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Title
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Discretetime signals are those
signal which occurs at particular instant of time for example, for example, I have a sin
wave which is varying with respect to a constant called n which is a function x of n
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Step signal is denoted as u of n which

is equal to a for n greater than an equal to 0
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A system is called as discretetime systems or short form as dt systems
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So we will
see an example of time varying on time invariant systems for time invariant systems
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Time invariance is a property of a system that states that the output will always be
equal to the input at the same instant
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This property is important because it means that
we can always predict the outcome of a system based on its inputs
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What is Convolution in Discrete time signal Processing - Discrete
Time Signal Processing

What Convolution is and what it means for linear time-invariant systems
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The period of a signal
after 4 samples is equal to 4, so 4 is the period of the signal after 4th sample
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The previous formula I get, y of 0 is equal to
summation k going from minus infinity to plus infinity x of k h of minus k is a mirror

g g
y
p
y
image signal
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Let
us draw with another color
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h of minus 1 plus x
of one and h of 2 minus 2 plus x x of 2 are equal to 3
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if i see on the negative side of n then this for overlays
with 0 this 3 overlays
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if i go for n is equal to 1 my equation
writes as y of 1 which is
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so many new signal comes like this is my 4 which is shifted by 1 on n is
equal to 0
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y often will have l plus m minus 1 samples now where is this l and where is m where l
is the number of samples in x of n x of n and minus 1
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there are n is equal to l plus m minus
1 samples in the output signal so there are basically two conclusions that we have drawn
that if we have a periodic signals then we will go with linear convolution and convolved
of periodic signals
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this method is normally used to cross verify or cross check the answers that you have
got using graphical method
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If these two conditions are met, then I can perform a circular
conolution
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This is the first point of a periodic signal to be noticed
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We multiplied the signal, then shifted it, and
then shifted it again
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Mirroring a periodic sequence is placing the sequence in a clockwise direction,
because the previous condition we used is anticlockwise
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To see the overlaps for a given sequence, you need to draw lines connecting
each point where the sequence overlaps with the previous one
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Condition so now i will be moving in anticlockwise direction: Placement of h of
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Job one: h of zero is one h of one
was two h of 2 is 3 and h of 3 is 4
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h of n is 1 2 3 4
mandatorily in this order only
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The one has traverse completely till the bottom there you have to stop that is
the first sample traverse completely till bottom
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The answer that i am going to get
is y of n which is we will be a matrix
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What is Representation of Linear Time Invariant Systems in
Discrete time signal Processing
Differential equation is used to represent continuoustime signals
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A system can be represented by a set
of outputs and a set of inputs
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By definition, a z
transform is equal to the summation of all the delta values, which goes from 0 to infinity
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The u of n with a raise to n multiplied value will give 1 upon 1 minus the z
inverse
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What is System Transfer Function in Z-Transform - Discrete Time
Signals Processing
The system transfer function is a mathematical equation that describes the relationship
between an input and an output
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The definition of system transfer function is written as h
of z, which is equal to the output upon input
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of z says it is the ratio of output upon input
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What is System Transfer Function in Z-Transform - Discrete Time
Signals Processing
The system transfer function is a mathematical equation that describes the relationship
between an input and an output
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The definition of system transfer function is written as h
of z, which is equal to the output upon input
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of z says it is the ratio of output upon input
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What is Pole-Zero Representation of a System in Z-Transform -

Discrete Time Signals Processing?
The pole zero representation of a system
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z minus p n because the difference equation is n order
with respect to x and end the order with
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In a jet plane we have two axis, real z and imaginary said, and
everything is on a circle
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In z transform everything is in a circle and in a plane, the radius of that circle
is 1 so whenever I am representing a pole, I will put a cross mark
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What is Significance of Pole-Zero of Transfer Functions - Discrete
Time Signals Processing
In a z domain, all circles will exist
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Z is a complex number, so where r denotes the radius or
sometimes we also called it as an amplitude and theta is denoted as the angle
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In general, if i wanted to
draw then let us select for r equals to 1
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Now my r let us value is one two and three so for r equals to
1 my let us say that this is the circle then for r is equal to 2
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Y axis is the real part of z and y axis the imaginary part
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There is a circle which passes through this point 5 which is minus 0
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5 which is far inside
the 1 unit circle
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Now how does this fold in zeros risk will it really affects my h of
z and why should i calculate the poles and zeros? A system transfer function is nothing but
output upon input if i rewrite this equation i will get x of z into h of z equals 2 y offset that
means output equals to the transfer function into the input
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The limits on omega are 0 2 pi 2 pi that
means it will go to 0
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If the input to a system is
an impulse that is delta n, then the output is called an impulse response
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Impulse response
is important because it tells us how a system responds to an input
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