קורס – DSP-L1 – 001 וראיה ממוחשבת

קורס פייטון הינו דרישת קדם לקורס – נעשה חזרה מהירה מאוד

מבוא לפייטון חזרה מהיררה (קורס פייטון הינו דרישת קדם לקורס – נעשה חזרה מהירה מאוד )

DTF – Discrete Fourier Transform

קליטת מידע ממקרו בקר ב UART ב פייתון ועיבוד אותות – על המידע

import serial
import numpy as np
import time

# Open a serial connection to the port
ser = serial.Serial('COM8', baudrate=115200, timeout=1)
time.sleep(2)
# Initialize an empty NumPy array to store the data
data = np.empty(0)


while True:
    t=t+1
    # Read a line of data from the serial port
    #print (ser.read())
    byte_val=ser.read(1)
    # byteorder is big where MSB is at start
    int_val = int.from_bytes(byte_val, "big")
    Print(int_val)

import serial

import numpy as np

import time

# Open a serial connection to the port

ser = serial.Serial('COM8', baudrate=115200, timeout=1)

time.sleep(2)

# Initialize an empty NumPy array to store the data

data = np.empty(0)

while True:

t=t+1

# Read a line of data from the serial port

#print (ser.read())

byte_val=ser.read(1)

# byteorder is big where MSB is at start

int_val = int.from_bytes(byte_val, "big")

Print(int_val)

קונבולוציה – חשוב moving average – filter

FIR filter

2014_apple_stock

https://robotronix.co.il/wp-content/uploads/2022/12/2014_apple_stock.csv

import pandas as pd
import plotly.express as px
import matplotlib.pyplot as plt
import numpy as np

df = pd.read_csv('https://robotronix.co.il/wp-content/uploads/2022/12/2014_apple_stock.csv')
#print(df)
df_x= pd.DataFrame(df,columns=['AAPL_x','AAPL_y'])

x=df_x[["AAPL_x"]].to_numpy()
y=df_x[["AAPL_y"]].to_numpy()
y2=y+20
#print(y)
plt.plot(y,label='y') 

y2 = df['AAPL_y'].rolling(window =10).mean().to_numpy()
plt.plot(y2,label='y2') 
plt.legend()

  
# function to show the plot
plt.show()
print("-----------------------------")
print(" some statistics ")
print("mean y" , round(np.mean(y),1))
print("mean y2" , round(np.mean(y2[9:]),1))
print("std" , round(np.std(y),1))
print("min" , round(np.min(y),1))
print("max" , round(np.max(y),1))
print("-----------------------------")

import pandas as pd

import plotly.express as px

import matplotlib.pyplot as plt

import numpy as np

df = pd.read_csv('https://robotronix.co.il/wp-content/uploads/2022/12/2014_apple_stock.csv')

#print(df)

df_x= pd.DataFrame(df,columns=['AAPL_x','AAPL_y'])

x=df_x[["AAPL_x"]].to_numpy()

y=df_x[["AAPL_y"]].to_numpy()

y2=y+20

#print(y)

plt.plot(y,label='y')

y2 = df['AAPL_y'].rolling(window =10).mean().to_numpy()

plt.plot(y2,label='y2')

plt.legend()

# function to show the plot

plt.show()

print("-----------------------------")

print(" some statistics ")

print("mean y" , round(np.mean(y),1))

print("mean y2" , round(np.mean(y2[9:]),1))

print("std" , round(np.std(y),1))

print("min" , round(np.min(y),1))

print("max" , round(np.max(y),1))

print("-----------------------------")

תרגיל כיתה :

טען את הקובץ הבא ישירות מהאתר

data2

https://robotronix.co.il/wp-content/uploads/2022/12/data2.csv

בנה תוכנה בשפת פייתון אשר קולטת קובץ אקסל

מציגה את הנתונים בגרף
מחליקה את הנתונים לפי חלון 5 ולפי חלון 20
מציגה את הגרף המוחלק
מחשב סטיית תקן , מינימום ומקסימום
התוכנה מחשבת את המקומו

מציאת מינימום ומקסימום בנתונים

חישוב מנימום ומקסימום של פונקציה בפייתון

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import find_peaks

from scipy.signal import find_peaks
import numpy as np
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt
days=10
total=480*days
total=1000
HES=pd.read_csv(r'D:\Stocks\sp-500\HES.csv',  nrows=total)


HES['x'] = range(len(HES))
#print(HES)
y = HES['Open'].values
x = HES['x'].values

fig = plt.figure()
ax = fig.subplots()
plt.title("data : pure")

ax.plot(x,y)

y2=HES['Open'].rolling(40,10).mean()
y1=HES['Open'].rolling(40,10).mean()


#print(y)
#print(y)
#defining the x and y arrays

print("data : reduce noise")
fig = plt.figure()
ax = fig.subplots()

plt.title("data : reduce noise")

ax.plot(x,y2)

print("data : reduce noise")
fig = plt.figure()
ax = fig.subplots()
ax.plot(x,y)
ax.plot(x,y2,color='red')
plt.title("data : reduce noise")
#print(y)
plt.show()



fig = plt.figure()
ax = fig.subplots()
ax.plot(x,y)
y2=y2+0.2
ax.plot(x,y2,color='red')
plt.title("data : reduce noise")
#print(y)
plt.show()




fig = plt.figure()
ax = fig.subplots()
x3=x-30
y3=y2
ax.plot(x,y)
ax.plot(x3,y3,color='red')
plt.title("data : reduce noise")
#print(y)
plt.show()



fig = plt.figure()
ax = fig.subplots()

y3=y2
y4=y2-0.4
ax.plot(x,y)

ax.plot(x3,y4,color='red')
ax.plot(x3,y3,color='red')
ax.plot(x3,y4,color='red')
plt.title("data : reduce noise envelop")
#print(y)
plt.show()


fig = plt.figure()
ax = fig.subplots()
ax.plot(x,y)
ax.plot(x3,y1,color='green')
ax.plot(x3,y4,color='red')
ax.plot(x3,y3,color='red')
ax.plot(x3,y4,color='red')
plt.title("data : reduce noise envelop + best fit")
#print(y)
plt.show()

peaks = find_peaks(y2, height = 1, threshold =  0, distance = None , width=10)
#print ("Peaks : " ,peaks)
height = peaks[1]['peak_heights'] #list of the heights of the peaks
peak_pos = x[peaks[0]] #list of the peaks positions

#Finding the minima
y2 = y*-1

minima = find_peaks(y2, distance = 10)
min_pos = x[minima[0]] #list of the minima positions
min_height = y2[minima[0]] #list of the mirrored minima heights
#Plotting
fig = plt.figure()
ax = fig.subplots()
ax.plot(x,y)
ax.scatter(peak_pos, height, color = 'r', s = 25, marker = 'D', label = 'Maxs')
ax.scatter(min_pos, min_height*-1, color = 'gold', s = 25, marker = 'X', label = 'Mins')
ax.legend()
ax.grid()
print ("Event Stock Corrlation Graph plot ver 1.1 ")
print ("Show  Min and Max in any stock - think - tech ltd")
plt.show()

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import numpy as np

import matplotlib.pyplot as plt

from scipy.signal import find_peaks

import numpy as np

import seaborn as sns

import pandas as pd

import matplotlib.pyplot as plt

days=10

total=480*days

total=1000

HES=pd.read_csv(r'D:\Stocks\sp-500\HES.csv', nrows=total)

HES['x'] = range(len(HES))

#print(HES)

y = HES['Open'].values

x = HES['x'].values

fig = plt.figure()

ax = fig.subplots()

plt.title("data : pure")

ax.plot(x,y)

y2=HES['Open'].rolling(40,10).mean()

y1=HES['Open'].rolling(40,10).mean()

#print(y)

#defining the x and y arrays

print("data : reduce noise")

fig = plt.figure()

ax = fig.subplots()

plt.title("data : reduce noise")

ax.plot(x,y2)

print("data : reduce noise")

fig = plt.figure()

ax = fig.subplots()

ax.plot(x,y)

ax.plot(x,y2,color='red')

plt.title("data : reduce noise")

#print(y)

plt.show()

fig = plt.figure()

ax = fig.subplots()

ax.plot(x,y)

y2=y2+0.2

ax.plot(x,y2,color='red')

plt.title("data : reduce noise")

#print(y)

plt.show()

fig = plt.figure()

ax = fig.subplots()

x3=x-30

y3=y2

ax.plot(x,y)

ax.plot(x3,y3,color='red')

plt.title("data : reduce noise")

#print(y)

plt.show()

fig = plt.figure()

ax = fig.subplots()

y3=y2

y4=y2-0.4

ax.plot(x,y)

ax.plot(x3,y4,color='red')

ax.plot(x3,y3,color='red')

ax.plot(x3,y4,color='red')

plt.title("data : reduce noise envelop")

#print(y)

plt.show()

fig = plt.figure()

ax = fig.subplots()

ax.plot(x,y)

ax.plot(x3,y1,color='green')

ax.plot(x3,y4,color='red')

ax.plot(x3,y3,color='red')

ax.plot(x3,y4,color='red')

plt.title("data : reduce noise envelop + best fit")

#print(y)

plt.show()

peaks = find_peaks(y2, height = 1, threshold = 0, distance = None , width=10)

#print ("Peaks : " ,peaks)

height = peaks[1]['peak_heights'] #list of the heights of the peaks

peak_pos = x[peaks[0]] #list of the peaks positions

#Finding the minima

y2 = y*-1

minima = find_peaks(y2, distance = 10)

min_pos = x[minima[0]] #list of the minima positions

min_height = y2[minima[0]] #list of the mirrored minima heights

#Plotting

fig = plt.figure()

ax = fig.subplots()

ax.plot(x,y)

ax.scatter(peak_pos, height, color = 'r', s = 25, marker = 'D', label = 'Maxs')

ax.scatter(min_pos, min_height*-1, color = 'gold', s = 25, marker = 'X', label = 'Mins')

ax.legend()

ax.grid()

print ("Event Stock Corrlation Graph plot ver 1.1 ")

print ("Show Min and Max in any stock - think - tech ltd")

plt.show()

גרף נתוני מקור כולל רעשים :

קובץ

HES

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import find_peaks

from scipy.signal import find_peaks
import numpy as np
import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt
days=10
total=480*days
total=1000
HES=pd.read_csv(r'D:\Stocks\sp-500\HES.csv',  nrows=total)


HES['x'] = range(len(HES))
#print(HES)
y = HES['Open'].values
x = HES['x'].values

fig = plt.figure()
ax = fig.subplots()
plt.title("data : pure  roboTronix.co.il")

ax.plot(x,y)

y2=HES['Open'].rolling(40,10).mean()
y1=HES['Open'].rolling(40,10).mean()


#print(y)
#print(y)
#defining the x and y arrays


fig = plt.figure()
ax = fig.subplots()

plt.title("data : reduce noise   roboTronix.co.il")

ax.plot(x,y2)

print("data analysis " )
fig = plt.figure()
ax = fig.subplots()
ax.plot(x,y)
ax.plot(x,y2,color='red')
plt.title("data : reduce noise  roboTronix.co.il")
#print(y)
plt.show()



fig = plt.figure()
ax = fig.subplots()
ax.plot(x,y)
y2=y2+0.2
ax.plot(x,y2,color='red')
plt.title("data : reduce noise  roboTronix.co.il")
#print(y)
plt.show()




fig = plt.figure()
ax = fig.subplots()
x3=x-30
y3=y2
ax.plot(x,y)
ax.plot(x3,y3,color='red')
plt.title("data : reduce noise  roboTronix.co.il")
#print(y)
plt.show()



fig = plt.figure()
ax = fig.subplots()

y3=y2
y4=y2-0.4
ax.plot(x,y)

ax.plot(x3,y4,color='red')
ax.plot(x3,y3,color='red')
ax.plot(x3,y4,color='red')
plt.title("data : reduce noise envelop  roboTronix.co.il")
#print(y)
plt.show()


fig = plt.figure()
ax = fig.subplots()
ax.plot(x,y)
ax.plot(x3,y1,color='green')
ax.plot(x3,y4,color='red')
ax.plot(x3,y3,color='red')
ax.plot(x3,y4,color='red')
plt.title("data : reduce noise envelop + best fit  roboTronix.co.il")
#print(y)
plt.show()

peaks = find_peaks(y2, height = 1, threshold =  0, distance = None , width=10)
#print ("Peaks : " ,peaks)
height = peaks[1]['peak_heights'] #list of the heights of the peaks
peak_pos = x[peaks[0]] #list of the peaks positions

#Finding the minima
ym = y3*-1

minima = find_peaks(ym ,distance = 70)
min_pos = x3[minima[0]] #list of the minima positions
min_height = ym[minima[0]] #list of the mirrored minima heights
#Plotting
fig = plt.figure()
ax = fig.subplots()
plt.title("data : Min , Max points ,  roboTronix.co.il")
ax.plot(x2,y3)
ax.scatter(peak_pos, height, color = 'r', s = 25, marker = 'D', label = 'Maxs')
ax.scatter(min_pos, min_height*-1, color = 'green', s = 10, marker = 'P', label = 'Mins')
ax.legend()
ax.grid()
#print ("Event Stock Corrlation Graph plot ver 1.1 ")
print ("Show  Min and Max roboTronix.co.il")
plt.show()

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import numpy as np

import matplotlib.pyplot as plt

from scipy.signal import find_peaks

import numpy as np

import seaborn as sns

import pandas as pd

import matplotlib.pyplot as plt

days=10

total=480*days

total=1000

HES=pd.read_csv(r'D:\Stocks\sp-500\HES.csv', nrows=total)

HES['x'] = range(len(HES))

#print(HES)

y = HES['Open'].values

x = HES['x'].values

fig = plt.figure()

ax = fig.subplots()

plt.title("data : pure roboTronix.co.il")

ax.plot(x,y)

y2=HES['Open'].rolling(40,10).mean()

y1=HES['Open'].rolling(40,10).mean()

#print(y)

#defining the x and y arrays

fig = plt.figure()

ax = fig.subplots()

plt.title("data : reduce noise roboTronix.co.il")

ax.plot(x,y2)

print("data analysis " )

fig = plt.figure()

ax = fig.subplots()

ax.plot(x,y)

ax.plot(x,y2,color='red')

plt.title("data : reduce noise roboTronix.co.il")

#print(y)

plt.show()

fig = plt.figure()

ax = fig.subplots()

ax.plot(x,y)

y2=y2+0.2

ax.plot(x,y2,color='red')

plt.title("data : reduce noise roboTronix.co.il")

#print(y)

plt.show()

fig = plt.figure()

ax = fig.subplots()

x3=x-30

y3=y2

ax.plot(x,y)

ax.plot(x3,y3,color='red')

plt.title("data : reduce noise roboTronix.co.il")

#print(y)

plt.show()

fig = plt.figure()

ax = fig.subplots()

y3=y2

y4=y2-0.4

ax.plot(x,y)

ax.plot(x3,y4,color='red')

ax.plot(x3,y3,color='red')

ax.plot(x3,y4,color='red')

plt.title("data : reduce noise envelop roboTronix.co.il")

#print(y)

plt.show()

fig = plt.figure()

ax = fig.subplots()

ax.plot(x,y)

ax.plot(x3,y1,color='green')

ax.plot(x3,y4,color='red')

ax.plot(x3,y3,color='red')

ax.plot(x3,y4,color='red')

plt.title("data : reduce noise envelop + best fit roboTronix.co.il")

#print(y)

plt.show()

peaks = find_peaks(y2, height = 1, threshold = 0, distance = None , width=10)

#print ("Peaks : " ,peaks)

height = peaks[1]['peak_heights'] #list of the heights of the peaks

peak_pos = x[peaks[0]] #list of the peaks positions

#Finding the minima

ym = y3*-1

minima = find_peaks(ym ,distance = 70)

min_pos = x3[minima[0]] #list of the minima positions

min_height = ym[minima[0]] #list of the mirrored minima heights

#Plotting

fig = plt.figure()

ax = fig.subplots()

plt.title("data : Min , Max points , roboTronix.co.il")

ax.plot(x2,y3)

ax.scatter(peak_pos, height, color = 'r', s = 25, marker = 'D', label = 'Maxs')

ax.scatter(min_pos, min_height*-1, color = 'green', s = 10, marker = 'P', label = 'Mins')

ax.legend()

ax.grid()

#print ("Event Stock Corrlation Graph plot ver 1.1 ")

print ("Show Min and Max roboTronix.co.il")

plt.show()

חישוב נגזרת

import matplotlib.pyplot as plt
import numpy as np
 
#Credit
#https://www.math.ubc.ca/~pwalls/math-python/integration/riemann-sums/
 
def derivative(f,a,method='central',h=0.01):
'''Compute the difference formula for f'(a) with step size h.
 
Parameters
----------
f : function
Vectorized function of one variable
a : number
Compute derivative at x = a
method : string
Difference formula: 'forward', 'backward' or 'central'
h : number
Step size in difference formula
 
Returns
-------
float
Difference formula:
central: f(a+h) - f(a-h))/2h
forward: f(a+h) - f(a))/h
backward: f(a) - f(a-h))/h
'''
if method == 'central':
return (f(a + h) - f(a - h))/(2*h)
elif method == 'forward':
return (f(a + h) - f(a))/h
elif method == 'backward':
return (f(a) - f(a - h))/h
else:
raise ValueError("Method must be 'central', 'forward' or 'backward'.")
 
x = np.linspace(-2,2,100)
f = lambda x: (2*x**2 + 2*x + 1)
y = f(x)
 
dydx = derivative(f,x)
print("dydx",type(dydx) , "\r\n",dydx)
 
# axes
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.spines['left'].set_position('center')
ax.spines['bottom'].set_position('center')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
 
# plot the functions
plt.plot(x,y, 'b', label='y')
 
plt.plot(x,dydx, 'r', label='dydx')
 
plt.legend(loc='upper left')
 
# show the plot
plt.show()

import matplotlib.pyplot as plt

import numpy as np

#Credit

#https://www.math.ubc.ca/~pwalls/math-python/integration/riemann-sums/

def derivative(f,a,method='central',h=0.01):

'''Compute the difference formula for f'(a) with step size h.

Parameters

----------

f : function

Vectorized function of one variable

a : number

Compute derivative at x = a

method : string

Difference formula: 'forward', 'backward' or 'central'

h : number

Step size in difference formula

Returns

-------

float

Difference formula:

central: f(a+h) - f(a-h))/2h

forward: f(a+h) - f(a))/h

backward: f(a) - f(a-h))/h

'''

if method == 'central':

return (f(a + h) - f(a - h))/(2*h)

elif method == 'forward':

return (f(a + h) - f(a))/h

elif method == 'backward':

return (f(a) - f(a - h))/h

else:

raise ValueError("Method must be 'central', 'forward' or 'backward'.")

x = np.linspace(-2,2,100)

f = lambda x: (2*x**2 + 2*x + 1)

y = f(x)

dydx = derivative(f,x)

print("dydx",type(dydx) , "\r\n",dydx)

# axes

fig = plt.figure()

ax = fig.add_subplot(1, 1, 1)

ax.spines['left'].set_position('center')

ax.spines['bottom'].set_position('center')

ax.spines['right'].set_color('none')

ax.spines['top'].set_color('none')

ax.xaxis.set_ticks_position('bottom')

ax.yaxis.set_ticks_position('left')

# plot the functions

plt.plot(x,y, 'b', label='y')

plt.plot(x,dydx, 'r', label='dydx')

plt.legend(loc='upper left')

# show the plot

plt.show()

קורלציית פירסון

https://towardsdatascience.com/python-statistics-for-beginners-pearson-correlation-coefficient-69c9b1ef17f7

גרפים – יצוג גרפים קריאת נתונים

קריאת מידע וניתוח , והצגה בגרף – מקובץ CSV

קריאת מידע וניתוח , והצגה בגרף מ SDCARD

קריאת מידע וניתוח , והצגה בגרף מ JSON XML

קריאת מידע וניתוח , והצגה בגרף מ WIFI SOCKET

תרגיל כיתה – ניסוי מעבדה – DSP UART

קליטת נתונים על ידי מיקרו בקר – שליחת נתונים בזמן אמת ב UART למחשב PC
קלוט על ידי מיקרו מעבד כ 4 שניות של נתונים , ב 10 ביט והעבר ל PC
הצג על מחשב PC גרף בפיטון את האות הנקלט על ידי UART
בצע קונבולוציה – של חלון 10 – הצג על גרף
חשב והדפס ממוצע, סטיית תקן , ערך גבוה ביותר וערך נמוך — אחרי החלקה
בצע TOGGLE בלד כתום כל דגימה
בתחילת דגימה הדלק לד ירוק , סוף דגימה כבה כל הלדים , המתן 1 דקה בין דגימה לדגימה

תרגיל כיתה – ניסוי מעבדה – DSP WIFI + ROUTER

קליטת נתונים על ידי מיקרו בקר – שליחת נתונים בזמן אמת ב WIFI CLIENT SERVER למחשב PC
קלוט על ידי מיקרו מעבד כ 4 שניות של נתונים , ב 10 ביט והעבר ל PC
הצג על מחשב PC גרף בפיטון את האות הנקלט על ידי שימוש ב SOCKET , כאשר ה PC הינו שרת , מיקרו בקר לקוח
בצע קונבולוציה – של חלון 10 – הצג על גרף
חשב והדפס ממוצע, סטיית תקן , ערך גבוה ביותר וערך נמוך — אחרי החלקה
בצע TOGGLE בלד כתום כל דגימה
בתחילת דגימה הדלק לד ירוק , סוף דגימה כבה כל הלדים , המתן 1 דקה בין דגימה לדגימה

הצגת גרפים בארדואינו :

https://arduinogetstarted.com/tutorials/arduino-serial-plotter

/*
 * Created by ArduinoGetStarted.com
 *
 * This example code is in the public domain
 *
 * Tutorial page: https://arduinogetstarted.com/tutorials/arduino-serial-plotter
 */

void setup() {
  Serial.begin(9600); 
}

void loop() {
  int y1 = analogRead(A0);

  Serial.println(y1);

  delay(100);
}

* Created by ArduinoGetStarted.com

* This example code is in the public domain

* Tutorial page: https://arduinogetstarted.com/tutorials/arduino-serial-plotter

void setup() {

Serial.begin(9600);

}

void loop() {

int y1 = analogRead(A0);

Serial.println(y1);

delay(100);

}

למה צריך DSP

גרפים ופוקציה

משתנה למבדה

x = lambda a: a + 10
print(x(5))

1 2	x = lambda a: a + 10 print(x(5))

פלט 15

פלוט :13

# learn python lesson 4 , www.robotronix.co.il
 
import matplotlib.pyplot as plt
import numpy as np
 
x = np.linspace(-2,2,100)
 
# the function
y = x**2-2
 
# setting the axes at the centre
fig = plt.figure()
 
# Add an Axes to the figure as part of a subplot arrangement. // default: (1, 1, 1)
ax = fig.add_subplot(1, 1, 1)
 
ax.spines['left'].set_position('center')
ax.spines['left'].set_color('blue')
 
ax.spines['bottom'].set_position('center')
ax.spines['bottom'].set_color('green')
 
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
 
# plot the function r='red'
plt.plot(x,y, 'red')
 
# show the plot
plt.show()
 
import matplotlib.pyplot as plt
import numpy as np
 
# 20 linearly spaced numbers
x = np.linspace( -np.pi , np.pi ,20)
print(x)
 
# function
y = np.sin(x)
print("print y array \r\n",y)
 
# setting the axes at the centre
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.spines['left'].set_position('center')
ax.spines['bottom'].set_position('center')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
 
# plot the function
plt.plot(x,y, 'b') # b = blue
 
# show the plot
plt.show()
 
import matplotlib.pyplot as plt
import numpy as np
 
# 20 linearly spaced numbers
x = np.linspace(-np.pi ,np.pi ,60)
 
# function
y1 = 1*np.sin(x)
 
y2 = 2*np.sin(2*x)
 
y3 = 3*np.sin(4*x)
 
# axes
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.spines['left'].set_position('center')
ax.spines['bottom'].set_position('center')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
 
# plot the functions
#x = np.linspace(-np.pi ,np.pi ,20)
plt.plot(x ,y1, 'b', label='y1=sin(x)')
plt.plot(x ,y2, 'r', label='y2=2sin(2x)')
plt.plot(x ,y3, 'y', label='y3=3sin(4x)')
 
plt.legend(loc='upper left')
 
# show the plot
plt.show()
 
import matplotlib.pyplot as plt
import numpy as np
 
# 20 linearly spaced numbers
x = np.linspace(-np.pi,np.pi,20)
 
# function
y1 = 1*np.sin(x)
 
y2 = 1*np.cos(x)
 
# axes
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.spines['left'].set_position('center')
ax.spines['bottom'].set_position('center')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
 
# plot the functions
plt.plot(x,y1, 'b', label='y1=sin(x)')
plt.plot(x,y2, 'r', label='y2=cos(x)')
 
plt.legend(loc='upper right')
 
# show the plot
plt.show()

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# learn python lesson 4 , www.robotronix.co.il

import matplotlib.pyplot as plt

import numpy as np

x = np.linspace(-2,2,100)

# the function

y = x**2-2

# setting the axes at the centre

fig = plt.figure()

# Add an Axes to the figure as part of a subplot arrangement. // default: (1, 1, 1)

ax = fig.add_subplot(1, 1, 1)

ax.spines['left'].set_position('center')

ax.spines['left'].set_color('blue')

ax.spines['bottom'].set_position('center')

ax.spines['bottom'].set_color('green')

ax.spines['right'].set_color('none')

ax.spines['top'].set_color('none')

ax.xaxis.set_ticks_position('bottom')

ax.yaxis.set_ticks_position('left')

# plot the function r='red'

plt.plot(x,y, 'red')

# show the plot

plt.show()

import matplotlib.pyplot as plt

import numpy as np

# 20 linearly spaced numbers

x = np.linspace( -np.pi , np.pi ,20)

print(x)

# function

y = np.sin(x)

print("print y array \r\n",y)

# setting the axes at the centre

fig = plt.figure()

ax = fig.add_subplot(1, 1, 1)

ax.spines['left'].set_position('center')

ax.spines['bottom'].set_position('center')

ax.spines['right'].set_color('none')

ax.spines['top'].set_color('none')

ax.xaxis.set_ticks_position('bottom')

ax.yaxis.set_ticks_position('left')

# plot the function

plt.plot(x,y, 'b') # b = blue

# show the plot

plt.show()

import matplotlib.pyplot as plt

import numpy as np

# 20 linearly spaced numbers

x = np.linspace(-np.pi ,np.pi ,60)

# function

y1 = 1*np.sin(x)

y2 = 2*np.sin(2*x)

y3 = 3*np.sin(4*x)

# axes

fig = plt.figure()

ax = fig.add_subplot(1, 1, 1)

ax.spines['left'].set_position('center')

ax.spines['bottom'].set_position('center')

ax.spines['right'].set_color('none')

ax.spines['top'].set_color('none')

ax.xaxis.set_ticks_position('bottom')

ax.yaxis.set_ticks_position('left')

# plot the functions

#x = np.linspace(-np.pi ,np.pi ,20)

plt.plot(x ,y1, 'b', label='y1=sin(x)')

plt.plot(x ,y2, 'r', label='y2=2sin(2x)')

plt.plot(x ,y3, 'y', label='y3=3sin(4x)')

plt.legend(loc='upper left')

# show the plot

plt.show()

import matplotlib.pyplot as plt

import numpy as np

# 20 linearly spaced numbers

x = np.linspace(-np.pi,np.pi,20)

# function

y1 = 1*np.sin(x)

y2 = 1*np.cos(x)

# axes

fig = plt.figure()

ax = fig.add_subplot(1, 1, 1)

ax.spines['left'].set_position('center')

ax.spines['bottom'].set_position('center')

ax.spines['right'].set_color('none')

ax.spines['top'].set_color('none')

ax.xaxis.set_ticks_position('bottom')

ax.yaxis.set_ticks_position('left')

# plot the functions

plt.plot(x,y1, 'b', label='y1=sin(x)')

plt.plot(x,y2, 'r', label='y2=cos(x)')

plt.legend(loc='upper right')

# show the plot

plt.show()

גרף e

Python
import matplotlib.pyplot as plt
import numpy as np
 
# 20 linearly spaced numbers
x = np.linspace(-10,10,200)
 
# function
y1 = 1*np.exp(x)
y2 = -1*np.exp(x)
 
# axes
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.spines['left'].set_position('center')
ax.spines['bottom'].set_position('center')
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
 
# plot the functions
plt.plot(x,y1, 'b', label='y1=exp(x)')
plt.plot(x,y2, 'r', label='y2=-exp(x)')
 
plt.legend(loc='upper left')
 
# show the plot
plt.show()
 
print("x",type(x))
print("y1",type(y1))

Python

import matplotlib.pyplot as plt

import numpy as np

# 20 linearly spaced numbers

x = np.linspace(-10,10,200)

# function

y1 = 1*np.exp(x)

y2 = -1*np.exp(x)

# axes

fig = plt.figure()

ax = fig.add_subplot(1, 1, 1)

ax.spines['left'].set_position('center')

ax.spines['bottom'].set_position('center')

ax.spines['right'].set_color('none')

ax.spines['top'].set_color('none')

ax.xaxis.set_ticks_position('bottom')

ax.yaxis.set_ticks_position('left')

# plot the functions

plt.plot(x,y1, 'b', label='y1=exp(x)')

plt.plot(x,y2, 'r', label='y2=-exp(x)')

plt.legend(loc='upper left')

# show the plot

plt.show()

print("x",type(x))

print("y1",type(y1))

דרך שניה לקרחת את הפונקציה y = 2*x**2 + 2*x + 1 , לגזור אותה אלגברית ואז להציב – גם זה טוב ! אבל זה בתנאי שיש פונקציה

import numpy as np
import matplotlib.pyplot as plt

# Define the function y = 2*x**2 + 2*x + 1
def y(x):
    return 2*x**2 + 2*x + 1

# Define the derivative of the function
def y_derivative(x):
    return 4*x + 2

# Generate x values from -10 to 10 in steps of 20
x = np.arange(-10, 10, 20)

# Calculate y and y_derivative for each x value
y_values = y(x)
y_derivative_values = y_derivative(x)

import numpy as np

import matplotlib.pyplot as plt

# Define the function y = 2*x**2 + 2*x + 1

def y(x):

return 2*x**2 + 2*x + 1

# Define the derivative of the function

def y_derivative(x):

return 4*x + 2

# Generate x values from -10 to 10 in steps of 20

x = np.arange(-10, 10, 20)

# Calculate y and y_derivative for each x value

y_values = y(x)

y_derivative_values = y_derivative(x)

אינטגל :

# learn python lesson 4 , www.robotronix.co.il
import matplotlib.pyplot as plt
import numpy as np
 
#Credit
#https://www.math.ubc.ca/~pwalls/math-python/integration/riemann-sums/
 
f = lambda x : 2*x**2+5
a = 0; b = 5; N = 50
n = 10 # Use n*N+1 points to plot the function smoothly
 
x = np.linspace(a,b,N+1)
y = f(x)
 
X = np.linspace(a,b,n*N+1)
Y = f(X)
 
plt.figure(figsize=(15,5))
 
plt.subplot(1,3,2)
plt.plot(X,Y,'b')
x_mid = (x[:-1] + x[1:])/2 # Midpoints
y_mid = f(x_mid)
plt.plot(x_mid,y_mid,'b.',markersize=10)
plt.bar(x_mid,y_mid,width=(b-a)/N,alpha=0.2,edgecolor='b')
plt.title('Midpoint Riemann Sum, N = {}'.format(N))
 
plt.show()

# learn python lesson 4 , www.robotronix.co.il

import matplotlib.pyplot as plt

import numpy as np

#Credit

#https://www.math.ubc.ca/~pwalls/math-python/integration/riemann-sums/

f = lambda x : 2*x**2+5

a = 0; b = 5; N = 50

n = 10 # Use n*N+1 points to plot the function smoothly

x = np.linspace(a,b,N+1)

y = f(x)

X = np.linspace(a,b,n*N+1)

Y = f(X)

plt.figure(figsize=(15,5))

plt.subplot(1,3,2)

plt.plot(X,Y,'b')

x_mid = (x[:-1] + x[1:])/2 # Midpoints

y_mid = f(x_mid)

plt.plot(x_mid,y_mid,'b.',markersize=10)

plt.bar(x_mid,y_mid,width=(b-a)/N,alpha=0.2,edgecolor='b')

plt.title('Midpoint Riemann Sum, N = {}'.format(N))

plt.show()

פילטרים : low pass , band pass ; hi -pass filters

תקרגיל כיתה :

הרץ את הדוגמאות הבאות

1. https://github.com/curiores/ArduinoTutorials/blob/main/BasicFilters/Design/LowPass/LowPassFilter.ipynb

הרץ את התרגיל בארדואינו :

2. https://github.com/curiores/ArduinoTutorials/tree/main/BasicFilters/ArduinoImplementations/LowPass/SimpleExamples

import numpy as np
from scipy.signal import butter, lfilter, freqz
import matplotlib.pyplot as plt


def butter_lowpass(cutoff, fs, order=5):
    nyq = 0.5 * fs
    normal_cutoff = cutoff / nyq
    b, a = butter(order, normal_cutoff, btype='low', analog=False)
    return b, a

def butter_lowpass_filter(data, cutoff, fs, order=5):
    b, a = butter_lowpass(cutoff, fs, order=order)
    y = lfilter(b, a, data)
    return y


# Setting standard filter requirements.
order = 6
fs = 30.0       
cutoff = 3.667  

b, a = butter_lowpass(cutoff, fs, order)

# Plotting the frequency response.
w, h = freqz(b, a, worN=8000)
plt.subplot(2, 1, 1)
plt.plot(0.5*fs*w/np.pi, np.abs(h), 'b')
plt.plot(cutoff, 0.5*np.sqrt(2), 'ko')
plt.axvline(cutoff, color='k')
plt.xlim(0, 0.5*fs)
plt.title("Lowpass Filter Frequency Response")
plt.xlabel('Frequency [Hz]')
plt.grid()


# Creating the data for filteration
T = 5.0         # value taken in seconds
n = int(T * fs) # indicates total samples
t = np.linspace(0, T, n, endpoint=False)

data = np.sin(1.2*2*np.pi*t) + 1.5*np.cos(9*2*np.pi*t) + 0.5*np.sin(12.0*2*np.pi*t)

# Filtering and plotting
y = butter_lowpass_filter(data, cutoff, fs, order)

plt.subplot(2, 1, 2)
plt.plot(t, data, 'b-', label='data')
plt.plot(t, y, 'g-', linewidth=2, label='filtered data')
plt.xlabel('Time [sec]')
plt.grid()
plt.legend()

plt.subplots_adjust(hspace=0.35)
plt.show()

import numpy as np

from scipy.signal import butter, lfilter, freqz

import matplotlib.pyplot as plt

def butter_lowpass(cutoff, fs, order=5):

nyq = 0.5 * fs

normal_cutoff = cutoff / nyq

b, a = butter(order, normal_cutoff, btype='low', analog=False)

return b, a

def butter_lowpass_filter(data, cutoff, fs, order=5):

b, a = butter_lowpass(cutoff, fs, order=order)

y = lfilter(b, a, data)

return y

# Setting standard filter requirements.

order = 6

fs = 30.0

cutoff = 3.667

b, a = butter_lowpass(cutoff, fs, order)

# Plotting the frequency response.

w, h = freqz(b, a, worN=8000)

plt.subplot(2, 1, 1)

plt.plot(0.5*fs*w/np.pi, np.abs(h), 'b')

plt.plot(cutoff, 0.5*np.sqrt(2), 'ko')

plt.axvline(cutoff, color='k')

plt.xlim(0, 0.5*fs)

plt.title("Lowpass Filter Frequency Response")

plt.xlabel('Frequency [Hz]')

plt.grid()

# Creating the data for filteration

T = 5.0 # value taken in seconds

n = int(T * fs) # indicates total samples

t = np.linspace(0, T, n, endpoint=False)

data = np.sin(1.2*2*np.pi*t) + 1.5*np.cos(9*2*np.pi*t) + 0.5*np.sin(12.0*2*np.pi*t)

# Filtering and plotting

y = butter_lowpass_filter(data, cutoff, fs, order)

plt.subplot(2, 1, 2)

plt.plot(t, data, 'b-', label='data')

plt.plot(t, y, 'g-', linewidth=2, label='filtered data')

plt.xlabel('Time [sec]')

plt.grid()

plt.legend()

plt.subplots_adjust(hspace=0.35)

plt.show()

גלי קול פיטון

תרגיל כיתה לבנות ספקטרום אנלייזר

import cv2
 
image = cv2.imread('rgb.png')
B, G, R = cv2.split(image)
# Corresponding channels are separated
 
cv2.imshow("original", image)
cv2.waitKey(0)
 
cv2.imshow("blue", B)
cv2.waitKey(0)
 
cv2.imshow("Green", G)
cv2.waitKey(0)
 
cv2.imshow("red", R)
cv2.waitKey(0)
 
cv2.destroyAllWindows()

import cv2

image = cv2.imread('rgb.png')

B, G, R = cv2.split(image)

# Corresponding channels are separated

cv2.imshow("original", image)

cv2.waitKey(0)

cv2.imshow("blue", B)

cv2.waitKey(0)

cv2.imshow("Green", G)

cv2.waitKey(0)

cv2.imshow("red", R)

cv2.waitKey(0)

cv2.destroyAllWindows()

cv2.add(img1, img2)

1	cv2.add(img1, img2)

# Python program to illustrate
# arithmetic operation of
# addition of two images

# organizing imports
import cv2
import numpy as np

# path to input images are specified and
# images are loaded with imread command
image1 = cv2.imread('input1.jpg')
image2 = cv2.imread('input2.jpg')

# cv2.addWeighted is applied over the
# image inputs with applied parameters
weightedSum = cv2.addWeighted(image1, 0.5, image2, 0.4, 0)

# the window showing output image
# with the weighted sum
cv2.imshow('Weighted Image', weightedSum)

# De-allocate any associated memory usage
if cv2.waitKey(0) & 0xff == 27:
	cv2.destroyAllWindows()

# Python program to illustrate

# arithmetic operation of

# addition of two images

# organizing imports

import cv2

import numpy as np

# path to input images are specified and

# images are loaded with imread command

image1 = cv2.imread('input1.jpg')

image2 = cv2.imread('input2.jpg')

# cv2.addWeighted is applied over the

# image inputs with applied parameters

weightedSum = cv2.addWeighted(image1, 0.5, image2, 0.4, 0)

# the window showing output image

# with the weighted sum

cv2.imshow('Weighted Image', weightedSum)

# De-allocate any associated memory usage

if cv2.waitKey(0) & 0xff == 27:

cv2.destroyAllWindows()

חיסור תמונות

# Python program to illustrate
# arithmetic operation of
# subtraction of pixels of two images
 
# organizing imports
import cv2
import numpy as np
   
# path to input images are specified and 
# images are loaded with imread command
image1 = cv2.imread('input1.jpg')
image2 = cv2.imread('input2.jpg')
 
# cv2.subtract is applied over the
# image inputs with applied parameters
sub = cv2.subtract(image1, image2)
 
# the window showing output image
# with the subtracted image
cv2.imshow('Subtracted Image', sub)
 
# De-allocate any associated memory usage 
if cv2.waitKey(0) & 0xff == 27:
    cv2.destroyAllWindows()

# Python program to illustrate

# arithmetic operation of

# subtraction of pixels of two images

# organizing imports

import cv2

import numpy as np

# path to input images are specified and

# images are loaded with imread command

image1 = cv2.imread('input1.jpg')

image2 = cv2.imread('input2.jpg')

# cv2.subtract is applied over the

# image inputs with applied parameters

sub = cv2.subtract(image1, image2)

# the window showing output image

# with the subtracted image

cv2.imshow('Subtracted Image', sub)

# De-allocate any associated memory usage

if cv2.waitKey(0) & 0xff == 27:

cv2.destroyAllWindows()

פעלות לוגיות על תמונה AND

# Python program to illustrate
# arithmetic operation of
# bitwise AND of two images
    
# organizing imports
import cv2
import numpy as np
    
# path to input images are specified and  
# images are loaded with imread command 
img1 = cv2.imread('input1.png') 
img2 = cv2.imread('input2.png')
 
# cv2.bitwise_and is applied over the
# image inputs with applied parameters
dest_and = cv2.bitwise_and(img2, img1, mask = None)
 
# the window showing output image
# with the Bitwise AND operation
# on the input images
cv2.imshow('Bitwise And', dest_and)
  
# De-allocate any associated memory usage 
if cv2.waitKey(0) & 0xff == 27:
    cv2.destroyAllWindows()

# Python program to illustrate

# arithmetic operation of

# bitwise AND of two images

# organizing imports

import cv2

import numpy as np

# path to input images are specified and

# images are loaded with imread command

img1 = cv2.imread('input1.png')

img2 = cv2.imread('input2.png')

# cv2.bitwise_and is applied over the

# image inputs with applied parameters

dest_and = cv2.bitwise_and(img2, img1, mask = None)

# the window showing output image

# with the Bitwise AND operation

# on the input images

cv2.imshow('Bitwise And', dest_and)

# De-allocate any associated memory usage

if cv2.waitKey(0) & 0xff == 27:

cv2.destroyAllWindows()

OR בין שתי תמונות

# Python program to illustrate
# arithmetic operation of
# bitwise OR of two images
    
# organizing imports
import cv2
import numpy as np
    
# path to input images are specified and  
# images are loaded with imread command 
img1 = cv2.imread('input1.png') 
img2 = cv2.imread('input2.png')
 
# cv2.bitwise_or is applied over the
# image inputs with applied parameters
dest_or = cv2.bitwise_or(img2, img1, mask = None)
 
# the window showing output image
# with the Bitwise OR operation
# on the input images
cv2.imshow('Bitwise OR', dest_or)
  
# De-allocate any associated memory usage 
if cv2.waitKey(0) & 0xff == 27:
    cv2.destroyAllWindows()

# Python program to illustrate

# arithmetic operation of

# bitwise OR of two images

# organizing imports

import cv2

import numpy as np

# path to input images are specified and

# images are loaded with imread command

img1 = cv2.imread('input1.png')

img2 = cv2.imread('input2.png')

# cv2.bitwise_or is applied over the

# image inputs with applied parameters

dest_or = cv2.bitwise_or(img2, img1, mask = None)

# the window showing output image

# with the Bitwise OR operation

# on the input images

cv2.imshow('Bitwise OR', dest_or)

# De-allocate any associated memory usage

if cv2.waitKey(0) & 0xff == 27:

cv2.destroyAllWindows()

XOR בין שתי תמונות

# Python program to illustrate
# arithmetic operation of
# bitwise XOR of two images
    
# organizing imports
import cv2
import numpy as np
    
# path to input images are specified and  
# images are loaded with imread command 
img1 = cv2.imread('input1.png') 
img2 = cv2.imread('input2.png')
 
# cv2.bitwise_xor is applied over the
# image inputs with applied parameters
dest_xor = cv2.bitwise_xor(img1, img2, mask = None)
 
# the window showing output image
# with the Bitwise XOR operation
# on the input images
cv2.imshow('Bitwise XOR', dest_xor)
  
# De-allocate any associated memory usage 
if cv2.waitKey(0) & 0xff == 27:
    cv2.destroyAllWindows()

# Python program to illustrate

# arithmetic operation of

# bitwise XOR of two images

# organizing imports

import cv2

import numpy as np

# path to input images are specified and

# images are loaded with imread command

img1 = cv2.imread('input1.png')

img2 = cv2.imread('input2.png')

# cv2.bitwise_xor is applied over the

# image inputs with applied parameters

dest_xor = cv2.bitwise_xor(img1, img2, mask = None)

# the window showing output image

# with the Bitwise XOR operation

# on the input images

cv2.imshow('Bitwise XOR', dest_xor)

# De-allocate any associated memory usage

if cv2.waitKey(0) & 0xff == 27:

cv2.destroyAllWindows()

אופרטור NOT

# Python program to illustrate
# arithmetic operation of
# bitwise NOT on input image
    
# organizing imports
import cv2
import numpy as np
    
# path to input images are specified and  
# images are loaded with imread command 
img1 = cv2.imread('input1.png') 
img2 = cv2.imread('input2.png')
 
# cv2.bitwise_not is applied over the
# image input with applied parameters
dest_not1 = cv2.bitwise_not(img1, mask = None)
dest_not2 = cv2.bitwise_not(img2, mask = None)
 
# the windows showing output image
# with the Bitwise NOT operation
# on the 1st and 2nd input image
cv2.imshow('Bitwise NOT on image 1', dest_not1)
cv2.imshow('Bitwise NOT on image 2', dest_not2)
  
# De-allocate any associated memory usage 
if cv2.waitKey(0) & 0xff == 27:
    cv2.destroyAllWindows()

# Python program to illustrate

# arithmetic operation of

# bitwise NOT on input image

# organizing imports

import cv2

import numpy as np

# path to input images are specified and

# images are loaded with imread command

img1 = cv2.imread('input1.png')

img2 = cv2.imread('input2.png')

# cv2.bitwise_not is applied over the

# image input with applied parameters

dest_not1 = cv2.bitwise_not(img1, mask = None)

dest_not2 = cv2.bitwise_not(img2, mask = None)

# the windows showing output image

# with the Bitwise NOT operation

# on the 1st and 2nd input image

cv2.imshow('Bitwise NOT on image 1', dest_not1)

cv2.imshow('Bitwise NOT on image 2', dest_not2)

# De-allocate any associated memory usage

if cv2.waitKey(0) & 0xff == 27:

cv2.destroyAllWindows()

או למשל התוצאה הבאה

שינוי גודל תמונה – שימושי ביותר !

import cv2
import numpy as np
import matplotlib.pyplot as plt
 
image = cv2.imread(r"test.png", 1)
# Loading the image
 
half = cv2.resize(image, (0, 0), fx = 0.1, fy = 0.1)
bigger = cv2.resize(image, (1050, 1610))
 
stretch_near = cv2.resize(image, (780, 540),
               interpolation = cv2.INTER_LINEAR)
 
 
Titles =["Original", "Half", "Bigger", "Interpolation Nearest"]
images =[image, half, bigger, stretch_near]
count = 4
 
for i in range(count):
    plt.subplot(2, 2, i + 1)
    plt.title(Titles[i])
    plt.imshow(images[i])
 
plt.show()

import cv2

import numpy as np

import matplotlib.pyplot as plt

image = cv2.imread(r"test.png", 1)

# Loading the image

half = cv2.resize(image, (0, 0), fx = 0.1, fy = 0.1)

bigger = cv2.resize(image, (1050, 1610))

stretch_near = cv2.resize(image, (780, 540),

interpolation = cv2.INTER_LINEAR)

Titles =["Original", "Half", "Bigger", "Interpolation Nearest"]

images =[image, half, bigger, stretch_near]

count = 4

for i in range(count):

plt.subplot(2, 2, i + 1)

plt.title(Titles[i])

plt.imshow(images[i])

plt.show()

https://www.geeksforgeeks.org/opencv-python-tutorial/

קורס – DSP-L1 – 001 ומבוא לראיה ממוחשבת

קליטת מידע ממקרו בקר ב UART ב פייתון ועיבוד אותות – על המידע

קונבולוציה – חשוב moving average – filter

מציאת מינימום ומקסימום בנתונים

קורלציית פירסון

גרפים – יצוג גרפים קריאת נתונים

תרגיל כיתה – ניסוי מעבדה – DSP UART

תרגיל כיתה – ניסוי מעבדה – DSP WIFI + ROUTER

הצגת גרפים בארדואינו :

למה צריך DSP

פילטרים : low pass , band pass ; hi -pass filters

תקרגיל כיתה :

הרץ את הדוגמאות הבאות

כתיבת תגובה לבטל

קליטת מידע ממקרו בקר ב UART ב פייתון ועיבוד אותות – על המידע

קונבולוציה – חשוב moving average – filter

מציאת מינימום ומקסימום בנתונים

קורלציית פירסון

גרפים – יצוג גרפים קריאת נתונים

תרגיל כיתה – ניסוי מעבדה – DSP UART

תרגיל כיתה – ניסוי מעבדה – DSP WIFI + ROUTER

הצגת גרפים בארדואינו :

למה צריך DSP

פילטרים : low pass , band pass ; hi -pass filters

תקרגיל כיתה :

הרץ את הדוגמאות הבאות

אולי תאהב/י גם

מה זה ווקטור אנלייזר ?

צילום מוצר 360

מנורה לגידול ירקות

כתיבת תגובה לבטל