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.

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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 the basic signal types and perform different operations. You’ll develop an understanding about the frequency domain and how to represent signals in time, and the transformation from one domain to the other using the Fourier transform. You’ll also learn about digital systems. Finally, you’ll develop a practical OFDM system focusing on modulation and demodulation.

By the end of this course, you’ll be able to model, analyze and design signals and systems in greater depth, in the time and frequency domains.

Fundamentals of Digital Signal Processing

Let's find out how complex numbers arose in the past. This will help us understand the use of complex signals in signal processing applications. DSP algorithms extensively use complex numbers to exploit the signal phase information in addition to the amplitude.

## X-axis

Initial applications of mathematics included taxation and trade. This led to an evolution of the number system as follows.

### Natural and whole numbers

The idea of countable objects comes naturally to humans, e.g., counting objects like fruits and houses. So the numbers $1, 2, 3, \cdots$ were called natural numbers. Whole numbers are natural numbers, which includes zero.


### Rational and irrational numbers

Since many quantities need to be divided into multiple parts, (e.g., a field), this led to the discovery of rational numbers that can be written in fractional form. The remaining gaps on the real line are filled by irrational numbers such as $\pi$ or $\sqrt{2}$.

This completes the positive real line. A mirror image of these numbers produces the negative part of the real line.

# X-axis

Initial applications of mathematics included taxation and trade. This led to an evolution of the number system as follows.

## Natural and whole numbers

The idea of countable objects comes naturally to humans, e.g., counting objects like fruits and houses. So the numbers $1, 2, 3, \cdots$ were called natural numbers. Whole numbers are natural numbers, which includes zero.


## Rational and irrational numbers

Since many quantities need to be divided into multiple parts, (e.g., a field), this led to the discovery of rational numbers that can be written in fractional form. The remaining gaps on the real line are filled by irrational numbers such as $\pi$ or $\sqrt{2}$.

This completes the positive real line. A mirror image of these numbers produces the negative part of the real line.

Learn about the origins of complex numbers.

Introduction to Signals

Basic Signals and Operations

Complex Signals and the Frequency Domain

Sampling a Signal

The Discrete Fourier Transform

Fourier Transform Properties

Digital Systems

Putting It All Together: An OFDM Modem

Demodulating an OFDM Signal Stream

The Last Words

Bibliography

Where Do Complex Numbers Come From?

X-axis

Natural and whole numbers

Rational and irrational numbers