SpKit: Signal Processing toolkit

# Signal Processing toolkit

## Installation

Requirement: numpy, matplotlib, scipy.stats, scikit-learn

### with pip

pip install spkit


### Build from the source

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

python setup.py install


## Functions list

#### 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

### View in 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()


## ICA

### View in notebook

from spkit import ICA

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

### Decision Trees - View in notebook

**view in repository **

## LFSR

import numpy as np
from spkit.pylfsr import LFSR
## Example 1  ## 5 bit LFSR with x^5 + x^2 + 1
L = LFSR()
L.info()
L.next()
L.runKCycle(10)
L.runFullCycle()
L.info()
tempseq = L.runKCycle(10000)    # generate 10000 bits from current state


# Contacts:

## Project details

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