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Title: Основы цифровой обработки сигналов: конспект лекции
Creators: Енученко Михаил Сергеевич; Пятак Иван Михайлович
Organization: Санкт-Петербургский политехнический университет Петра Великого
Imprint: Санкт-Петербург, 2022
Collection: Учебная и учебно-методическая литература; Общая коллекция
Subjects: Электрические сигналы — Обработка цифровая; Преобразования (мат.) Фурье; дискретизация; цифровые фильтры; учебники и пособия для вузов
UDC: 621.391(075.8)
Document type: Tutorial
File type: PDF
Language: Russian; English
Speciality code (FGOS): 11.04.02
Speciality group (FGOS): 110000 - Электроника, радиотехника и системы связи
DOI: 10.18720/SPBPU/5/tr22-3
Rights: Доступ по паролю из сети Интернет (чтение, печать, копирование)
Record key: RU\SPSTU\edoc\67537

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В конспекте лекций представлен материал, читаемый в рамках курса «Основы цифровой обработки сигналов». В конспекте отражён базовый материал, необходимый для освоения данного курса и для подготовки к практическим работам, семинарам, зачётам и экзаменам. Конспект лекций предназначен для магистров направлений 11.04.02 «Инфокоммуникационные технологии и системы связи» и 11.04.04 «Электроника и наноэлектроника».

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Table of Contents

  • Chapter 1 Basic knowledge
    • §1.1 Geometric progression and series
    • §1.2 Complex numbers
    • §1.3 Trigonometric expressions
      • 1.3.1 Basic formulas
      • 1.3.2 Integrals
      • 1.3.3 Orthogonality
    • §1.4 Linear operators
    • §1.5 Convolution
      • 1.5.1 Linear convolution
      • 1.5.2 Cyclic convolution
    • §1.6 Fourier series
    • §1.7 Integral Fourier Transform
      • 1.7.1 Definition
      • 1.7.2 Spectrum of signal
      • 1.7.3 Properties
      • 1.7.4 Sine and cosine transforms
      • 1.7.5 Shifting theorem
      • 1.7.6 Theorem of convolution
      • 1.7.7 General formulas
    • §1.8 Laplace Transform
      • 1.8.1 Definition and properties
      • 1.8.2 Impulse response and transfer function
      • 1.8.3 Poles and stability
    • §1.9 Z-transform
      • 1.9.1 Definition
      • 1.9.2 Connection with other transforms
    • §1.10 Dirac delta function
  • Chapter 2 Discrete sequences and systems
    • §2.1 Introduction
    • §2.2 Operations on discrete sequences
    • §2.3 Real-time systems
    • §2.4 Complexity metrics
    • §2.5 Unit delay element
    • §2.6 Discrete linear systems
    • §2.7 Time-invariance systems
  • Chapter 3 Sampling signals
    • §3.1 Ambiguity of signal presentation
    • §3.2 Discrete-Time Fourier transform
      • Home exercise: check that spectrum is periodic.
    • §3.3 Discrete sequence spectrum
    • §3.4 Signal reconstruction
      • Home exercise: get spectrum of the ideal DAC.
    • §3.5 Sampling low-pass signals
    • §3.6 Sampling band-pass signals
      • 3.6.1 Limits for band-pass sampling
      • 3.6.2 Inversion
      • 3.6.3 Recommendations
      • Home exercise: prove the statement above.
  • Chapter 4 Discrete Fourier Transform
    • §4.1 Derivation
    • §4.2 DFT example
    • §4.3 Properties of DFT
      • 4.3.1 Axes conversion (magnitude and frequency)
      • 4.3.2 How T, fs and N effect on spectrum?
      • 4.3.3 Linearity
      • Home exercises: proof linearity.
      • 4.3.4 Shifting theorem
      • 4.3.5 Theorem of convolution
      • Home exercise: proof theorem of convolution.
      • 4.3.6 Symmetry
    • §4.4 Symmetric DFT forms
    • §4.5 DFT matrix
    • §4.6 DFT of typical functions
      • 4.6.1 General rectangular function
      • 4.6.2 Symmetric rectangular function
      • 4.6.3 Constant level
      • 4.6.4 IDFT of rectangular function
      • 4.6.5 Complex signal
      • 4.6.6 Real signal
    • §4.7 Leakage
    • §4.8 Windows
    • §4.9 Signal to noise ratio in DFT
    • §4.10 Conclusion
  • Chapter 5 Fast Fourier Transform
    • §5.1 Algorithm
      • 5.1.1 Derivation
      • 5.1.2 Illustration of calculation flow
      • 5.1.3 Complexity of calculation
    • §5.2 Bit-reversed order
    • §5.3 Butterfly structures

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