# 1.2 Signal properties

## Signal classification

Signals can be broadly classified as discrete-time or continuous-time, depending on whether the independent variable is integer-valued or real-valued. Signals may also be either real-valued or complex-valued. We will now consider some of the other ways we can classify signals.

## Signal length: finite/infinite

This classification is just as it sounds. An infinite-length discrete-time signal takes values for all time indices: all integer values $n$ on the number line from $-$ all the way up to  . A finite-length signal is defined only for a certain range of $n$ , from some ${N}_{1}$ to ${N}_{2}$ . The signal is not defined outside of that range.

## Signal periodicity

As the name suggests, periodic signals are those that repeat themselves. Mathematically, this means that there exists some integer value $N$ for which $x(n+N)=x(n)$ , for all values of $n$ . So if we define a fundamental period of this particular signal of length, like $N=8$ , then we will see the same signal values shifted by $8$ time indices, by $16$ , $-8$ , $-16$ , etc. Below is an example of a periodic signal: So periodic signals repeat, and clearly periodic signals are going to be, therefore, infinite in length.It's also important to remember that to be periodic in discrete-time, the period $N$ must be an integer. If there is no such integer-valued $N$ for which $x(n+N)=x(n)$ (for all values of $n$ ), then we classify the signal as being aperiodic .

## Converting between infinite and finite length

In different applications, the need will arise to convert a signal from infinite-length to finite-length, and vice versa. There are many ways this operation can be accomplished, but we will consider the most common.

The most straightforward way to create a finite-length signal from an infinite-length one is through the process of windowing . A windowing operation extracts a contiguous portion of an infinite-length signal, that portion becoming the new finite-length signal. Sometimes a window will also scale the smaller portion in a particular way. Below is a mathematical expression of windowing (without any scaling):

$y(n)=\begin{cases}x(n) & \text{if {N}_{1}\le n\le {N}_{2}}\\ \text{undefined} & \text{if \text{else}}\end{cases}$

Below is a signal $x(n)$ (assume it is infinite-length, with only a part of it shown), with a portion of it extracted to create $y(n)$ :

There are two ways a signal can be converted from a finite-length to infinite-length. The first is referred to as zero-padding . It is easy to take a finite-length signal and then make a larger finite-length signal out of it: just extend the time axis. We have to decide what values to put in the new time locations, and simply putting $0$ at all the new locations is a common approach. Here is how it looks, mathematically, to create a longer signal $y(n)$ from a shorter signal $x(n)$ defined only on ${N}_{1}\le n\le {N}_{2}$ :

$y(n)=\begin{cases}0 & \text{if {N}_{0}\le n< {N}_{1}}\\ x(n) & \text{if {N}_{1}\le n\le {N}_{2}}\\ 0 & \text{if {N}_{2}< n\le {N}_{3}}\end{cases}$

Here, obviously ${N}_{0}< {N}_{1}< {N}_{2}< {N}_{3}$ , and if we extend ${N}_{0}$ and ${N}_{3}$ to negative and positive infinity, respectively, then $y(n)$ will end up being infinite-length.

find the 15th term of the geometric sequince whose first is 18 and last term of 387
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
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can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
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Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
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Abhi
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Abhi
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Abhi
Commplementary angles
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Sherica
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Sherica
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Uday
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a perfect square v²+2v+_
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algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
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Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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what's the easiest and fastest way to the synthesize AgNP?
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Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
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Porter
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Yasmin
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Cesar
I'm interested in nanotube
Uday
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
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Prasenjit
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Azam
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Prasenjit
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Damian
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Damian
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Azam
Hello
Uday
I'm interested in Nanotube
Uday
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Prasenjit
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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