# NLMS算法的模拟测试

``````# -*- coding: utf-8 -*-
# filename: nlms_test.py

import numpy as np
import pylab as pl
import nlms_numpy
import scipy.signal

# 随机产生FIR滤波器的系数，长度为length， 延时为delay， 指数衰减
def make_path(delay, length):
path_length = length - delay
h = np.zeros(length, np.float64)
h[delay:] = np.random.standard_normal(path_length) * np.exp( np.linspace(0, -4, path_length) )
h /= np.sqrt(np.sum(h*h))
return h

def plot_converge(y, u, label=""):
size = len(u)
avg_number = 200
e = np.power(y[:size] - u, 2)
tmp = e[:int(size/avg_number)*avg_number]
tmp.shape = -1, avg_number
avg = np.average( tmp, axis=1 )
pl.plot(np.linspace(0, size, len(avg)), 10*np.log10(avg), linewidth=2.0, label=label)

def diff_db(h0, h):
return 10*np.log10(np.sum((h0-h)*(h0-h)) / np.sum(h0*h0))

# 用NLMS进行系统辨识的模拟, 未知系统的传递函数为h0, 使用的参照信号为x
def sim_system_identify(nlms, x, h0, step_size, noise_scale):
y = np.convolve(x, h0)
d = y + np.random.standard_normal(len(y)) * noise_scale # 添加白色噪声的外部干扰
h = np.zeros(len(h0), np.float64) # 自适应滤波器的长度和未知系统长度相同，初始值为0
u = nlms( x, d, h, step_size )
return y, u, h

def system_identify_test1():
h0 = make_path(32, 256) # 随机产生一个未知系统的传递函数
x = np.random.standard_normal(10000)  # 参照信号为白噪声
y, u, h = sim_system_identify(nlms_numpy.nlms, x, h0, 0.5, 0.1)
print diff_db(h0, h)
pl.figure( figsize=(8, 6) )
pl.subplot(211)
pl.plot(h0, c="r")
pl.plot(h, c="b")
pl.title(u"未知系统和收敛后的滤波器的系数比较")
pl.subplot(212)
plot_converge(y, u)
pl.title(u"自适应滤波器收敛特性")
pl.xlabel("Iterations (samples)")
pl.ylabel("Converge Level (dB)")
pl.show()

def system_identify_test2():
h0 = make_path(32, 256) # 随机产生一个未知系统的传递函数
x = np.random.standard_normal(20000)  # 参照信号为白噪声
pl.figure(figsize=(8,4))
for step_size in np.arange(0.1, 1.0, 0.2):
y, u, h = sim_system_identify(nlms_numpy.nlms, x, h0, step_size, 0.1)
plot_converge(y, u, label=u"μ=%s" % step_size)
pl.title(u"更新系数和收敛特性的关系")
pl.xlabel("Iterations (samples)")
pl.ylabel("Converge Level (dB)")
pl.legend()
pl.show()

def system_identify_test3():
h0 = make_path(32, 256) # 随机产生一个未知系统的传递函数
x = np.random.standard_normal(20000)  # 参照信号为白噪声
pl.figure(figsize=(8,4))
for noise_scale in [0.05, 0.1, 0.2, 0.4, 0.8]:
y, u, h = sim_system_identify(nlms_numpy.nlms, x, h0, 0.5, noise_scale)
plot_converge(y, u, label=u"noise=%s" % noise_scale)
pl.title(u"外部干扰和收敛特性的关系")
pl.xlabel("Iterations (samples)")
pl.ylabel("Converge Level (dB)")
pl.legend()
pl.show()

def sim_signal_equation(nlms, x, h0, D, step_size, noise_scale):
d = x[:-D]
x = x[D:]
y = np.convolve(x, h0)[:len(x)]
h = np.zeros(2*len(h0)+2*D, np.float64)
y += np.random.standard_normal(len(y)) * noise_scale
u = nlms(y, d, h, step_size)
return h

def signal_equation_test1():
h0 = make_path(5, 64)
D = 128
length = 20000
data = np.random.standard_normal(length+D)
h = sim_signal_equation(nlms_numpy.nlms, data, h0, D, 0.5, 0.1)
pl.figure(figsize=(8,4))
pl.plot(h0, label=u"未知系统")
pl.plot(h, label=u"自适应滤波器")
pl.plot(np.convolve(h0, h), label=u"二者卷积")
pl.title(u"信号均衡演示")
pl.legend()
w0, H0 = scipy.signal.freqz(h0, worN = 1000)
w, H = scipy.signal.freqz(h, worN = 1000)
pl.figure(figsize=(8,4))
pl.plot(w0, 20*np.log10(np.abs(H0)), w, 20*np.log10(np.abs(H)))
pl.title(u"未知系统和自适应滤波器的振幅特性")
pl.xlabel(u"圆频率")
pl.ylabel(u"振幅(dB)")
pl.show()

signal_equation_test1()
``````