Signal Processing toolkit

Links

• Github Page : https://github.com/Nikeshbajaj/spkit

• PyPi-project: https://pypi.org/project/spkit/

Installation

With pip

pip install spkit

Build from source

Download the repository or clone it with git, after cd in directory build it from source with

python setup.py install

List of all functions

Signal Processing Techniques

Information Theory functions for real valued signals

• Entropy : Shannon entropy, Rényi entropy of order α, Collision entropy

• Joint entropy

• Conditional entropy

• Mutual Information

• Cross entropy

• Kullback–Leibler divergence

• Computation of optimal bin size for histogram using FD-rule

• Plot histogram with optimal bin size

Matrix Decomposition

• SVD

• ICA using InfoMax, Extended-InfoMax, FastICA & Picard

Linear Feedback Shift Register

• pylfsr

Continuase Wavelet Transform and other functions comming soon..

Machine Learning models - with visualizations

• Logistic Regression

• Naive Bayes

• Decision Trees

• DeepNet (to be updated)

Examples

Information Theory

Jupyter-Notebook

import numpy as np
import matplotlib.pyplot as plt
import spkit as sp

x = np.random.rand(10000)
y = np.random.randn(10000)

#Shannan entropy
H_x= sp.entropy(x,alpha=1)
H_y= sp.entropy(y,alpha=1)

#Rényi entropy
Hr_x= sp.entropy(x,alpha=2)
Hr_y= sp.entropy(y,alpha=2)

H_xy= sp.entropy_joint(x,y)

H_x1y= sp.entropy_cond(x,y)
H_y1x= sp.entropy_cond(y,x)

I_xy = sp.mutual_Info(x,y)

H_xy_cross= sp.entropy_cross(x,y)

D_xy= sp.entropy_kld(x,y)


print('Shannan entropy')
print('Entropy of x: H(x) = ',H_x)
print('Entropy of y: H(y) = ',H_y)
print('-')
print('Rényi entropy')
print('Entropy of x: H(x) = ',Hr_x)
print('Entropy of y: H(y) = ',Hr_y)
print('-')
print('Mutual Information I(x,y) = ',I_xy)
print('Joint Entropy H(x,y) = ',H_xy)
print('Conditional Entropy of : H(x|y) = ',H_x1y)
print('Conditional Entropy of : H(y|x) = ',H_y1x)
print('-')
print('Cross Entropy of : H(x,y) = :',H_xy_cross)
print('Kullback–Leibler divergence : Dkl(x,y) = :',D_xy)



plt.figure(figsize=(12,5))
plt.subplot(121)
sp.HistPlot(x,show=False)

plt.subplot(122)
sp.HistPlot(y,show=False)
plt.show()

Independent Component Analysis - ICA Jupyter-Notebook

from spkit import ICA
from spkit.data import load_data
X,ch_names = load_data.eegSample()

x = X[128*10:128*12,:]
t = np.arange(x.shape[0])/128.0

ica = ICA(n_components=14,method='fastica')
ica.fit(x.T)
s1 = ica.transform(x.T)

ica = ICA(n_components=14,method='infomax')
ica.fit(x.T)
s2 = ica.transform(x.T)

ica = ICA(n_components=14,method='picard')
ica.fit(x.T)
s3 = ica.transform(x.T)

ica = ICA(n_components=14,method='extended-infomax')
ica.fit(x.T)
s4 = ica.transform(x.T)

Machine Learning

• Logistic Regression Jupyter-Notebook

• Naive Bayes Jupyter-Notebook

• Decision Trees Jupyter-Notebook

Plottng tree while training

Linear Feedback Shift Register

Example: 5 bit LFSR with x^5 + x^2 + 1

import numpy as np
from spkit.pylfsr import LFSR

L = LFSR()
L.info()
L.next()
L.runKCycle(10)
L.runFullCycle()
L.info()
tempseq = L.runKCycle(10000)    # generate 10000 bits from current state

Contacts

If any doubt, confusion or feedback please contact me

Nikesh Bajaj: http://nikeshbajaj.in

• n.bajaj@qmul.ac.uk

• nikkeshbajaj@gmail.com

PhD Student: Queen Mary University of London