This course focuses on the fundamentals of digital signal processing that covers the fundamentals of signals, systems and transforms.

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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

Complex sinusoids are disproportionately emphasized among all signals in DSP formulations. Why? This is what we are going to investigate now.

## System input

Let’s probe a system that has an impulse response  $h[n]$ with a complex sinusoid $x[n]=e^{j\omega_0 n}$ as shown in the figure below:

Complex sinusoids are disproportionately emphasized among all signals in DSP formulations. Why? This is what we are going to investigate now.

# System input

Let’s probe a system that has an impulse response  $h[n]$ with a complex sinusoid $x[n]=e^{j\omega_0 n}$ as shown in the figure below:

Investigate the role of complex sinusoids to determine the frequency and impulse response of a system.

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

The Role of Complex Sinusoids in System Characterization

System input