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Both are programming processes whereas OOP stands for “OBJECT Oriented Programming” and POP stands for “Procedure Oriented Programming”. Both are programming languages that use high-level programming to solve a problem but USING different approaches. These approaches in technical terms are known as programming PARADIGMS. A programmer can take different approaches to write a program because there’s no direct APPROACH to solve a particular problem. This is where programming languages come to the picture. A program makes it easy to resolve the problem using just the right approach or you can say ‘paradigm’. Object-oriented programming and procedure-oriented programming are TWO such paradigms.

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ECONOMIES OF SCALE IS THE COMPETITIVE ADVANTAGE THAT LARGE ENTITIES HAVE OVER SMALKER ONES. THE LARGER THE BUSINESS, NON-PROFIT, OR GOVERNMENT THE LOWER ITS PER-UNIT COSTS.

when more UNITS of a good or a service can be produced on a larger scale , yet with (on average) fewer INPUT costs, economies of scale are said to be achieved.


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Resistivity means measuring of resisting power
of a SPECIFIC material to the FLOW of an electric CURRENT.its unit is ohm- Meter. conductivity means the degree of a specific material conducts ELECTRICITY,it is the ratio of current density in the material to the electric field.its unit is Siemens/meter

Small-signal modeling is a common ANALYSIS technique in electronics engineering which is used to approximate the behavior of ELECTRONIC circuits CONTAINING nonlinear devices with linear equations. It is applicable to electronic circuits in which the AC signals, the time-varying currents and voltages in the circuit, have a small magnitude compared to the DC bias currents and voltages. A small-signal model is an AC equivalent circuit in which the nonlinear circuit elements are replaced by linear elements whose VALUES are GIVEN by the first-order (linear) approximation of their characteristic curve near the bias point.

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BJT Configurations. The BIPOLAR JUNCTION transistor (BJT) has three TERMINALS, so can be USED in THREEDIFFERENT configurations with one terminal common to both input and output signal

The Fourier transforms of real-valued functions are symmetrical around the 0 Hzaxis. After sampling, only a periodic summation of the Fourier transform (called discrete-time Fourier transform) is still available. The individual frequency-shifted copies of the original transform are called aliases. The frequency offset between adjacent aliases is the sampling-rate, denoted by fs. When the aliases are mutually exclusive (spectrally), the original transform and the original continuous function, or a frequency-shifted version of it (if desired), can be recovered from the SAMPLES. The first and third graphs of Figure 1 depict a basebandspectrum before and after being sampled at a rate that completely separates the aliases.
The second graph of Figure 1 depicts the frequency profile of a bandpass function occupying the band (A, A+B) (shaded blue) and its mirror image (shaded beige). The condition for a non-destructive sample rate is that the aliases of both bands do not overlap when shifted by all integer multiples of fs. The FOURTH graph depicts the spectral result of sampling at the same rate as the baseband function. The rate was chosen by finding the lowest rate that is an integer sub-multiple of Aand also satisfies the baseband Nyquist criterion: fs > 2B.  Consequently, the bandpass function has effectively been converted to baseband. All the other rates that avoid overlap are given by these more general criteria, where A and A+B are replaced by fLand fH, respectively:[2][3]
{\displaystyle {\frac {2f_{H}}{n}}\leq f_{s}\leq {\frac {2f_{L}}{n-1}}}, for any integer nsatisfying: {\displaystyle 1\leq n\leq \left\lfloor {\frac {f_{H}}{f_{H}-f_{L}}}\right\rfloor }
The highest n for which the condition is satisfied leads to the lowest possible sampling rates.
Important signals of this sort include a radio's intermediate-frequency (IF), radio-frequency (RF) signal, and the individual channels of a filter bank.
If n > 1, then the CONDITIONS result in what is sometimes referred to as undersampling, bandpass sampling, or using a sampling rate less than the Nyquist rate (2fH). For the case of a given sampling frequency, simpler formulae for the constraints on the signal's spectral band are given below.



Spectrum of the FM radio band (88–108 MHz) and its baseband alias under 44 MHz (n = 5) sampling. An anti-alias filter quite tight to the FM radio band is required, and there's not room for stations at nearby expansion channels such as 87.9 without aliasing.



Spectrum of the FM radio band (88–108 MHz) and its baseband alias under 56 MHz (n = 4) sampling, showing plenty of room for bandpass anti-aliasing filter transition bands. The baseband image is frequency-reversed in this case (even n).

Example: Consider FM radio to illustrate the idea of undersampling.In the US, FM radio operates on the frequency band from fL = 88 MHz to fH = 108 MHz. The bandwidth is given by{\displaystyle W=f_{H}-f_{L}=108\ \mathrm {MHz} -88\ \mathrm {MHz} =20\ \mathrm {MHz} }The sampling conditions are satisfied for{\displaystyle 1\leq n\leq \lfloor 5.4\rfloor =\left\lfloor {108\ \mathrm {MHz} \over 20\ \mathrm {MHz} }\right\rfloor }Therefore, n can be 1, 2, 3, 4, or 5.The value n = 5 gives the lowest sampling frequencies interval {\displaystyle 43.2\ \mathrm {MHz}

In single processing, UNDERSAMPLING or band PASS SAMPLING is a Tecinque where one sampling a band pass filterd single at a sample rate below it's Nyquist rate, but is still able to reconstruct the SIGNAL...

If the sampling theorem is interpreted as requiring twice the highest frequency, then the required sampling rate would be assumed to be greater than the Nyquist rate216 MHz. While this does satisfy the last CONDITION on the sampling rate, it is grossly oversampled.Note that if a band is sampled with n > 1, then a band-pass filter is required for the anti-aliasing filter, instead of a lowpass filter.
As we have seen, the normal baseband condition for reversible sampling is that X(f) = 0 outside the interval:   {\displaystyle \scriptstyle \left(-{\frac {1}{2}}f_{\mathrm {s} },{\frac {1}{2}}f_{\mathrm {s} }\right),}
and the reconstructive interpolation function, or lowpass filter impulse response, is  {\displaystyle \scriptstyle \operatorname {sinc} \left(t/T\right).}
To accommodate undersampling, the bandpass condition is that X(f) = 0 outside the union of open positive and negative frequency bands
{\displaystyle \left(-{\frac {n}{2}}f_{\mathrm {s} },-{\frac {n-1}{2}}f_{\mathrm {s} }\right)\cup \left({\frac {n-1}{2}}f_{\mathrm {s} },{\frac {n}{2}}f_{\mathrm {s} }\right)}for some positive integer {\displaystyle n\,}.which INCLUDES the normal baseband condition as case n = 1 (except that where the intervals come together at 0 frequency, they can be CLOSED).
The corresponding interpolation function is the bandpass filter given by this difference of lowpass impulse responses:
{\displaystyle n\operatorname {sinc} \left({\frac {nt}{T}}\right)-(n-1)\operatorname {sinc} \left({\frac {(n-1)t}{T}}\right)}.
On the other hand, reconstruction is not usually the goal with sampled IF or RF signals. Rather, the sample sequence can be treated as ordinary samples of the signal frequency-shifted to near baseband, and digital demodulation can proceed on that basis, RECOGNIZING the spectrum mirroring when n is even.
Further generalizations of undersampling for the case of signals with multiple bands are possible, and signals over MULTIDIMENSIONAL domains (space or space-time) and have been worked out in detail by Igor Kluvánek.

IaC or Infrastructure as Code was initially evolved to support entire IT landscape however it PROVED to be very critical for cloud computing, DEVOPS and Infrastructure as a Services (IaaS). It is a METHOD of writing and deploying machine-readable description files that PRODUCE service elements, and hence supporting the delivery of business systems and IT-enabled processes.

In signal processing, sampling is the REDUCTION of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave (a continuous signal) to a sequence of samples (a discrete-time signal).
A sample is a value or set of values at a point in time and/or space.
A sampler is a subsystem or operation that extracts samples from a continuous signal.
A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points.

TheoryEdit

See also: Nyquist–Shannon sampling theorem

Sampling can be done for functions varying in space, time, or any other dimension, and similar results are obtained in two or more dimensions.
For functions that vary with time, let s(t) be a continuous function (or "signal") to be sampled, and let sampling be performed by measuring the value of the continuous function every T seconds, which is called the sampling interval or the sampling period.[1]  Then the sampled function is given by the sequence:
s(nT),   for integer values of n.
The sampling frequency or sampling rate, fs,is the average number of samples obtained in one second (samples per second), thus fs = 1/T.
Reconstructing a continuous function from samples is done by interpolation algorithms. The Whittaker–Shannon interpolation formulais mathematically equivalent to an ideal lowpass filter whose input is a sequence of Dirac delta functions that are modulated (multiplied) by the sample values. When the time interval between adjacent samples is a constant (T), the sequence of delta functions is called a Dirac comb. Mathematically, the modulated Dirac comb is equivalent to the product of the comb function with s(t). That purely mathematical abstraction is sometimes referred to as impulse sampling.[2]
Most sampled signals are not SIMPLY stored and reconstructed. But the fidelity of a theoretical reconstruction is a customary measure of the effectiveness of sampling. That fidelity is reduced when s(t) contains frequency COMPONENTS whose periodicity is smaller than two samples; or EQUIVALENTLY the ratio of cycles to samples exceeds ½ (see Aliasing). The quantity ½ cycles/sample × fs samples/sec = fs/2 cycles/sec (hertz) is known as the Nyquist frequency of the sampler. Therefore, s(t) is usually the output of a lowpass filter, functionally known as an anti-aliasing filter. Without an anti-aliasing filter, frequencies higher than the Nyquist frequency will influence the samples in a way that is misinterpreted by the interpolation process.[3

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The PALEY wiener CRITERION is the theorem which deals with the DECAY properties of a function.

This theorem was named by Raymond Paley and Norbert Wiener.

The Original theorems didnt use the distribution language and square integrable functions are used INSTEAD of that.

The paley wiener theorem supports SMOOTH functions.

The basic difference between a Trojan andworm is in their functionality. Trojan HORSE is: An imposter that claims to be something affordable but actually is MALICIOUS. The maindifference between virus and Trojan horse is that the FORMER can't replicate itself. ... Often worms exist within other files.

This is both out of curiosity and ALSO because I want to get how much the step response of a first order system will be exciting the RESONANCE of a mechanical assembly. Therefore I need an accurate Fourier transform of the response... Which I don't trust anymore. What COULD I do to improve the accuracy then, BASED on the "sine wave" case?

The FULL FORM of ROM is READ Only MEMORY

The continuous time unit impulse andunit step FUNCTION are. then RELATED by. The continuous time unit step function is a running integral of the delta function. It follows that the continuous time unit impulse can be THOUGHT of as the derivative of the continuous time unit step function.

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Dirichlet CONDITIONS are sufficient conditions for a real-valued, periodic function f to be equal to the sum of its Fourier series at each point where f is continuous. Moreover, the behavior of the Fourier series at points of discontinuity is determined as well (it is the midpoint of the values of the discontinuity). These conditions are named after PETER Gustav Lejeune Dirichlet.

The conditions are[1]:

f must be absolutely integrable over a period.

f must be of bounded VARIATION in any given bounded INTERVAL.

f must have a finite number of discontinuities in any given bounded interval

Linear filters process time-varying INPUT SIGNALS to produce output signals, subject to the CONSTRAINT of linearity. This RESULTS from systems composed SOLELY of components (or digital algorithms) classified as having a linear response.

In mathematics (and, in particular, functional analysis) convolution is a MATHEMATICAL operation on two functions (F and g) to produce a third function that expresses how the shape of one is modified by the other. The term convolution refers to both the result function and to the process of computing it. Convolution is similar to cross-correlation. For discrete, real-valued functions, they DIFFER only in a time reversal in one of the functions. For continuous functions, the cross-correlation operator is the adjoint of the convolution operator.
It has applications that include probability, statistics, computer vision, natural language processing, image and signal processing, engineering, and differential equations.[citation needed]
The convolution can be defined for functions on EUCLIDEAN space, and other GROUPS.[citation needed] For example, periodic functions, such as the discrete-time Fourier transform, can be defined on a circle and convolved by periodic convolution. (See row 13 at DTFT § Properties.) A discrete convolution can be defined for functions on the set of integers.
Generalizations of convolution have applications in the field of numerical analysisand numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing.[citation needed]
Computing the inverse of the convolution operation is known as deconvolution

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Region of CONVERGENCE (ROC) WHETHER the Laplace transform of a signal exists or not depends on the complex variable as well as the signal itself. All complex values of for which the integral in the DEFINITION converges FORM a region of convergence (ROC) in the s-plane.

In signal processing, specifically control theory,bounded-input,bounded-output (BIBO) stability is a form of stability for linear SIGNALS that take inputs.If a system is BIBO stable,then the output will be bounded for every input to the system that is bounded.f or continuous-time signals .
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A signal is a discription of how ONE parameter varies with another parameter. for Instance , VOLTAGE changing over time in electronic circuit, or brightness varying with distance in an IMAGE. A SYSTEM is any process that produces an output signal in RESPONSE to an input signal.


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It is typically measured in hertz, and depending on CONTEXT, MAY specifically refer to passband bandwidth or baseband bandwidth. Passband bandwidth is the difference between the UPPER and lower CUTOFF frequencies of, for example, a band-pass filter, a COMMUNICATION channel, or a signal spectrum.

The ROC cannot contain any poles.B y definition a pole is awhereX(z) is infinite.Since X(z) must be finite for all z for CONVERGENCE,t here cannot be a pole in the ROC.If x(n)is afinite-duration sequence,then the ROC is the entire z-plane,E except possibly z=0
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In mathematics, the Dirichlet CONDITIONS are SUFFICIENT conditions for a real-valued, PERIODIC function F to be equal to the sum of its Fourier series at each point where f is CONTINUOUS. ... These conditions are named after Peter Gustav Lejeune Dirichlet. The conditions are: f must be absolutely integrable over a period.

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The Hilbert TRANSFORM has a PARTICULARLY SIMPLE REPRESENTATION in the frequency domain: it IMPARTS a phase shift of 90° to every Fouriercomponent of a function. ... The Hilbert transform is important insignal processing, where it derives theanalytic representation of a real-valued signal u(t).

Sampling Theorem. An important issue in sampling is the determination of the sampling frequency. We WANT to MINIMIZE the sampling frequency to reduce the data size, THEREBY lowering the computational complexity in data processing and the costs for data STORAGE and transmission

In mathematics and in signal processing , the HILBERT transform is aspecific LINEAR operator that takes a function, u of a rap variable and PRODUCES ANOTHER function of a real variable H.


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1.convolution OBEYS COMMUTATIVE PROPERTIES. 2.It also obeys DISTRIBUTIVE and associative properties

Any TWO signals say 500Hz and 1000Hz (On a constraint that both frequencies are MULTIPLE of its fundamental here lets say 100Hz) ,when both are mixed the RESULTANT wave obtained is said to be orthogonal. Meaning: Orthogonalmeans having exactly 90 DEGREE shift between those 2 signals.

. Noise factor

For components such as resistors, the noise factor is the ratio of the noise produced by a real resistor to the simple thermal noise of an ideal resistor. The noise factor of a system is the ratio of output noise power (Pno) to input noise power (Pni):





To make comparisons easier, the noise factor is always measured at the standard temperature (To) 290°K (standardized room temperature).

The input noise power Pni is defined as the product of the source noise at standard temperature (To) and the amplifier GAIN (G):

Pni = GKBT0 (5-16)


It is also possible to define noise factor Fn in terms of output and input S/N ratio:



which is also:



where

Sni is the input signal-to-noise ratio
Sno is the output signal-to-noise ratio
Pno is the output noise power
K is Boltzmann's constant
(1.38 X 10-23 J/°K)
To is 290°K
B is the network bandwidth in hertz (Hz)
G is the amplifier gain

The noise factor can be evaluated in a model that considers the amplifier ideal and therefore amplifies only through gain G the noise produced by the input noise source:



or



where

N is the noise added by the network or amplifier
(Other terms as previously defined)

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2. Noise figure


The noise figure is a frequently used measure of an amplifier's goodness, or its departure from the ideal. Thus it is a figure of merit. The noise figure is the noise factor converted to decibel notation:

NF = 10 LOG Fn (5-21)


where

NF is the noise figure in DECIBELS (dB)
Fn is the noise factor
LOG refers to the system of base-10 logarithms

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3. Noise temperature


The noise temperature is a means for specifying noise in terms of an equivalent temperature. Evaluating Equation 5-18 shows that the noise power is directly proportional to temperature in degrees Kelvin and that noise power collapses to zero at absolute zero (0°K).

Note that the equivalent noise temperature TE is not the PHYSICAL temperature of the amplifier, but rather a theoretical construct that is an equivalent temperature that produces that amount of noise power. The noise temperature is related to the noise factor by:

Te = (Fn - 1) To (5-22)


and to noise figure by:




Now that we have noise temperature Te, we can also define noise factor and noise figure in terms of noise temperature:




and




The total noise in any amplifier or network is the sum of internally and externally GENERATED noise. In terms of noise temperature:

 Pn(total) = GKB(To + Te) (5-26)


where

Pn(total) is the total noise power
(other terms as previously defined)

Answer:

Properties of Laplace Transform

The Laplace transform has a set of properties in parallel with that of the Fourier transform. The DIFFERENCE is that we need to pay special attention to the ROCs. In the following, we always assume

\begin{displaymath}{\cal L}[x(t)]=X(s),\;\;\;\;ROC=R_x,\;\;\;\;\;\mbox{and}\;\;\;\;\;\;

{\cal L}[y(t)]=Y(s),\;\;\;\;ROC=R_y \end{displaymath}

Linearity

\begin{displaymath}{\cal L}[a x(t)+b y(t)]=aX(s)+bY(s), \;\;\;\;ROC \supseteq (R_x \cap R_y) \end{displaymath}

( $ A \supseteq B$ means set $A$ contains or equals to set $B$, i.e,. $A$ is a subset of $B$, or $B$ is a superset of $A$.)

It is obvious that the ROC of the linear combination of $x(t)$ and $y(t)$ should be the intersection of the their INDIVIDUAL ROCs $R_x \cap R_y$ in which both $X(s)$ and $Y(s)$ exist. But also NOTE that in some cases when zero-pole cancellation occurs, the ROC of the linear combination could be larger than $R_x \cap R_y$, as shown in the example below.

Example: LET

\begin{displaymath}X(s)={\cal L}[x(t)]=\frac{1}{s+1},\;\;\;\;Re[s]>-1,\;\;\;\;\;\;\;\;

Y(s)={\cal L}[y(t)]=\frac{1}{(s+1)(s+2)},\;\;\;\;Re[s]>-1 \end{displaymath}

then

\begin{displaymath}{\cal L}[x(t)-y(t)]=\frac{1}{s+1}-\frac{1}{(s+1)(s+2)}

=\frac{s+1}{(s+1)(s+2)}=\frac{1}{s+2}, \;\;\;\;Re[s]>-2 \end{displaymath}

We see that the ROC of the combination is larger than the intersection of the ROCs of the two individual terms.

Time Shifting

\begin{displaymath}{\cal L}[x(t-t_0)]=e^{-t_0s} X(s),\;\;\;\;ROC=R_x \end{displaymath}

Shifting in s-Domain

\begin{displaymath}{\cal L}[e^{s_0t}x(t)]=X(s-s_0),\;\;\;\;ROC=R_x+Re[s_0] \end{displaymath}

Note that the ROC is shifted by $s_0$, i.e., it is shifted vertically by $Im[s_0]$ (with no effect to ROC) and horizontally by $Re[s_0]$.

Time Scaling

Gaussian means of or relating to Karl GAUSS or his mathematical theories of MAGNETIC or ELECTRICITY or astronomy or probability. And distribution means ISSUANCE

1. GAUSSIAN and UNIFORM White Noise:
2. Power Spectral Density
3. Strictly and WEAKLY DEFINED White noise:

Several Artificial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among PROBABILITIES of various states of their uncertain domain models. Even though the correct working of these schemes is practically contingent upon the existence of a SMALL number of probable states, no formal justification has been proposed of why this should be the case. This paper attempts to fill this apparent gap by studying asymmetries among probabilities of various states of uncertain models. By rewriting the joint probability distribution over a MODEL's variables into a product of individual variables' prior and conditional probability distributions, and applying central limit theorem to this product, we can demonstrate that the probabilities of individual states of the model can be expected to be drawn from highly skewed, log-normal distributions. With sufficient asymmetry in individual prior and conditional probability distributions, a small fraction of states can be expected to cover a large portion of the total probability SPACE with the REMAINING states having practically negligible probability. Theoretical discussion is supplemented by simulation results and an illustrative real-world example.

In probability theory and statistics, covariance is a measure of how much two variables change TOGETHER, and the covariance function, or kernel, DESCRIBES the spatial or temporal covariance of a random variable PROCESS or field

Number of ace and king in deck of playing CARD = 8
Probability of GETTING an ace and a king
= 8/52
= 2/13
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In probability theory and statistics, given two jointly DISTRIBUTED RANDOM VARIABLES ... The properties of a CONDITIONAL distribution