What are **samples? **

Points of data

What are **sampling intervals**?

The distance between the sample points

**Discrete-time signals** can be defined in 2 ways...

###
- As a function
- As a list of values of a sequence

In this picture, the arrow indicates....?

And if the arrow is not shown, where is the ____ point?

The n=0 point

The first value in the sequence is the n=0 point

Define **analog signals**

**Analog Signals:** An analog signal is a **continuous-time signal** x(t) that can take on any value in the continuous interval (a, b), where a may be - ∞ and b may be +∞.

Define **Digital Signals**

**Digital Signals: **A digital signal is a **discrete-time signal** x[n] that can only take on only a finite number of distinct values.

What is a **real signal?**

**Real Signals: **A signal x(t) is said to be a real signal if its value is a real

number

What is a **complex signal?**

**Complex Signals:** A signal x(t) is said to be a complex signal if its value is a complex number

A general (continuous- or discrete-time) complex signal x(t) is a function of the form

where x1(t) and x2(t) are real signals and j = √−1

Define **Deterministic Signals**

**Deterministic Signals:** Those signals whose **values are exactly specified** for any given **time** in the time span of interest are called deterministic signals. Such signals may be represented by a known function of time t.

Define **Random Signals**

**Random Signals**: Those signals that take random values at any given time are called random or non-deterministic signals. Such signals must be characterized statistically (that is, represented in probabilistic terms)

Any signal x(t) or x[n] can be expressed as a sum of ____ ____, one of which is ____ and one of which is ____

Any signal x(t) or x[n] can be expressed as a sum of **two**__ signals__, one of which is

__and one of which is__

**even**

**odd**The product of two even signals or of two odd signals is a...?

...even signal

The product of an even signal and an odd signal is an...?

...odd signal

Define **Periodic continuous-time signals**

**Periodic Continuous-time Signals**: A continuous-time signal x(t) is said to be a periodic signal with period T if there is a unique positive nonzero value of T for which the following expression is valid

A dc signal is a signal in which x(t) is ____; such a signal is not periodic since its fundamental period is ____

A dc signal is a signal in which x(t) is __ constant__; such a signal is not periodic since its fundamental period is

**undefined**Define **Aperiodic Continuous-time Signals**

**Aperiodic Continuous-time Signals**: Any **continuous-time signal** which is **not** **periodic** is called a non-periodic signal or an aperiodic signal

Define **Periodic Discrete-time Signals**

**Periodic Discrete-time Signals**: A sequence (discrete-time signal) x[n] is periodic with period N if there is a unique positive integer N for which the following expression is valid

Define **Aperiodic Discrete-time Signals**

**Aperiodic Discrete-time Signals:** Any sequence which is not periodic is called a non-periodic sequence or an aperiodic sequence

A sequence obtained by uniform sampling of a periodic continuous-time signal may...

...not be periodic

The sum of two continuous-time periodic signals may...

... not be periodic

The sum of two periodic sequences is...

...always periodic

For any continuous-time signal x(t), the total energy of the signal over the interval t1 ≤ t ≤ t2 is defined as

The average power of the signal x(t) over the interval t1 ≤ t ≤ t2 is defined as

|x(t)| denotes the ____ of x(t) and the signal x(t) could be a ____ or ____ signal.

|x(t)| denotes the __ magnitude__ of x(t) and the signal x(t) could be a

__or__

**real**__signal.__

**complex**For any discrete-time signal x[n], the total energy of the signal over the interval n1 ≤ n ≤ n2 is defined as

The average power of the signal x[n] over the interval n1 ≤ n ≤ n2 is defined as

A signal x(t) (or x[n]) is said to be an ____ ____ (or sequence) if and only if 0 < E∞ < ∞, in which case, P∞ = 0.

A signal x(t) (or x[n]) is said to be an **energy**__ signal__ (or sequence) if and only if 0 < E∞ < ∞, in which case, P∞ = 0.

A signal x(t) (or x[n]) is said to be a ____ signal (or sequence) if and only if 0 < P∞ < ∞, in which case, E∞ = ∞

A signal x(t) (or x[n]) is said to be a __ power__ signal (or sequence) if and only if 0 < P∞ < ∞, in which case, E∞ = ∞

A signal that does not satisfy 0 < E∞ < ∞ and 0 < P∞ < ∞ is not an ____ or a ____ signal

A signal that does not satisfy 0 < E∞ < ∞ and 0 < P∞ < ∞ is not an __ energy__ or a

__signal__

**power**