Module DigiCommPy.scripts.chapter_5.lms_test

Script: DigiCommPy.chapter_5.lms_test.py Verify LMS filter update equations (adaptive filter design) System identification using LMS algorithm

@author: Mathuranathan Viswanathan Created on Sep 4, 2019

"""
Script: DigiCommPy.chapter_5.lms_test.py
Verify LMS filter update equations (adaptive filter design)
System identification using LMS algorithm

@author: Mathuranathan Viswanathan
Created on Sep 4, 2019
"""
import numpy as np
from numpy.random import randn
from numpy import convolve
N = 5 # length of the desired filter
mu=0.1 # step size for LMS algorithm
r=randn(10000) # random input sequence of length 10000
h=randn(N)+1j*randn(N) # random complex system
a=convolve(h,r) # reference signal

from equalizers import LMSEQ
lms_eq = LMSEQ(N) #initialize the LMS filter object
lms_eq.design(mu,r,a) # design using input and reference sequences
print('System impulse response (h): {}'.format(h))
print('LMS adapted filter (w): {}'.format(lms_eq.w))

Functions

def randn(...)

randn(d0, d1, …, dn)

Return a sample (or samples) from the "standard normal" distribution.

If positive, int_like or int-convertible arguments are provided, RandomState.randn() generates an array of shape (d0, d1, ..., dn), filled with random floats sampled from a univariate "normal" (Gaussian) distribution of mean 0 and variance 1 (if any of the :math:d_i are floats, they are first converted to integers by truncation). A single float randomly sampled from the distribution is returned if no argument is provided.

This is a convenience function. If you want an interface that takes a tuple as the first argument, use numpy.random.standard_normal instead.

Parameters

d0, d1, …, dn : int, optional The dimensions of the returned array, should be all positive. If no argument is given a single Python float is returned.

Returns

Z : ndarray or float

A (d0, d1, ..., dn)-shaped array of floating-point samples from the standard normal distribution, or a single such float if no parameters were supplied.

See Also

standard_normal

Similar, but takes a tuple as its argument.

Notes

For random samples from :math:N(\mu, \sigma^2), use:

sigma * np.random.randn(...) + mu

Examples

>>> np.random.randn()
2.1923875335537315 #random

Two-by-four array of samples from N(3, 6.25):

>>> 2.5 * np.random.randn(2, 4) + 3
array([[-4.49401501,  4.00950034, -1.81814867,  7.29718677],  #random


   [ 0.39924804,  4.68456316,  4.99394529,  4.84057254]]) #random