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

When learning DSP, it’s important to know how to shift a signal in time. This is an important part of all DSP operations.
- Some applications require signals to be shifted by a processor. For example, a signal needs to be aligned with the output of another signal processing chain.
- In some other applications, we encounter a signal shifted in time by nature. For example, a localization receiver attempts to estimate the time shift of the received signal to compute its range from the transmitter.
- In almost all DSP operations, like filtering, a signal needs to be shifted in time to compute the output response of the system.

# The logic

For a discrete-time signal $x[n]$, its delayed version by $m$ units is denoted by $x[n-m]$. Taking the time $n$ as the present moment, we need to go $m$ samples in the past **on the time axis**. 

On the other hand, its advanced version by $m$ units is denoted by $x[n+m]$. Taking the time $n$ as the present moment, we need to go $m$ samples into the future **on the time axis**. 

In both cases, our focus should be on the time axis. An example of a delay and advance by 1 unit of time is plotted in the figure below. It's clear that the time axis is pulled back by 1 unit in the second subfigure while it's advanced by 1 unit in the third subfigure. If this sounds confusing, check the time index $n=0$ in all subfigures.

Discover the techniques that can shift a signal in time.

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

How to Shift a Signal in Time Domain