使用ADC欠采样直采与使用混频器进行频谱搬移后采样，怎么衡量最终的SNDR？

原信号（40kHz） × LO（35kHz） →→ 混频后产生 5kHz（目标）+ 75kHz（镜像）→ 滤波器抑制 75kHz 分量（-30 dB）→ ADC 正常采样（比如 100kHz）

原信号（40kHz） →→ 直接用 35kSps ADC 采样（欠采样）→ 频谱折叠 → 5kHz 落入基带

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import butter, lfilter, fftconvolve
from numpy.fft import fft, fftfreq

# 设置参数

fs_high = 100_000   # 高采样率用于混频方案
fs_low = 35_000     # 欠采样率
f_signal = 40_000   # 原始信号频率
f_lo = 35_000       # 混频本振频率

duration = 0.01  # 10ms 信号持续时间
t_high = np.arange(0, duration, 1/fs_high)
t_low = np.arange(0, duration, 1/fs_low)

# 生成信号：40kHz 正弦波 + 微小失真项 + 噪声

signal = np.sin(2 * np.pi * f_signal * t_high)
signal += 0.01 * np.sin(2 * np.pi * 2 * f_signal * t_high)  # 二次谐波
signal += 0.005 * np.random.randn(len(t_high))  # 噪声

# 混频方案

lo = np.sin(2 * np.pi * f_lo * t_high)
mixed_signal = signal * lo  # 乘法混频

# 滤波器设计：带通滤波器，通带5kHz ± 2.5kHz

def bandpass_filter(data, fs, lowcut, highcut, order=5):
    nyq = 0.5 * fs
    b, a = butter(order, [lowcut/nyq, highcut/nyq], btype='band')
    return lfilter(b, a, data)

filtered_mixed = bandpass_filter(mixed_signal, fs_high, 2.5e3, 7.5e3)

# 重新采样（模拟ADC采样）

def downsample(signal, orig_fs, target_fs):
    factor = int(orig_fs / target_fs)
    return signal[::factor]

mixed_sampled = downsample(filtered_mixed, fs_high, fs_low)

# 欠采样方案（直接35k采样原始40k信号）

signal_alias = np.sin(2 * np.pi * f_signal * t_low)
signal_alias += 0.01 * np.sin(2 * np.pi * 2 * f_signal * t_low)
signal_alias += 0.005 * np.random.randn(len(t_low))

# 计算 SNDR

def compute_sndr(signal, fs):
    N = len(signal)
    fft_vals = np.abs(fft(signal))[:N//2]
    freqs = fftfreq(N, d=1/fs)[:N//2]

    peak_idx = np.argmax(fft_vals)
    signal_power = fft_vals[peak_idx] ** 2
    total_power = np.sum(fft_vals ** 2)
    noise_dist_power = total_power - signal_power
    sndr = 10 * np.log10(signal_power / noise_dist_power)
    return sndr, freqs, fft_vals

sndr_mixed, freq_mixed, fft_mixed = compute_sndr(mixed_sampled, fs_low)
sndr_alias, freq_alias, fft_alias = compute_sndr(signal_alias, fs_low)

# 画图

plt.figure()
plt.plot(freq_mixed, 20*np.log10(fft_mixed), label=f'Mixed Sampling SNDR={sndr_mixed:.2f} dB')
plt.plot(freq_alias, 20*np.log10(fft_alias), label=f'Undersampling SNDR={sndr_alias:.2f} dB')
plt.title("FFT Comparison of Mixed Sampling vs Undersampling")
plt.xlabel("Frequency (Hz)")
plt.ylabel("Magnitude (dB)")
plt.grid(True)
plt.legend()
plt.tight_layout()
plt.show()