# 1.8 Discrete-time processing of ct signals

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The module will provide analysis and examples of how a continuous-time signal is converted to a digital signal and processed.

## Analysis

${Y}_{c}()={H}_{\mathrm{LP}}()Y(T)$
where we know that $Y()=X()G()$ and $G()$ is the frequency response of the DT LTI system. Also, remember that $\equiv T$ So,
${Y}_{c}()={H}_{\mathrm{LP}}()G(T)X(T)$
where ${Y}_{c}()$ and ${H}_{\mathrm{LP}}()$ are CTFTs and $G(T)$ and $X(T)$ are DTFTs.
$X()=\frac{2\pi }{T}\sum$ X c 2 k T OR $X(T)=\frac{2\pi }{T}\sum$ X c k s
Therefore our final output signal, ${Y}_{c}()$ , will be:
${Y}_{c}()={H}_{\mathrm{LP}}()G(T)\frac{2\pi }{T}\sum$ X c k s
Now, if ${X}_{c}()$ is bandlimited to $\left[-\left(\frac{{}_{s}}{2}\right) , \frac{{}_{s}}{2}\right]$ and we use the usual lowpass reconstruction filter in the D/A, :

Then,

${Y}_{c}()=\begin{cases}G(T){X}_{c}() & \text{if \left|\right|< \frac{{}_{s}}{2}}\\ 0 & \text{otherwise}\end{cases}$

## Summary

For bandlimited signals sampled at or above the Nyquist rate, we can relate the input and output of the DSP systemby:

${Y}_{c}()={G}_{\mathrm{eff}}(){X}_{c}()$
where ${G}_{\mathrm{eff}}()=\begin{cases}G(T) & \text{if \left|\right|< \frac{{}_{s}}{2}}\\ 0 & \text{otherwise}\end{cases}$

## Note

${G}_{\mathrm{eff}}()$ is LTI if and only if the following two conditions are satisfied:

• $G()$ is LTI (in DT).
• ${X}_{c}(T)$ is bandlimited and sampling rate equal to or greater than Nyquist. For example, if we had a simplepulse described by ${X}_{c}(t)=u(t-{T}_{0})-u(t-{T}_{1})$ where ${T}_{1}> {T}_{0}$ . If the sampling period $T> {T}_{1}-{T}_{0}$ , then some samples might "miss" the pulse while othersmight not be "missed." This is what we term time-varying behavior .

If $\frac{2\pi }{T}> 2B$ and ${}_{1}< BT$ , determine and sketch ${Y}_{c}()$ using .

## Application: 60hz noise removal

Unfortunately, in real-world situations electrodes also pick up ambient 60 Hz signals from lights, computers, etc. . In fact, usually this "60 Hz noise" is much greater in amplitude than the EKG signal shown in . shows the EKG signal; it is barely noticeable as it has become overwhelmed by noise.

## Sampling period/rate

First we must note that $\left|Y()\right|$ is bandlimited to60 Hz. Therefore, the minimum rate should be 120 Hz. In order toget the best results we should set ${f}_{s}=\mathrm{240}\mathrm{Hz}$ . ${}_{s}=2\pi 240\frac{\mathrm{rad}}{s}$

## Digital filter

Therefore, we want to design a digital filter that will remove the 60Hz component and preserve the rest.

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Suman
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Alter
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Alter
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Suman
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Raynard
how did psychology begin?
of psychologys commencement, the traces can be seen in the work of Aristotle, where he talk about soul and body, likewise work in durrant, de anima, all these were somewhere supporting dualism, in which soul could exist separately from body
amaan
but if you talk about the moder psychology, Gustav fechner, is credited with performing scientific experiments, basis of his experiments in psychology with his studies perception.
amaan
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Heba
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Mark
does psychology deal with love?
Maybe, i think
edem
I definitely would say yes
Clara
how so
Isaiah
*triarchic
Meredith
there are so many different reasons why you can fall in love with someone, many of them develope subconsciously -> psychology
Clara
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I would like an example as to what and how you think it deals with.
Tyler
how can I discover that this individual has a long-term memory and shot- term memory?
Namuaha
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Shonna
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Johan
by testing his memory
Johan
psychology deals with love bcz basically psy deals with all kinds of feelings
Johan
love as different feelings towards a person, an idea maybe , we can love an idea about a person or something so what am saying is that psychology doubtless deals and studies feelings wish love is one of
Johan
what is synapse
In the central nervous system, a synapse is a small gap at the end of a neuron that allows a signal to pass from one neuron to the next. synapse are found where nerve cells connect with other nerve cells
Najeem
a synapse the connection is where a neuron cell connects to another neuron cell.
Shaun
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Jobe
what is psychology
Jobe
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usef
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MD
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Najeem
how to avoid theory of bias confirmation in real life
Scar
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Jobe
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Bhavin
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Genevieve
hey, may I join the conversation?
samra
salaam
Ibrahim
so i cn even do this after ba hons in psychology?
Avneet
the only eligibility criteria is that you should have 50% of aggregate in your psychology papers. (bachelors)
syeda
okay thank you so much❤ have a lovely day🙂
Avneet
you're welcome. glad it helped ^_^
syeda
To pursue a career as a psychotherapist you'll have to do your bachelors in psychology. (bsc honors is preferable). since there are many fields and you've chosen as a therapist. a masters degree in clinical psychology or therapy and family counseling is preferable.
syeda
so i cn even do this after ba hons in psychology?
Avneet
yes you can.
syeda
you're welcome. glad it helped ^_^
syeda
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Vhikkie
yh
Parker
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Avneet
is there any psychotherapist here? i need to know the qualification one hve to pursue.
Avneet
I'm clinic psychologist...
Shilan
Hey. I'm pursuing BA in Clinical Psychology
Aakarshan
the only eligibility criteria is that you should have 50% of aggregate in your psychology papers. (bachelors)
syeda
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Vhikkie
who is the father of psychology
aristatil
and please, how would you guys, describe the study of psychology at college ?
edem
psychologist student?
Aspen
i mean not yet but am about to start college so wanna know how is it(college in general and psychology course) please
edem
Psychology is the study of mind and behaviour. So if you will take psychology as a subject so you will get to know how your everything (physical, mental, social, spiritual aspects) effects your behaviour
sakina
With this brief knowledge you can help people to cope up with their problems and only you can guide them correctly
sakina
And if you go for further specialisations you can study hypnosis, face reading, body language etc
sakina
Thanks a lot🙏🏾 And ik some of the stuffs u said but i am also going to write thesis, right ?
edem
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edem
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Khan
hae everyone, hope you are well this evning my question is what is the difference between drive and motivation
Michael
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Rainee
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edem
@ Michael Drive is delivered to be innate without the use of an external stimuli, motivation normally evolves an outside stimuli which may include praise, appreciate, or reward.
Reginald
*believed...sorry for typo
Reginald
@Reginald, can't the motivation come from the inner self?
edem
Good question, please give an example.
Reginald
can we say desire of success for example
edem
Wilhelm Wundt is the father of psychology
ipau
Wilhem Wundt thank you for the road that you opened.
Qwanta
You mean who is the father of having a great educated argumentative guess? nothing is more wrong than this question. The question is you should ask yourselfs is, how sure are you abour their scientific studying? one's percieved assimilated approach to judging another person and saying they are
Roger
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Roger
no facts about human behavior in the scientific context, but more in the trial and error.. sorry to tell you, but so far no one has proven Father of anything, thats up to you and i, judgement is bias, science is good enough lazy
Roger
cognitive development is the growing and development of the brain.
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ipau
what's the big difference between prejudice and discrimination?
A prejudiced person may not act on their attitude.  Therefore, someone can be prejudiced towards a certain group but not discriminate against them.  Also, prejudice includes all three components of an attitude (affective, behavioral and cognitive), whereas discrimination just involves behavior
Nancy Lee
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basher
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Rahul
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Kamohelo
cognitive development is the growing and development of the brain
Jessy
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Johan
Prejudice has to do with the inflexible and irrational attitudes and opinions held by members of one group about another, while discriminationrefers to behaviors directed against another group. Beingprejudiced usually means having preconceived beliefs about groups of people or cultural practices.
Shonna
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lord
cognitive development is a science that studies the development of human being from pregnancy to childhood to adulthood to death _ human cycle life _ it study the wag we develop mentally and physically, behaviors and learning...
Johan
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Samantha
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jewel
how do you control a variable when using spss whilst running a pearsons correlation analysis?
it dependa on your study. according to what you want to say and explain your result
Pouran
Hello
Jobe
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stages of cognitive development
sensory preoperatinal concrete formal
Rajendra
What's mental memory?
Namuaha
Memory is our ability to encode, store, retain and subsequently recall information and past experiences in the human brain. It can be thought of in general terms as the use of past experience to affect or influence current behaviour.
Shilan
What I mental memory?
Namuaha
What's mental memory?
Namuaha
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Namuaha
Jobe
what is psychology
the study of insecurities and the effect on the host .
Sera
Psychology is the scientific study of behavior & mental processes
Angela
psychology is science about learning human behaviour
Zhamshid
behaviorosm
Khan
is the study of human behaviour and mental processes
Jobe
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