Conclusion
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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 continuoustime signals while the computing world relies on discretetime 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 timedomain 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 manmade 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 datarate wireless communication systems.
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