# 1.1 Discrete time signals

 Page 1 / 1
Important discrete time signals

The signals and relations presented in this module are quite similar to those in the Analog signals module. So do compare and find similarities and differences!

## Sequences

Generally a time discrete signal is a sequence of real or complex numbers. Each component in the sequence is identifiedby an index: ...x(n-1),x(n), x(n+1),...

[x(n)] = [0.5 2.4 3.2 4.5]is a sequence. Using the index to identify a component we have $x(0)=0.5$ , $x(1)=2.4$ and so on.

## Manipulating sequences

Add individually each component with similar index
• ## Multiplication by a constant

Multiply every component by the constant
• ## Multiplication of sequences

Multiply each component individually
• ## Delay

A delay by $k$ implies that we shift the sequence by k. For this to make sense the sequence has to be of infinite length.

Given the sequences [x(n)] = [0.5 2.4 3.2 4.5]and [y(n)]= [0.0 2.2 7.2 5.5].

b)Multiplication by a constant c=2. [w(n)]= 2 *[x(n)]= [1.0 4.8 6.4 9.0]

## The unit sample

The unit sample is a signal which is zero everywhere except when its argument is zero, thenit is equal to 1. Mathematically

$(n)=\begin{cases}1 & \text{if n=0}\\ 0 & \text{otherwise}\end{cases}$
The unit sample function is very useful in that it can be seen as the elementary constituent in any discrete signal.Let $x(n)$ be a sequence. Then we can express $x(n)$ as follows (using the unit sample definition and the delay operation)
$x(n)=\sum_{k=()}$ x k n k

## The unit step

The unit step function is equal to zero when its index is negative and equal to one for non-negative indexes,see for plots.

$u(n)=\begin{cases}1 & \text{if n\ge 0}\\ 0 & \text{otherwise}\end{cases}$

## Trigonometric functions

The discrete trigonometric functions are defined as follows. $n$ is the sequence index and  is the angular frequency. $=2\pi f$ , where f is the digital frequency.

$x(n)=\sin (n)$
$x(n)=\cos (n)$

## The complex exponential function

The complex exponential function is central to signal processing and some call it the most important signal. Remember that it is a sequence and that $i=\sqrt{-1}$ is the imaginary unit.

$x(n)=e^{in}$

## Euler's relations

The complex exponential function can be written as a sum of its real and imaginary part.

$x(n)=e^{in}=\cos (n)+i\sin (n)$
By complex conjugating and add / subtract the result with we obtain Euler's relations.
$\cos (n)=\frac{e^{in}+e^{-(in)}}{2}$
$\sin (n)=\frac{e^{in}-e^{-(in)}}{2i}$
The importance of Euler's relations can hardly be stressed enough.

## Matlab files

Take a look at

• Introduction
• Analog signals
• Discrete vs Analog signals
• Frequency definitions and periodicity
• Energy&Power
• Exercises
?

What are the ways in which computer work as mind
How does the computer serve as model for mind
baraka
in what ways does the computer serve as model for the mind?
what ways does the computer serve as a model for the mind?
Erick
Ways in which computer work as Brain mind
baraka
learning is facilitated by
What
Angel
What is Repression?
Repression, In psychoanalytic theory, the exclusion of distressing memories, thoughts, or feelings from the conscious mind. Often involving sexual or aggressive urges or painful childhood memories, these unwanted mental contents are pushed into the unconscious mind.
Forqan
in psychoanalytic terms a basic defense mechanism that shuts out anxiety arousing thoghts feelings and memories from one consciousness
Berrel
Repression is holding something painful inside because you're afraid to let it out for fear of what trouble it might csuse
Connie
It helps students to understand the behavior of people they encounter.
what are the types of learning?
frederick
thanks @Frederick. But I still want to understand something. Classical conditioning, Operants conditioning and Observational learning are not types of learning?
Ogbeyemi
I believe there are several types of learning besides just the four I mentioned.
frederick
so, I can also say those I mentioned are part of learning?
Ogbeyemi
i would say so
frederick
Operant conditioning is a type of associative learning process through which the strength of a behavior is modified by reinforcement or punishment.
Forqan
what is psychology
in simple explanation, it is the study and understanding of the human behavior
Edmar
the scientific study of the human mind and its functions, especially those affecting behaviour in a given context.
naina
the scientific study of human mind and behaviour
NishaOfficial
but I thought psychology is not limited to humans. I think it is the scientific study of behavior and mental process of organisms
Ogbeyemi
processes*
Ogbeyemi
Trish
the study of human behavior, the reasons for the behavior, and ways to change the undesirable behaviors into desirable behaviors
RD
psychology is the study of the soul or mind of man through scientific studies relating to environmental factors and human behaviours.
Audley
not only man but animals as well
Audley
psychology is the study of the mind and behaviors*
Emely
the definition you gave Audley is incorrect
Emely
Hey Audley, also humans are animals, so the correct way to say it is.. Not only man but other animals as well. 👍🏽
Emely
Audley, you are both correct in the definition of psychology. Yours was textually from the book, while the other was simple and to the heart of it where a novice would understand.
Bosie
Emely, you stated that man is a animal as well. Explain?
Bosie
_____are the memory images that are related to particular place ,date and time .
what is psychology
he or she can
Edward
I have been wondering of minor Autism I have estrange daughter that has I have been divorced and things like the ex wife sister told bad things about Me, Which I was not there to defend my self was said. one part) the other is the ex wife mom took care of her and never gave her kind of up bringing
Edward
Much and now she is 28 has a pension cause of her Autism she has everyone like her 2brothers her mom and her father had said to go on andfor-get the past she had not wanting to only seen her once I tried to make contact online she does not my contact from G circle
Edward
Ibrahim
God bless you Edward 🙏 I pray that God heals you and your family he will make things right
Joseph
Ibrahim it's too bad you couldn't take the time to give encouragement to your brother with a few more positive words at the end were all brothers and sisters in Christ 🙏
Joseph
hi
Bong
hello
Marcela
hello
Manuel
hello everyone
artgalang
what is rootology
Rootology is a blend of 13 concentrated herbal extracts that support against sneezing, congestion, sinus pressure, runny nose, itchy watery eyes, and headache.
Labdhee
a child playing with the friend without complaining is called
free child
Nisha
psycosocial development
Anita
playful & sporty child
Jaga
The scope of Experimental Psychology is widening with the invention of new tools and instruments for experiments.
like what kind?
MissRoyal
hello, what kind of people talk throught here
Juan
?
John
thought is autonomous. it is up to us compartmentalizing these random various thoughts that we too often incorrectly give them the title of (ideas)
John
what is the scope of experimental psychology?
Fareha
who is pavlo
he believed in classic conditioning
just
he created classical conditioning
naina
Ivan Petrovich Pavlov was a Russian physiologist known primarily for his work in classical conditioning.
lavanya
he developed the theory is classical conditioning on a dog
NishaOfficial
Hello... Gyatri, angel and thinker.. I am MJ.
hi
naina
Hello
Jeanica
How are you...?
Mujtaba
Fine
Jeanica
Where are you from?
Jeanica
hi everyone 😊
Luis
I'm not trying to be a killjoy but I don't think this is a conversation thread for meeting new people.
Aspen
there are plenty of apps for that
Aspen
hai
kumpulan
@Aspen German well you're right there are other apps that offers ways into meeting new people. however I don't see anything wrong in here? just saying hi and hello.
Luis
but if they turn it into something like a "dating app" then for me that's another story. just saying. 😊.
Luis
hello Everyone
artgalang
Hello Luis, this app is for friends to everyone. 😊🙏
Jeanica
Anyone having problem can leave
Mujtaba
Hi
Red
Hi
Esther
Hello
Jeanica
hello^^
Girlie
is this a Psychology Course GC?
artgalang
Hi I'm from Philippines 🇵🇭
Esther
hellow
Erick
Can anyone.... What is basic criteria for abnormalities...?
Mujtaba
Is here any psychologist or psychiatrist.
Mujtaba
hi Jeanica yes I know that 😊
Luis
hello
Fermin
yes psychologist I am
kirti
me too
artgalang
Can you please explain me Diathesis stress model and its application
Mujtaba
And how can it applied..
Mujtaba
Got questions? Join the online conversation and get instant answers!