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Fundamentals of Digital Signal Processing

Discover digital signal processing fundamentals, delve into signal design and analysis, learn about transforms, and develop practical OFDM systems focusing on modulation and demodulation. Gain insights into time and frequency domains.

Beginner

77 Lessons

20h

Certificate of Completion

AI-POWERED

Explanations

AI-POWERED

Explanations

This course includes

1 Assessment

41 Playgrounds

6 Quizzes

Course Overview

What You'll Learn

Course Content

Course Overview

We live in a world filled with signals which can be represented by sequences of numbers in a digital machine. These sequences of numbers can be manipulated by algorithms and have numerous applications in audio, images, video, wireless transmission and countless other domains. In this course, you’ll understand the field of digital signal processing with a focus on the design and analysis of signals, and algorithms. You’ll cover the DSP fundamentals of signals, systems and transforms. You’lll learn about th...Show More

We live in a world filled with signals which can be represented by sequences of numbers in a digital machine. These sequences of...Show More

TAKEAWAY SKILLS

Scientific Algorithms

Python Basics

What You'll Learn

An understanding of digital signals in the time and frequency domains

Familiarity with basic signal types and operations on them

An understanding of the sampling of signals

Knowledge about the Fourier transform and its properties

A working knowledge of Linear Time Invariant (LTI) systems and their applications

The ability to modulate and demodulate a digital signal and utilizing its spectrum

An understanding of digital signals in the time and frequency domains

Course Content

Introduction to Signals

4 Lessons

Learn how to use digital signal processing to analyze, transform, and apply signals.

The World of Signals

Signals Are Everywhere

What is Digital Signal Processing?

Applications of DSP

Basic Signals and Operations

8 Lessons

Unpack the core of generating and manipulating basic signals, including time and circular shifts.

How to Generate a Basic Sinusoid

A Unit Impulse Signal

Operations on Signals

How to Shift a Signal in Time Domain

The Relation between Time Shift and Phase

Circular Shift

Correlation between Signals

Activity 1

Complex Signals and the Frequency Domain

11 Lessons

Examine complex signals, their operations, phase rotations, and roles in digital signal processing.

Where Do Complex Numbers Come From?

Simplify Complex Operations

Phase Rotations

Complex Sinusoids: The Doorway to DSP

Negative Frequencies

A Real Sinusoid: The DNA of Signals

Frequency Domain

Building Blocks of All Signals

Spectrum and Bandwidth

Spectral Shift in Wireless Communication

Quiz 1

Sampling a Signal

8 Lessons

Grasp the fundamentals of signal sampling, aliasing, frequency representation, orthogonality, and numeric representations in DSP.

From Continuous Time to DiscreteTime

Why Do Spectral Aliases Arise?

Aliasing and the Sampling Theorem

Sample Rate and Discrete Frequency

The Idea of Orthogonality

Discrete Frequency Axis

Number Representation

Quiz 2

The Discrete Fourier Transform

12 Lessons

Take a closer look at the Discrete Fourier Transform (DFT) and its critical applications.

DFT and the Mysteries of the Universe

DFT Definition

The Spectrum of the Unit Impulse

Reading Amplitude and Phase Plots

Periodicity in Frequency and Time Domains

A Rectangular Signal

Main Lobe Peak: Width and Zero Crossings

DFT Phase

DFT Leakage

Fast Fourier Transform

The Inverse Discrete Fourier Transform

Quiz 3

Fourier Transform Properties

8 Lessons

Follow the process of exploring Fourier Transform properties for efficient signal analysis.

DFT Linearity

Spectrum After the Time Shift I

Spectrum After the Time Shift II

The Significance of a Linear Phase

Frequency Shifting and Modulation

Parseval's Theorem

Symmetry Properties

Quiz 4

Digital Systems

16 Lessons

Build on the concepts of digital systems, including linearity, time invariance, and convolution.

What Is a System?

Linear Systems

Time Invariance

System Impulse Response

System Frequency Response

Decomposition of a Signal into Scaled Unit Impulses

Response of an LTI System

How to Implement Convolution

Simplified Convolution

Convolution of Complex Signals

The Role of Complex Sinusoids in System Characterization

Circular Convolution

Convolution and the Frequency Domain

Filter Classifications in the Time Domain

Filter Classifications in the Frequency Domain

Activity 2

Putting It All Together: An OFDM Modem

8 Lessons

Learn how to use OFDM for efficient digital modulation, equalization, and demodulation.

Introduction to Orthogonal Frequency Division Multiplexing

Demodulating an OFDM Signal Stream

Assessment

10.

The Last Words

1 Lessons

Unpack the core of digital signal processing, exploring signals, transforms, and OFDM modems.

Conclusion

11.

Bibliography

1 Lessons

Explore essential references for understanding digital signal processing concepts.

Appendix

Course Author

Qasim Chaudhari

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