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

Time shifting a signal is one of the most fundamental ideas of digital signal processing. **Circular shift** is very similar to time shift with the following difference:
- In a regular time shift, the available axis is from $-\infty$ to $+\infty$.
- In circular shift, we only focus on a segment of $N$ samples.

Let us discuss how this is done.

- If a signal $x[n]$ is circularly right shifted by $m$, the samples of the signal $x[n]$ that **fall off** to the right of length-$N$ segment reappear at the start. 
- Similarly, if $x[n]$ is circularly left shifted by $m$, the samples of the signal $x[n]$ that **fall off** to the left of length-$N$ segment reappear from the end. 

This is just like the video game character Pac-Man who disappears at one end of the screen then emerges from the other.

Investigate the important property of circular shifts that helps in understanding the discrete Fourier transform (DFT).

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

Circular Shift