对输入信号和参考信号进行零padding
    signal_src = np.pad(signal_src, (0, fft_len - len(signal_src)), 'constant')
    signal_ref = np.pad(signal_ref, (0, fft_len - len(signal_ref)), 'constant')

    # 进行FFT和卷积
    signal_src_fft = np.fft.fft(signal_src, fft_len)
    signal_ref_fft = np.fft.fft(signal_ref, fft_len)
    signal_dst_fft = signal_src_fft * signal_ref_fft

    # 执行IFFT得到脉冲压缩信号
    signal_dst = np.fft.ifft(signal_dst_fft, fft_len)

    return signal_dst

def lfm(tau, fs, fl, bw):
    times = np.linspace(0, tau - 1 / fs, int(tau * fs))
    phase = 2 * np.pi * fl * times + np.pi * bw / tau * times ** 2
    signal = np.exp(1j * phase)
    
    return signal

signal = np.real(lfm(7e-6, 20e6, 222e6, 6e6))

noise_samples = []

for _ in range(100):
    noise = wgn(signal, 0)
    noise = hilbert(noise)
    noise = pulse_compress(noise, noise)
    
    noise_samples.extend(noise)

xpower = np.sum(signal ** 2) / len(signal)
npower = np.sum(np.abs(noise_samples) ** 2) / len(noise_samples)

noise_samples = np.abs(noise_samples)

mean = np.mean(noise_samples)
var = np.var(noise_samples)
print(mean, var)
print(xpower, npower)
print(np.max(noise_samples))

# 概率密度函数（PDF）图
plt.figure()
sns.kdeplot(noise_samples, bw_adjust=0.5)
plt.title('Probability Density Function (PDF)')
plt.savefig('./img/noise_pdf.png')

# 累积分布函数（CDF）图
plt.figure()
sns.ecdfplot(noise_samples)
plt.title('Cumulative Distribution Function (CDF)')
plt.savefig('./img/noise_cdf.png')

# 箱线图（Box Plot）
plt.figure()
sns.boxplot(x=noise_samples)
plt.title('Box Plot')
plt.savefig('./img/noise_boxplot.png')

# 显示所有图像
plt.show()