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

We have learned that the field of digital signal processing manipulates sequences of numbers. In a digital machine, these numbers can only be represented in a binary format. In the case of fixed-point arithmetic, there is a set procedure that converts a decimal number (e.g., a voltage or current signal) into its binary representation for positive numbers. For example, the number $13$ can be written as:
$$
13 = 1\times 10^1 + 3\times 10^0=10+3
$$

Similarly, its binary equivalent $1101$ is written as
$$
13 = 1\times 2^3+ 1\times 2^2 + 0\times 2^1 +1\times 2^0=8+4+1
$$

There are three major formats in use today when dealing with negative numbers.

## Sign magnitude

In this system, the **most significant bit (MSB)** is used as a sign bit—for example, 0 represents a positive number while a 1 represents a negative number. As a consequence, a negative number can simply be obtained by inverting the sign bit of its positive counterpart. A 3-bit example is as follows:

We have learned that the field of digital signal processing manipulates sequences of numbers. In a digital machine, these numbers can only be represented in a binary format. In the case of fixed-point arithmetic, there is a set procedure that converts a decimal number (e.g., a voltage or current signal) into its binary representation for positive numbers. For example, the number $13$ can be written as:
$$
13 = 1\times 10^1 + 3\times 10^0=10+3
$$

Similarly, its binary equivalent $1101$ is written as
$$
13 = 1\times 2^3+ 1\times 2^2 + 0\times 2^1 +1\times 2^0=8+4+1
$$

There are three major formats in use today when dealing with negative numbers.

# Sign magnitude

In this system, the **most significant bit (MSB)** is used as a sign bit—for example, 0 represents a positive number while a 1 represents a negative number. As a consequence, a negative number can simply be obtained by inverting the sign bit of its positive counterpart. A 3-bit example is as follows:

Investigate how to represent numbers in any digital machine.

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

Number Representation