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

Once we learn about systems, both natural and man-made, we want to characterize them through a method. This is a standard scientific approach that is utilized in biology, physics, and space science. In physics, for example, we observe back-and-forth vibrations for a certain time when the strings of a guitar are plucked or when a tuning fork is struck on a surface. The term impulse response is not much different than this.

# Response to an impulse

As the name implies, an **impulse response** is simply the output signal of a system when a unit impulse $\delta[n]$ is applied to its input. The impulse response of a system is denoted as $h[n]$.

For instance, an amplifier multiplies the input signal by a certain amount, say, by a factor of $10$. In the simplest terms, we can write its impulse response as:
$$
    \begin{equation*}
      h[n] = 10\delta[n]
    \end{equation*}
$$

The impulse response of a discrete-time system $h[n]$ is in general a complex discrete-time signal, as shown in the figure below:

Learn how to characterize a system by choosing a particular input and observing the output.

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

System Impulse Response

Response to an impulse