{\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fnil\fcharset0 Calibri;}{\f1\fnil\fcharset238 Calibri;}}
{\colortbl ;\red0\green0\blue255;\red0\green176\blue80;\red247\green150\blue70;}
{\*\generator Msftedit 5.41.21.2509;}\viewkind4\uc1\pard\sa200\sl276\slmult1\qc\lang9\ul\b\f0\fs22 Signal Processing laboratory\ulnone\b0\par
Robert Kawecki\par
\par
\pard\sa200\sl276\slmult1 Numpy library description: {\field{\*\fldinst{HYPERLINK "http://wiki.scipy.org/Tentative_NumPy_Tutorial"}}{\fldrslt{\ul\cf1 http://wiki.scipy.org/Tentative_NumPy_Tutorial}}}\f0\fs22\par
\pard\sl240\slmult1\b Basic Python commands to operate with folders:\b0\par
\cf2\tab # check current working directory\par
\tab # pwd\cf0\par
print os.getcwd()\par
\par
\cf2\tab # change directory to D\par
\tab # cd D:/\cf0\par
os.chdir('D:/')\par
\par
\cf2\tab # check current working directory\par
\tab # pwd\cf0\par
print os.getcwd()\par
\par
\cf2\tab # make a Biomed directory\par
\tab # mkdir Biomed\cf0\par
os.mkdir("Biomed")\par
\par
\cf2\tab # check a content of the D drive\par
\tab # ls\cf0\par
\cf2\tab # Example: '.' lists files and directories in the current folder.\par
\tab # Example2: 'D:\\canopy' lists files and directories in the D:\\canopy folder.\cf0\par
print os.listdir('.')\par
\par
\b Examples of chosen basic commands to create arrays:\b0\par
from numpy  import *  \cf2  # sign '*' means that you import all commands/methods from numpy \tab\tab\tab\tab library\par
\cf0 import os\tab\tab\cf2 # imports standard operating system methods. See more: \tab\tab\tab\tab\tab\cf0{\field{\*\fldinst{HYPERLINK "https://docs.python.org/3/library/os.html"}}{\fldrslt{\ul\cf1 https://docs.python.org/3/library/os.html}}}\cf2\f0\fs22\par
\cf0 a = arange(15)\tab\tab\cf2 # generates array with N=15 elements, starting from 0 till N-1.\cf0\par
print a \tab\tab\tab\cf2 #Output: [ 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14]\cf0\par
b = a.reshape(3,5)\tab\cf2 # reshapes 1x15 matrix to the matrix which has 3 rows and 5 columns\cf0\par
print b\tab\tab\tab\cf2 #Output: \tab [[ 0  1  2  3  4]\par
\tab\tab\tab  \tab\tab [ 5  6  7  8  9]\par
 \tab\tab\tab\tab\tab [10 11 12 13 14]]\par
\cf0 print zeros( 10 )\tab\cf2 #Output: [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.], 0 with '.' means that this is a \tab\tab\tab\tab float  value. See more: \tab\tab\tab\tab\tab\tab\tab\tab\tab\tab\cf0{\field{\*\fldinst{HYPERLINK "https://www.tutorialspoint.com/python/python_variable_types.htm"}}{\fldrslt{\ul\cf1 https://www.tutorialspoint.com/python/python_variable_types.htm}}}\cf2\f0\fs22\par
\cf0 print ones( 10 )\tab\tab\cf2 #Output: [ 1.  1.  1.  1.  1.  1.  1.  1.  1.  1.]\par
\par
\cf0 print arange(2,24,3)\cf2\tab #Output: [ 2  5  8 11 14 17 20 23], Generates array from 2 to 24. Each \tab\tab\tab\tab successive element in the array is greater than the previous by 3.\par
\tab\tab\tab # arange( FROM , TO , STEP ) - step parameter can be also negative\par
\par
\cf0 t = array([[1.1, 4.56, 8.999],[2,3,4],[6.78,2.44,5.55]]) \par
print 't=',t \tab\tab\cf2 #t= [[ 1.1    4.56   8.999]\par
\pard\li2160\sl240\slmult1  [ 2.     3.     4.   ]\par
 [ 6.78   2.44   5.55 ]]\cf0\par
\pard\sl240\slmult1 print 't.min()=',t.min()\tab\cf2 #t.min()= 1.1\cf0\par
print 't.max()=',t.max()\tab\cf2 #t.max()= 8.999\cf0\par
print 't.min(axis=0)=',t.min(axis=0)\tab\cf2 #t.min(axis=0)= [ 1.1   2.44  4.  ]\cf0\par
print 't.min(axis=1)=',t.min(axis=1)\tab\cf2 #t.min(axis=1)= [ 1.1   2.    2.44]\cf0\par
print 't.max(axis=0)=',t.max(axis=0)\tab\cf2 #t.max(axis=0)= [ 6.78   4.56   8.999]\cf0\par
print 't.max(axis=1)=',t.max(axis=1)\tab\cf2 #t.max(axis=1)= [ 8.999  4.     6.78 ]\cf0\par
print 't.prod()=', t.prod()\tab\tab\cf2 #t.prod()= 99466.1995825\cf0\par
print 'average(t)=',average(t)\tab\tab\cf2 #average(t)= 4.26988888889\cf0\par
print 't.std()=',t.std()\tab\tab\tab\cf2 #t.std()= 2.37165064152\cf0\par
print 't.var()=',t.var()\tab\tab\tab\cf2 #t.var()= 5.62472676543\cf0\par
print 't.round()=',t.round()\tab\tab\cf2 #t.round()= [[ 1.  5.  9.]\par
\tab\tab\tab\tab\tab\tab         [ 2.  3.  4.]\par
 \tab\tab\tab\tab\tab\tab         [ 7.  2.  6.]]\cf0\par
print 't.clip(1,3)=',t.clip(1,3)\tab\tab\cf2 #t.clip(1,3)= [[ 1.1   3.    3.  ]\par
 \tab\tab\tab\tab\tab\tab           [ 2.    3.    3.  ]\par
 \tab\tab\tab\tab\tab\tab           [ 3.    2.44  3.  ]]\cf0\par
print 'floor(t)=',floor(t)\tab\tab\tab\cf2 #floor(t)= [[ 1.  4.  8.]\par
 \tab\tab\tab\tab\tab\tab      [ 2.  3.  4.]\par
                                                                                           [ 6.  2.  5.]]\cf0\par
print 'ceil(t)=',ceil(t)\tab\tab\tab\cf2 #ceil(t)= [[ 2.  5.  9.]\par
 \tab\tab\tab\tab\tab\tab    [ 2.  3.  4.]\par
 \tab\tab\tab\tab\tab\tab    [ 7.  3.  6.]]\cf0\par
print 'flipud(t)=',flipud(t)\tab\tab\cf2 #flipud(t)= [[ 6.78   2.44   5.55 ]\par
\tab\tab\tab\tab\tab\tab        [ 2.     3.     4.   ]\par
\tab\tab\tab\tab\tab\tab        [ 1.1    4.56   8.999]]\cf0\par
print 'fliplr(t)=',fliplr(t)\tab\tab\tab\cf2 #fliplr(t)= [[ 8.999  4.56   1.1  ]\par
 \tab\tab\tab\tab\tab\tab      [ 4.     3.     2.   ]\par
 \tab\tab\tab\tab\tab\tab      [ 5.55   2.44   6.78 ]]\cf0\par
print 'rot90(t)=',rot90(t)\tab\tab\cf2 #rot90(t)= [[ 8.999  4.     5.55 ]\par
 \tab\tab\tab\tab\tab\tab       [ 4.56   3.     2.44 ]\par
 \tab\tab\tab\tab\tab\tab       [ 1.1    2.     6.78 ]]\par
\par
\cf0\b Defining functions:\par
Tutorial:  {\field{\*\fldinst{HYPERLINK "http://www.diveintopython.net/getting_to_know_python/indenting_code.html"}}{\fldrslt{\ul\cf1 http://www.diveintopython.net/getting_to_know_python/indenting_code.html}}}\f0\fs22\par
or if you prefer polish: {\field{\*\fldinst{HYPERLINK "https://pl.wikibooks.org/wiki/Zanurkuj_w_Pythonie/Wci\f1\'eacia_kodu"}}{\fldrslt{\ul\cf1 https://pl.wikibooks.org/wiki/Zanurkuj_w_Pythonie/Wci\lang1045\f1\'eacia_kodu\f1 }}}\f1\fs22\par
\lang9\f0\par
\b0 def motion(a,t):\tab\tab\cf2 #type def before the function name. you can type input args in (), ':' at \tab\tab\tab\tab the end of the definition\par
\cf3\tab """Here enter help description for your function\par
\tab Syntax: v,s=motion(a,t)""" \cf2 #Function description here- optional but useful\par
\par
\tab # Some operations below\cf0\par
\tab print "The result of the function motion(a,t) for a = ",a," t = ",t, ": ", \par
\tab v=a*t          \tab\tab\cf2 # velocity\cf0\par
\tab s=(a*t**2)/2.  \tab\tab\cf2 #distance\par
\tab #Functions in python can return one, two or many parameters, lists, arrays, tuples etc.\cf0\par
\tab return v,s\par
\cf2 #Function execution\par
\cf0 print "#### FUNCTION: MOTION #####"\par
a=5\par
t=10\par
print "Motion: ", motion(a,t)\par
\par
\b Ploting arrays / signals:\par
\b0 import matplotlib.pyplot as plt\par
import os\cf2\par
\par
\cf0 plt.cla()\cf2  #clears an axis, i.e. the currently active axis in the current figure. It leaves the other axes untouched.\par
\cf0 plt.clf()\cf2  #clears the entire current figure with all its axes, but leaves the window opened, such that it may be reused for other plots.\par
\cf0 plt.close() \cf2 #closes a window, which will be the current window, if not specified otherwise.\par
\par
\cf0 dt=0.5\par
t=arange(0,10,dt)\cf2  # time scale\par
\cf0 a=9.81\cf2  # acceleration\par
\cf0 v=a*t \cf2 # velocity\par
\cf0 s=(a*t**2)/2. \cf2 # distance\par
\cf0\par
plt.figure(1)\tab\cf2 #new windows\cf0\par
plt.plot(t,v,'.') \tab\cf2 #plot velocity parameter. '.' arg means that plot line style will be dotted.\par
\cf0 plt.title('Velocity') \cf2 #plot title shown on the output figure\cf0\par
plt.xlabel('t[s]')\tab\tab\cf2 # add labels to axes\cf0\par
plt.ylabel('v[m/s]')\cf2\par
\cf0 plt.legend() \tab\cf2\tab #adds legend\cf0\par
plt.grid()\tab\cf2\tab #adds grid\cf0\par
plt.show() \tab\cf2\tab #displays windows to the user\par
\par
# Example 2, printing sinus\par
\cf0 from numpy import *\par
import os\par
from matplotlib.pyplot import *\par
x = arange(100)\par
y=sin(x*pi/50.)\par
plot(x,y)\par
show()\cf2\par
\par
\cf0\b Playing sounds:\b0\par
from scipy.io.wavfile import read as read_wav\par
from scipy.io.wavfile import write as write_wav\par
import winsound\par
\par
sampling_rate, data = read_wav('noise_voice.wav')\tab\cf2 # File is included in signals.zip folder.\cf0\par
print sampling_rate\par
print data\par
print "#######################################"\par
write_wav('male_voice.wav',sampling_rate,data[::-1])\tab\cf2 # This method \par
\cf0 winsound.PlaySound("male_voice.wav", winsound.SND_ALIAS)\tab\cf2 # Play .wav file\par
\cf0 print "#######################################"\par
\par
\b Plotting signals with the defined frequency:\par
\par
\b0 import pylab\par
import numpy\par
N=2000\par
A=10\par
f1=10\par
f2=20\par
f3=25\par
fs=1000.\par
t = numpy.arange(2000)/fs\par
y1=A*numpy.sin(2*numpy.pi*f1*t)\par
pylab.plot(t,y1)\par
pylab.show()\par
y2=A*numpy.sin(2*numpy.pi*f1*t)+A*numpy.sin(2*numpy.pi*f2*t)+A*numpy.sin(2*numpy.pi*f3*t)\par
pylab.plot(t,y2)\par
pylab.show()\par
\b\par
Scalling A/D converter values into voltage\par
\par
Example script:\par
\b0 from scipy.io import loadmat, savemat\par
from numpy import *\par
from pylab import *\par
import os\par
print os.getcwd()\par
fs = 360.\par
N=2000\par
ecg=loadmat('ecg_mit.mat')['ecg_mit']\par
ecg=(5.*(reshape(ecg,len(ecg)) - 1024.))/1024.\par
t= arange(N)/fs\par
plot(t,ecg[:N])\par
show() \par
\b\par
Using n-bit A/D convertes\par
{\field{\*\fldinst{HYPERLINK "https://en.wikipedia.org/wiki/Analog-to-digital_converter"}}{\fldrslt{\ul\cf1 https://en.wikipedia.org/wiki/Analog-to-digital_converter}}}\f0\fs22   Chapter: Resolution\par
\par
\b0 from scipy.io import loadmat, savemat\par
from numpy import *\par
from pylab import *\par
import os\par
\par
ecg=loadmat('ecg_mit.mat')['ecg_mit']\par
ecg=reshape(ecg,len(ecg))\par
\par
def quantize_ecg(vec,b):\par
\par
    ecg1=(vec[:2000]>>b)<<b\par
    plot(ecg1)\par
    show() \par
    \par
quantize_ecg(ecg,7)    \par
\par
\b Example useful imports for excercises:\par
\par
EX1\b0\par
import numpy as np\par
import os\par
\par
\b EX2\b0\par
from numpy import *\par
from my_functions import motion,my_sign\par
import matplotlib.pyplot as plt\par
import os\par
\par
\b EX3\b0\par
from pylab import plot, show, title\par
from numpy import arange,sin,pi\par
import pylab as pl\par
import numpy as np\par
\par
\b EX4\b0\par
from numpy import sin,pi,cos, linspace, arange, reshape\par
from pylab import plot,show, xlabel, title, figure\par
from scipy.io import loadmat\par
\par
\b EX5\b0\par
from scipy.fftpack import fft,ifft\par
from numpy import random\par
from numpy import sin,pi,cos,arange,linspace, where, reshape\par
from pylab import plot,show, xlabel, title, figure, stem, semilogy\par
from scipy.io import loadmat\par
\par
\b EX6\b0\par
from numpy import array, arange, zeros, angle, linspace, reshape\par
from pylab import stem, show, plot, title, figure, grid, close\par
from scipy.signal import lfilter, freqz, convolve, firwin\par
from scipy.fftpack import fft,ifft\par
\par
-------\par
\b Some links to the basic theory:\b0\par
\b Signal\b0 : {\field{\*\fldinst{HYPERLINK "https://en.wikipedia.org/wiki/Signal_(electrical_engineering"}}{\fldrslt{\ul\cf1 https://en.wikipedia.org/wiki/Signal_(electrical_engineering}}}\f0\fs22 )\b\par
Sampling: \b0{\field{\*\fldinst{HYPERLINK "https://en.wikipedia.org/wiki/Sampling_(signal_processing"}}{\fldrslt{\ul\cf1 https://en.wikipedia.org/wiki/Sampling_(signal_processing}}}\f0\fs22 )\b\par
Quantization: \ul\b0{\field{\*\fldinst{HYPERLINK "https://en.wikipedia.org/wiki/Quantization_(signal_processing"}}{\fldrslt{\ul\cf1 https://en.wikipedia.org/wiki/Quantization_(signal_processing}}}\f0\fs22 )\ulnone\b\par
FTT: \ul\b0{\field{\*\fldinst{HYPERLINK "https://en.wikipedia.org/wiki/Fast_Fourier_transform"}}{\fldrslt{\ul\cf1 https://en.wikipedia.org/wiki/Fast_Fourier_transform}}}\f0\fs22\par
\cf2\ulnone\par
}