OE-8.1 Discrete Time Signals & Systems
You can state the sampling theorem, describe ADC and DAC, and test a discrete-time system for linearity, time invariance, causality and stability.
The sampling theorem is the bridge between the analog world and everything else in this course; understand aliasing as what happens when you cross the bridge carelessly. Linearity and time invariance are the two properties that let convolution and transforms work at all, so checking them is not a formality. Causality and stability are the conditions a system must meet to be buildable and to stay bounded - BIBO stability in terms of the impulse response is the version to remember.
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Basic elements of a digital signal processing system
The blocks between a real signal and a processed one, and the map for the whole course. Every topic below is one of these blocks in detail.
Advantages and disadvantages of digital over analog signal processing
Why anyone converts to numbers at all, stated with the costs as well as the benefits. The honest list includes the conversion delay and the anti-aliasing filter, which people forget.
The sampling theorem
The result the whole field depends on: how often you must sample to lose nothing. Aliasing is what happens when you disobey it, and seeing that once is worth more than the statement.
Analog-to-digital and digital-to-analog conversion
The two conversions in both directions, and the practical circuits that do them. The reconstruction side is the one usually treated too quickly.
Mathematical representation of discrete-time systems
How a discrete-time system is written down, which is the notation the rest of the course uses. Difference equations are the discrete counterpart of what you already know.
Impulse response and transfer function
Two descriptions of the same system, one in time and one as a ratio. Moving fluently between them is the core skill of this subject.
Linear and time-invariant systems
The two properties that make a system tractable at all. Almost everything you will design has both, and almost every technique assumes them.
Concept of causality and stability
Whether a system can be built, and whether it will stay bounded. These are the checks to run on any design before spending effort on it.
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