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

## Summary

- This course started with a basic **introduction to signals** and their role in your everyday life. You learned that all activity in the universe can be traced back to signals and the ability to manipulate them through DSP techniques that give those signals unprecedented powers.

- You reviewed **basic signals** and the mathematical operations needed to manipulate them such as additions, multiplications, time shifts, and correlation. The fundamental relation between time shift and phase was also explored.

- Next, the idea of the **frequency domain** was introduced, which governs much of the signal processing world. You studied the details of how real and complex sinusoids combine to form almost all practical signals. Moreover, the concepts of spectrum and bandwidth were explained.

- Almost all of the natural world generates **continuous-time signals** while the computing world relies on **discrete-time signals**. Therefore, this course covered how an analog signal can be converted into a digital signal. In particular, the relation between bandwidth and sampling rate needs to be considered for a faithful representation of an analog signal in the digital world.

- The question that arises then is how to take a time-domain signal to the frequency domain. For this purpose, the **discrete Fourier transform (DFT)** was analyzed along with amplitude and phase plots. You went through the topic of DFT leakage, which is present in almost all practical signals, and the fast Fourier transform (FFT), which is an efficient implementation of the DFT. Fourier transform properties such as the time shift, frequency shift, and modulation were explored in detail.

- This course then turned to **digital systems** and found how to compute the output of a system for any given input. This process is known as convolution, which forms the backbone of digital signal processing techniques in both natural and man-made systems. In the end, digital filter classifications with respect to time and frequency domains were discussed.

- All the knowledge from this course is now applied to build an **orthogonal frequency division multiplexing (OFDM)** modem that is used in cellphones, WiFi modems, and most other high data-rate wireless communication systems.

# Summary

- This course started with a basic **introduction to signals** and their role in your everyday life. You learned that all activity in the universe can be traced back to signals and the ability to manipulate them through DSP techniques that give those signals unprecedented powers.

- You reviewed **basic signals** and the mathematical operations needed to manipulate them such as additions, multiplications, time shifts, and correlation. The fundamental relation between time shift and phase was also explored.

- Next, the idea of the **frequency domain** was introduced, which governs much of the signal processing world. You studied the details of how real and complex sinusoids combine to form almost all practical signals. Moreover, the concepts of spectrum and bandwidth were explained.

- Almost all of the natural world generates **continuous-time signals** while the computing world relies on **discrete-time signals**. Therefore, this course covered how an analog signal can be converted into a digital signal. In particular, the relation between bandwidth and sampling rate needs to be considered for a faithful representation of an analog signal in the digital world.

- The question that arises then is how to take a time-domain signal to the frequency domain. For this purpose, the **discrete Fourier transform (DFT)** was analyzed along with amplitude and phase plots. You went through the topic of DFT leakage, which is present in almost all practical signals, and the fast Fourier transform (FFT), which is an efficient implementation of the DFT. Fourier transform properties such as the time shift, frequency shift, and modulation were explored in detail.

- This course then turned to **digital systems** and found how to compute the output of a system for any given input. This process is known as convolution, which forms the backbone of digital signal processing techniques in both natural and man-made systems. In the end, digital filter classifications with respect to time and frequency domains were discussed.

- All the knowledge from this course is now applied to build an **orthogonal frequency division multiplexing (OFDM)** modem that is used in cellphones, WiFi modems, and most other high data-rate wireless communication systems.

Summarize what you’ve learned in this course.

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

Conclusion

Summary