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

Understanding the DFT starts with the spectrum of a unit impulse. This case gives us an interesting result, as we will now see.

## The signal

A unit impulse is a signal that is $0$ everywhere, except at time index $0$ where its value is $1$. In mathematical terms, we say:
$$
\begin{equation*}
\delta[n] = \left\{ \begin{array}{l}
1, \quad n = 0 \\
0, \quad n \neq 0 \\
\end{array} \right.
\end{equation*}
$$
This is drawn in the figure below:

Understanding the DFT starts with the spectrum of a unit impulse. This case gives us an interesting result, as we will now see.

# The signal

A unit impulse is a signal that is $0$ everywhere, except at time index $0$ where its value is $1$. In mathematical terms, we say:
$$
\begin{equation*}
\delta[n] = \left\{ \begin{array}{l}
1, \quad n = 0 \\
0, \quad n \neq 0 \\
\end{array} \right.
\end{equation*}
$$
This is drawn in the figure below:

Learn to derive the DFT of a unit impulse and observe the fundamental result.

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 Spectrum of the Unit Impulse

The signal