L1_2022

Какие методы необходимо применять в предлагаемой схеме?
Signal processing methods for telecommunication systems
А какие методы вообще существуют?

А какие сигналы мы обрабатываем?
Signal processing methods for telecommunication systems
А какие методы вообще существуют?

Analog signals Digital signals
Infinite precision in amplitude
Continuous signal
Continuous mathematics
Signal processing methods for telecommunication systems
Finite precision in amplitude
Only present at certain points
Discrete mathematics

Analog signals Digital signals
восстановление
разделение информационных потоков
подавление шумов
сжатие данных
фильтрация
усиление сигналов
Signal processing methods for telecommunication systems
спектральный анализ
линейная фильтрация
свертка традиционных типов
частотно-временной анализ
нелинейная обработка
адаптивная фильтрация
многоскоростная обработка
секционная свертка

Базовые операции
задержка сигналов
сложение сигналов
вычитание сигналов
умножение сигналов
деление сигналов
интегрирование
дифференцирование
фильтрация
Signal processing methods for telecommunication systems
спектральный анализ
линейная фильтрация
свертка традиционных типов
частотно-временной анализ
нелинейная обработка
адаптивная фильтрация
многоскоростная обработка
секционная свертка

Какие ещё виды обработки сигналов возможны?
Статистическая обработка сигналов
Обработка звука
Распознавание речи
Обработка изображений
Обработка видео
Обработка сигналов нужна для обработки информации
Включая экспериментальные данные
Signal processing methods for telecommunication systems

Signal processing methods
Today:
Part 1
Digital signals
Part 2
Basic programming in Python
Data types (in Python)
Correct notations in coding
Visualizing your signals
Signal processing methods for telecommunication systems

Why digital signals are useful?
Storage (generalized computer memory, compatibility)
Processing (coding, no mechanical or physical interactions)
Transmission (signal regeneration)
Signal processing methods for telecommunication systems

Transmission - signal regeneration
Signal processing methods for telecommunication systems
channel
TX
RX
+
1/G

Transmission - signal regeneration
Signal processing methods for telecommunication systems

Transmission - signal regeneration
Signal processing methods for telecommunication systems
G

Transmission - signal regeneration
Signal processing methods for telecommunication systems
G

Transmission - signal regeneration
Signal processing methods for telecommunication systems
G

Why digital signals are useful?
Storage (generalized computer memory, compatibility)
Processing (coding, no mechanical or physical interactions)
Transmission (signal regeneration)
Signal processing methods for telecommunication systems

Digital signals
One dimensional (for now)
Notation x[n] where «n» is an integer
Two sides sequences x : ℤ ? ℂ
n is a-dimensional
Analysis (by taking periodic measurements
Synthesis (program that generates a stream of samples)
Signal processing methods for telecommunication systems

Digital Signals – common signals
Delta Dirac function
Unit step function
Exponential decay
Sinusoidal signals
Signal processing methods for telecommunication systems

Delta signal
Signal processing methods for telecommunication systems

Unit Step function
Signal processing methods for telecommunication systems

Exponential functions
Signal processing methods for telecommunication systems

Sinusoidal functions
Signal processing methods for telecommunication systems

Signal classes
Finite length x[n] for n = 0,1, … ,N-1
Infinite length
Periodic
Finite-support
Signal processing methods for telecommunication systems

Finite length
Sequence notation
Vector notation
Easy to process in numerical packages (numPy)
Signal processing methods for telecommunication systems

Infinite length
Sequence notation
Good for theorems
Signal processing methods for telecommunication systems
ℤ

Periodic
N-periodic Sequence
The same information as finite signals with length N
Useful as a bridge between finite and infinite signals
Signal processing methods for telecommunication systems

Finite support signals
The same information as finite signals of length N
Useful as a bridge between finite and infinite signals
Signal processing methods for telecommunication systems

Energy and Power
Signal processing methods for telecommunication systems

Elementary operators
Delay
Scaling
Summation
Signal processing methods for telecommunication systems

Elementary operators
Delay
Signal processing methods for telecommunication systems

Elementary operators
Scaling
Signal processing methods for telecommunication systems

Elementary operators
Summation
Signal processing methods for telecommunication systems

Karplus-Strong algorithm - simplified
Signal processing methods for telecommunication systems

Karplus-Strong algorithm - simplified
Signal processing methods for telecommunication systems

Karplus-Strong algorithm - simplified
Signal processing methods for telecommunication systems

Karplus-Strong algorithm
Signal processing methods for telecommunication systems

Karplus-Strong algorithm
Signal processing methods for telecommunication systems

Karplus-Strong algorithm
Signal processing methods for telecommunication systems
Understanding the Karplus-Strong with Python (Synthetic Guitar Sounds Included) | Frolian's blog (flothesof.github.io)

Python 3 Anaconda - Spyder
Signal processing methods for telecommunication systems

Data types
Text Type: str
Numeric Types: int, float, complex
Sequence Types: list, tuple, range
Mapping Type: dict
Set Types: set, frozenset
Boolean Type: bool
Binary Types: bytes, bytearray, memoryview
Signal processing methods for telecommunication systems

Data types
You can assign the datatype manually (like programming in C)
OR
You can assign the datatype automatically
Signal processing methods for telecommunication systems

Data types
Some data types can interact
Try assigning the INTEGER 5 to variable ‘x’
Try assigning the float 7 to variable ‘y’
Multiply ‘x’ and ‘y’ and assign the result to ‘z’ (you type ‘z=x*y’)
Determine the data type of ‘z’
Signal processing methods for telecommunication systems

Importing libraries
For example try to print the number π
Signal processing methods for telecommunication systems

Importing functions
For example try to print the number π
Signal processing methods for telecommunication systems

Visualizing numbers – plotting a sine wave
Signal processing methods for telecommunication systems

Visualizing numbers – plotting a sine wave
Import module numpy
Import the function pyplot from the module matplotlib
Signal processing methods for telecommunication systems

Visualizing numbers – plotting a sine wave
Create time points for the x-axis
Numbers 0 until 10 with step size 0.01
(so you will get a range from [0 0.01 0.02 0.03 … 1] )
Signal processing methods for telecommunication systems

Visualizing numbers – plotting a sine wave
Create the amplitude points for each point in time
Use the sin function of the numpy module
(which you loaded and renamed as ‘np’
Signal processing methods for telecommunication systems

Visualizing numbers – plotting a sine wave
Signal processing methods for telecommunication systems

Visualizing numbers – plotting a sine wave
Create the plot.
Create the mark up for the plot
Signal processing methods for telecommunication systems

Visualizing numbers – plotting a sine wave
Display the plot.
Signal processing methods for telecommunication systems

Python
Try to adhere to good practice!!
Code is written once, but read multiple times.
Find ground rules here:
https://www.python.org/dev/peps/pep-0008/
Signal processing methods for telecommunication systems

Digital signals - limitations
1 + 1e20 - 1e20 = ?
1 + (1e20 - 1e20) = ?
Why?
Signal processing methods for telecommunication systems

(1e20 · 1e20) · 1e-20 = ?
1e20 · (1e20 · 1e-20) = ?
1e20 ·(1e20-1e20)= ?
1e20 · 1e20 – 1e20 · 1e20 = ?
Signal processing methods for telecommunication systems

Data types - Integer (int)
Signal processing methods for telecommunication systems

Floating point - Single precision (single) / double precision (double)
Signal processing methods for telecommunication systems
double precision (64 bit) floating numbers
-123.4567890123 = -1.234567890123 e2
sign
mantissa
(significant numbers)
exponent
sign
exponent
mantissa
(significant numbers)

Floating point - Single precision (single) / double precision (double)
Signal processing methods for telecommunication systems
double precision (64 bit) floating numbers
x = ± ( 1 + f ) · 2e
With fraction f
0 ≤ f < 1
In the interval where
252·f is an integer
0 ≤ 252·f < 252
Giving the decimal interval for e as
-1022 ≤ e ≤ 1023
Using offset binary representation

Floating point - Single precision (single) / double precision (double)
Signal processing methods for telecommunication systems
double precision (64 bit) floating numbers
x = ± ( 1 + f ) · 2e
With fraction f
0 ≤ f < 1
In the interval where
252·f is an integer
0 ≤ 252·f < 252
With exponent e as integer in the interval
-1022 ≤ e ≤ 1023

Не сравнивайте числа с плавающей запятой
Signal processing methods for telecommunication systems

Будьте аккуратны с числами с плавающей запятой
Точность уменьшается по мере роста величины
Ошибки переполнения и округления
Ракета-носитель «Ариан-5» 4 июня 1996 была подорвана на 34-й секунде полёта
Конвертация данных из 64-разрядного числа с плавающей запятой в 16-разрядное привела к зависанию компьютера
Точность ракет Patriot в 1991 (Война в Персидском заливе) была ограничена ошибкой округления
Signal processing methods for telecommunication systems

Data types - Fixed point
A fixed decimal point. Often used in low level devices.
example
10001011
23 + 2-1 + 2-3 + 2-4 = 8.675
Signal processing methods for telecommunication systems
Radix point

5 steps of a method/function in any language
1 Initialization
2 input
3 process
4 output
5 Termination
Signal processing methods for telecommunication systems

1) Define a function
def myFirstFunction(input):
print(“This will be the output, %s” %(input))
Signal processing methods for telecommunication systems

Importing the function
Calling the function
Signal processing methods for telecommunication systems

Data types
Text Type: str
Numeric Types: int, float, complex
Sequence Types: list, tuple, range
Mapping Type: dict
Set Types: set, frozenset
Boolean Type: bool
Binary Types: bytes, bytearray, memoryview
Signal processing methods for telecommunication systems

Writing a Karplus-Strong algorithm in Python
Signal processing methods for telecommunication systems

Writing a Karplus-Strong algorithm in Python
Generate a random input
Process the input using the algorithm
Show the Result
Save the result
Signal processing methods for telecommunication systems

Writing a Karplus-Strong algorithm in Python
Generate a random input
Signal processing methods for telecommunication systems
Understanding the Karplus-Strong with Python (Synthetic Guitar Sounds Included) | Frolian's blog (flothesof.github.io)

Data types
Text Type: str
Numeric Types: int, float, complex
Sequence Types: list, tuple, range
Mapping Type: dict
Set Types: set, frozenset
Boolean Type: bool
Binary Types: bytes, bytearray, memoryview
Signal processing methods for telecommunication systems

Writing a Karplus-Strong algorithm in Python
Generate a random input
numpy.random.uniform
Syntax
import numpy as np
np.random.uniform(low=0.0, high=1.0, size=None)
np.random.uniform(-1,1,1000)
Signal processing methods for telecommunication systems

Writing a Karplus-Strong algorithm in Python
Generate a random input
Process the input using the algorithm
Show the Result
Save the result
Signal processing methods for telecommunication systems

Writing a Karplus-Strong algorithm in Python
First solution
Signal processing methods for telecommunication systems
1) Create variable y as a copy of input x;
Append N zeros in front of y
OR
Create y as zeros for a lenght of x plus N
Replace the indexed values in y with values of x
2) Write a for-loop, which goes through all indexes of y
Replace indexed values of y, with a sum of the current value
plus scaled previous values

Writing a Karplus-Strong algorithm in Python
First solution
Signal processing methods for telecommunication systems

Writing a Karplus-Strong algorithm in Python
Second solution
Signal processing methods for telecommunication systems

Second solution
Writing a Karplus-Strong algorithm in Python
Signal processing methods for telecommunication systems
1
2
N
. . .
0
0
0
1
. . .
1
2
. . .
N
N+1
1/2
0
0
1/2

Second solution:
IIR Filter
b-coefficients
b0, b1, … bN-1 are 0
bN is 1
a-coefficients
a0 is 1
a1 .. aN-1 are 0
aN and aN+1 are 0.5
Writing a Karplus-Strong algorithm in Python
Signal processing methods for telecommunication systems

Writing a Karplus-Strong algorithm in Python
Signal processing methods for telecommunication systems

Save your output
Signal processing methods for telecommunication systems

Homework Task 1
Write your own function and generate outputs
(for example your own random number generator, a lookup table etc.)
Change the code to match «good practice»
Create a function that has multiple outputs, and optimize the memory usage and processing speed.
Retrieve the outputs from the function and display them (or plot them)
Signal processing methods for telecommunication systems
https://www.python.org/dev/peps/pep-0008/