# Signals and Systems Flashcards

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__Define a **periodic signal**

A **periodic signal** is a power signal if its energy content per period is finite

If a > 1, the time scaling operation is a ‘____ __’ process (it looks like a ‘____’ process)

If a > 1, the time scaling operation is a ‘__speed__** up**’ process (it looks like a ‘

**’ process)**

__compression__If 0 < a < 1, the operation is a ‘____ __’ process (it looks like an ‘____’ process

If 0 < a < 1, the operation is a ‘** slow down**’ process (it looks like an ‘

**’ process**

__expansion__What would this sketch look like if it goes from x(t) to x(3t-5)?

Define a **system** (long)

A **SYSTEM** is a combination, collection or set of things or physical components connected or related together in such a manner to form a whole unit in order to achieve a certain task (or set of tasks) or objective(s). A system achieves its objective or set of objectives by transforming input signal(s) into output signal(s)

What is the **input** of a system?

An excitation or a stimulus that is applied to the system from an external source

What is the **output** of a system?

The actual response of the system due to the application of an input signal

What is a **system** (short)

A **system** can be considered a unit that transforms an input signal into an output signal using a well-defined rule or mathematical operation.

y = T(x) where T is the ____ ____ that maps _ onto _

y = T(x) where T is the __mathematical__** operation** that maps

**onto**

__x__

__y__What does **SISO** systems stand for and what does it look like?

What does **MIMO system** stand for and what does it look like?

A system whose output at any time depends on only the input at that same time is called a…?

…memoryless system; otherwise, the system is said to have memory.

Example of a memoryless system?

A continuous-time signal

A discrete-time signal turns into a…?

…Continuous signal

What is a system with aid and memory?

A capacitor

System **with** memory are…

Systems **without** memory are…

…Dynamic

…Static

A causal system is one whose output 𝑦(𝑡) at time 𝑡 = 𝑡_{0} depends on only the inputs 𝑥(𝑡) for…?

…𝑡 ≤ 𝑡

If a system is not casual, it is a…?

…non-casual system

**All** **memoryless** **systems** are ____, but **not** **all** **causal** **systems** are ____

**All** **memoryless** **systems** are ** casual**, but

**not**

**all**

**causal**

**systems**are

__memoryless__The system is a linear system if it satisfies the following two conditions…?

- Superposition (or Additivity)
- Homogeneity (or Scaling)

For the system to satisfy the superposition condition,

y_{1}+y_{2 }= ?

y_{1}+y_{2} = T(x_{1}+x_{2})

For the system 𝑦 = 𝑇(𝑥) to satisfy the homogeneity condition, it behaviour must satisfy…

𝛼∙𝑦 = 𝑇(𝛼∙𝑥)

A time-varying, or time-variant, system is one in which…?

…one or more of the parameters of the system vary as a function of time

Example of time-varying system

y = tx

A time-invariant system is one whose parameter(s)…?

…does not vary as a function of time

A time-invariant system: Mathematically…

𝑦 = 𝑇(𝑥)

A time-variant system: Mathematically

𝑦 = 𝑇(𝑥, 𝑡)

For time-invariant systems, a time-shift in the input signal leads to…

Although this is not true for…?

…the same time-shift in the output signal

…time-variant systems in general

- A linear system that is also time-invariant is called a…
- A nonlinear system that is time-invariant is called a…
- A linear system that is not time-invariant is called a…
- A nonlinear system that is not time-invariant is called a…
- Static or dynamic systems can be ____ or ____ and can be ____- ____ or ____-____

- Linear Time - Invariant System
- Nonlinear Time - Invariant System
- Linear Time - Varying System
- Nonlinear Time - Varying Systems.
- Static or dynamic systems can be
or__linear__and can be__nonlinear__-__time____variant__or-__time____invariant__

In terms of impulse response, a system is ____ if its impulse response approaches ____ as time approaches ____

In terms of impulse response, a system is ** stable** if its impulse response approaches

**as time approaches**

__zero__

__infinity__In terms of response to bounded input, a system is stable if…

…every bounded input produces a bounded output

Control systems can be classified into two general categories

- Open-loop control systems
- Closed-loop control system

A control system is a system whose function is to ____, ____, or ____ itself or another system

A control system is a system whose function is to ** command**,

**, or**

__direct__**itself or another system**

__regulate__Define **open-loop control systems**

A control system whose input signal is independent of the output signal