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## Continuous-Time Signals and Systems

#### Signals and Systems Definitions

2/12/2022

Running Time: 5:35

This video provides the basic definitions of signal and system that we'll use in the course. A signal is function of one or more variables that contains information. A system is an entity that manipulates signals to generate new signals.

#### Continuous-Time vs. Discrete-Time Signals

2/12/2022

Running Time: 6:54

This and the subsequent videos work through a list of signal properties that signals may (or may not) have. This first video discusses the difference between continuous-time and discrete time signals. Continuous-time signals are denoted as x(t) and are defined for all time t. Discrete-time signals are denoted as x[k] are are defined for discrete-time k.

#### Analog and Digital Signal Definitions

2/12/2022

Running Time: 5:00

This video defines and shows examples of both analog signals and digital signals. Analog signals have amplitudes that take on a continuum of values. Digital signals have amplitudes that only take on values from a finite list of possible values.

#### Continuous-Time Even and Odd Signals

2/12/2022

Running Time: 7:57

This video defines even and odd signals and provides several examples. An even signal satisfies x(t) = x(-t) for all time. An odd signal satisfies x(t) = -x(-t) for all time.

#### Continuous-Time Conjugate Symmetric Signals

2/12/2022

Running Time: 3:21

The previous video examined even and odd real-valued signals. Complex-valued signals may have a different type of symmetry. A complex-valued conjugate symmetric signal satisfies x(-t) = conj(x(t)) for all time.

#### Even and Odd Signal Properties With Proofs

2/13/2022

Running Time: 6:06

This video provides a variety of proofs with respect to summations ad products of even/odd signals. For example, we prove that the summation of two even signals is itself an even signal. Similar proofs are provided for various other combinations of even, odd, summations, and products.

#### Continuous-Time Periodic and Non-Periodic Signals

2/13/2022

Running Time: 9:24

A continuous-time periodic signal x(t) satisfies the equality x(t+T) = x(t) for all time t, for some value T greater than zero. The smallest value T that satisfies the equality is called the fundamental period. The fundamental period and fundamental frequency f are related by T = 1/f. Signals that don't have a fundamental period are non-periodic (or aperiodic) signals.

#### Sums of Periodic Signals Example

2/13/2022

Running Time: 5:55

This video examines the summation of periodic signals. We show that the summation of two periodic signals is not always periodic. Let T1 be the period of signal x1(t) and T2 be the summation of x2(t). We show that the signal y(t) = x1(t) + x2(t) is only periodic if the ratio of T1/T2 can be written as a rational fraction.

#### Simply-Defined and Piecewise-Defined Signals

2/14/2022

Running Time: 2:28

This short video provides definitions and examples for simply-defined and piecewise-defined signals. A simply-defined signal is a signal that has a single equation that is valid for all time. A piecewise-defined signal has different equation defined for different portions of time.

#### Continuous-Time Deterministic and Random Signals

2/14/2022

Running Time: 2:40

This short video provides definitions and examples for deterministic and random signals. A deterministic continuous-time signal x(t) is has known values for all time t, and deterministic signals are the exclusive focus on most undergraduate courses on signals and systems. A random signal X(t), (also called a random process) is a random variable at each time t, and must be analyzed much differently. Random processes and their analysis are typically covered in graduate-level courses.

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