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 spectral aliases arise after sampling at integer multiples of the sample rate $f_s$. An example of this is shown in the figure below:

We’ll now look at the **sampling theorem**, which puts a fundamental limit on the sample rate for signal representation in discrete time.

## Background

How should we choose the sample rate $f_s$?
- We know that a closer time spacing, i.e., a smaller $T_s$, produces a better approximation of the signal in discrete time and pushes the spectral aliases further away due to the large $f_s$. However, we can't have too many samples because they will overload the processor memory and result in unnecessary power consumption. 
- On the other hand, we can’t take too few samples because that will result in distortion in the original analog signal.

What is the ultimate limit of this phenomenon? We’ll formally derive the exact relation between signal bandwidth  $B$ and a sample rate of $f_s$ in this lesson.

We’ll now look at the **sampling theorem**, which puts a fundamental limit on the sample rate for signal representation in discrete time.

# Background

How should we choose the sample rate $f_s$?
- We know that a closer time spacing, i.e., a smaller $T_s$, produces a better approximation of the signal in discrete time and pushes the spectral aliases further away due to the large $f_s$. However, we can't have too many samples because they will overload the processor memory and result in unnecessary power consumption. 
- On the other hand, we can’t take too few samples because that will result in distortion in the original analog signal.

What is the ultimate limit of this phenomenon? We’ll formally derive the exact relation between signal bandwidth  $B$ and a sample rate of $f_s$ in this lesson.

Discover how the sampling theorem acts as a fundamental limit on the sample rate beyond which distortion in the signal is unavoidable.

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

Aliasing and the Sampling Theorem

Background