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.

Octave.tar.gz

octave-codewidget

octave-jupyter

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

In this lesson, we learn how to determine the output response of a system for any arbitrary input.

# Finding the output

To find the answer to this question, the following two results are needed:
1. System impulse response $h[n]$ is the output when the input is a unit impulse $\delta [n]$.
2. Any signal can be decomposed as a set of scaled and shifted unit impulses as:
$$    \begin{align*}
      x[n]&= \cdots + x[-1]\delta[n+1] + \nonumber \\
          &\quad\quad\quad\quad\quad x[0]\delta[n] + x[1]\delta[n-1] + \cdots \nonumber \\
          &= \sum _mx[m] \delta[n-m]
    \end{align*}
$$

# The algorithm

From here, we can follow the steps below:
- For a time-invariant system, the response to a delayed unit impulse $\delta[n-m]$ becomes $h[n-m]$.
$$
\delta[n-m] \qquad \rightarrow \qquad h[n-m]
$$

Learn how an LTI system responds to a discrete-time signal built with scaled and shifted unit impulses.

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

Response of an LTI System

Finding the output