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computer science
systems analysis and design 12th

Questions and Answers of Systems Analysis And Design 12th

Using Eq. (7.167), plot the multitime spread for asymmetry factors of \(g=0.8,0.9\), and 0.95 for the optical thickness range from 10 to 100. Assume that \(c=0.2286, b=0.16\), and \(a=0.0686\).
Using Eq. (7.167), plot the multitime spread for single scatter albedos of \(\omega_{0}=0.5,0.65\), and 0.0 .8 for the optical thickness range from 10 to 100. Assume that \(g=0.875\). Explain the
An abrupt silicon \(\left(n_{i}=10^{10} \mathrm{~cm}^{-3}ight) \mathrm{p}-\mathrm{n}\) junction consists of a p-type region containing \(10^{16} \mathrm{~cm}^{-3}\) acceptors and an n-type region
An abrupt silicon \(\left(n_{i}=10^{10} \mathrm{~cm}^{-3}ight) \mathrm{p}-\mathrm{n}\) junction consists of a p-type region containing \(2 \times 10^{16} \mathrm{~cm}^{-3}\) acceptors and an
Consider an abrupt p-n diode with \(N_{a}=10^{18} \mathrm{~cm}^{-3}\) and \(N_{a}=10^{16}\). Calculate the junction capacitance at zero bias. The diode area equals \(10^{-4} \mathrm{~cm}^{2}\).
An ideal photodiode is made of a material with a bandgap energy of \(2.35 \mathrm{eV}\). It operates at \(300 \mathrm{~K}\) and is illuminated by monochromatic light with wavelength of \(400
What is the short-circuit current delivered by a \(10 \mathrm{~cm} \times 10 \mathrm{~cm}\) photodetector (with 100\% quantum efficiency) illuminated by monochromatic light of \(400 \mathrm{~nm}\)
Assume the photodiode of this problem as an ideal structure with \(100 \%\) quantum efficiency and area \(1 \mathrm{~cm}^{2}(=1 \mathrm{~cm} \times 1 \mathrm{~cm})\). In addition, assume it is
A photodiode is exposed to radiation of uniform spectral power density(covering the range from \(300-500 \mathrm{THz}\). Outside this range there is no radiation. The total power density is \(2000
The power density of monochromatic laser light \((586 \mathrm{~nm})\) is to be monitored by a silicon photodiode with area equal to \(1 \mathrm{~mm}^{2}\) (= \(\left.1 \mathrm{~mm} \times 1
What is the theoretical efficiency of a photodetector with a \(2.5 \mathrm{eV}\) bandgap when exposed to \(100 \mathrm{~W} / \mathrm{m}^{2}\) solar radiation through with transmittance, 1; if 600 nm
Consider a small silicon photodiode with a \(100 \mathrm{~cm}^{2}=10 \mathrm{~cm} \times 10 \mathrm{~cm}\) area. When \(2 \mathrm{~V}\) of reversed bias is applied, the reverse saturation current is
Referring to Problem 8.11, consider an ideal photodiode with no internal resistance.(a) Under an illumination of \(1000 \mathrm{~W} / \mathrm{m}^{2}\), at \(300 \mathrm{~K}\), what is the maximum
Assume that we have an EDFA FSOC communications receiver whereunder high amplifier gain levels. For \(\lambda=1.55 \mu \mathrm{m}, B_{0}=75 \mathrm{GHz}\), \(B_{e}=7.5 \mathrm{GHz}, n_{p}=1.4,
Assume that we have a horizontal \(10 \mathrm{~km}\) FSOC link at height \(h_{0}\) above the ground. If the refractive index structure function at altitude is \(C_{n}^{2}\left(h_{0}ight) \approx 3
A photomultiplier (PMT) has a dark count noise level of 100 counts per seconds. Calculate the minimum optical power \((S N R=1)\) at \(500 \mathrm{~nm}\) that can be detected within a \(10
A \(\mathrm{p}-\mathrm{i}-\mathrm{n}\) photodiode has a responsivity of \(0.8 \mathrm{~A} / \mathrm{W}\) at \(1.55 \mu \mathrm{m}\). The effective resistance of the detector circuit is \(50 \Omega\).
Referring to problem 8.16, what would the NEP be if the detector is now feeding an amplifier with a noise temperature of \(600 \mathrm{~K}\) ?The Noise Figure \(F_{\text {rf }}\) is related to its
Prove the statement on page (5) that the average risk is minimized by choosing the hypothesis for which the conditional risk is the smaller.
Derive the conditions that the line of equal risk does not intersect the operating characteristic in the region \(0 \ll Q_{0} C11 < Co
Find the Bayes test to choose between the hypotheses, \(H_{0}\) and \(H_{1}\), whose prior probabilities are \(\frac{5}{8}\) and \(\frac{3}{8}\), respectively, when under \(H_{0}\) the datum \(x\)
The random variables \(x\) and \(y\) are Gaussian with mean value 0 and variance 1 . Their covariance may be 0 or some know positive value \(r>0\). Show that the best choice between these
A sequence of \(N\) independent measurements is taken from a Poisson distribution \(\{x\}\) whose mean is \(m_{0}\) under \(H_{0}\), and \(m_{1}\) under \(H_{1}\). On what combination of the
A random variable \(x\) is distributed according to the Cauchy distribution,The parameter \(m\) can take on either of two values, \(m_{0}\) or \(m_{1}\), where \(m_{0} P(x) = = m (m + x)
Under Hypotheses \(H_{0}\) and \(H_{1}\), a random variable has the following probability density functionsChoosing \(H_{0}\) when \(H_{1}\) is true costs twice as much as choosing \(H_{1}\) when
A choice is made between Hypotheses \(H_{0}\) and \(H_{1}\) on the basis of a single measurement \(x\). Under Hypothesis \(H_{0}, x=n\); under Hypothesis \(H_{1}, x=s+n\). Here both \(s\) and \(n\)
Derive Eqs. (9.105) and (9.106).Equation 9.105Equation 9.106 SNRDD-PIN rn Prec 2hvRb = (nrno)/2,
Using Eq. (9.108), calculate the value of \(Q\) for (a) \(10^{-9}\) and (b) \(10^{-12}\).Equation 9.108 rEb = m SNRQL No Ps (hv R) =
Determine the \(Q\) expression for preamplifier noise-limited receiver. Let \(i_{0}=0\).
Show that if a circular aperture lens of diameter \(d\) is used when heterodyning with two match Airy patterns, the equivalent suppression factor for misaligned angles is proportional towhere
Show that Qfa N40 ** (N-2) -(d+v) IN-I (20v)dv Ngo 1 N 20 N 90 W2 ew dw=1 -1). as 20 - (). 0 0. Here, I(u,p) is the Pearson's form of the incomplete gamma function given by 1 I(u,p) = ye dy. (p+1).
Show thatfor large even values of \(N\). 1 40 N (Nv N . (N-2) -(1+Nv) IN-2 (VANV) dv (N-3) 90 (Nv) 4 -VA-N dv (N-1) 24
Assume we have a \(5 \times 5\) pixel target with equal signal level at every pixel, and background clutter with equal estimated mean as well. Specifically, we set \(s_{n}=6\) and \(\widehat{\mu}_{b
Let \(\Pi\) be the plane in \(R^{3}\) spanned by vectors \(\boldsymbol{x}_{1}=(1,2,2)\) and \(\boldsymbol{x}_{2}=\) \((-1,0,2)\).(i) Find an orthonormal basis for \(\Pi\).(ii) Extend it to an
Find the QR factorization of 12 A=12 03
The ratio of the spontaneous to stimulated emission rates is given byWhat is the ratio at \(\lambda=600 \mathrm{~nm}\) for a tungsten lamp operating at \(2000 \mathrm{~K}\) ? Rspon hv = NT 1. Rstim
Assume that we have a lamp that has a radiance of \(95 \mathrm{~W} /\left(\mathrm{cm}^{2} \mathrm{sr}ight)\) at \(\lambda=546 \mathrm{~nm}\). What is the radiance of a \(1 \mathrm{~W}\) Argon laser
Consider a lower energy level situated \(200 \mathrm{~cm}^{-1}\) from the ground state. There are no other energy levels nearby. Determine the fraction of the population found in this level compared
Find the FSR, \(Q\), and \(F\) of the cavity shown as follows.Assume that the wavelength of light equals \(1 \mu \mathrm{m}\). R = 0.995 d = 1 mm R2 = 0.995 n = 1
Find the FSR, \(Q\), and \(F\) of the cavity shown as follows.Assume that the wavelength of light equals \(1 \mu \mathrm{m}\) and \(\alpha=\) \(0.001 \mathrm{~cm}^{-1}\).If we have a cavity with a
The amplifying medium of a helium-neon laser has an amplification spectral band equal to \(\Delta v=1 \mathrm{GHz}\) at \(\lambda=632.8 \mathrm{~nm}\). For simplicity, the spectral profile is assumed
Assume that we have a \(\mathrm{CO}_{2}\) laser that has a bandwidth of \(\Delta v=\) \(1 \mathrm{GHz}\) at \(=10.6 \mu \mathrm{m}\). For simplicity, the spectral profile is assumed to be
Verify that for \(m=n=0\), with plane-parallel mirrors \(\left(c_{1}=c_{2}=ight.\) \(\infty\) ) in a cavity of length \(d\), the resonant longitudinal modes are given by Equation (10.114).
Calculate the gap in frequency between two longitudinal modes in a linear cavity with a length of \(300 \mathrm{~mm}\).
A helium-neon laser emitting at \(632.8 \mathrm{~nm}\) light makes a spot with a radius equal to \(100 \mathrm{~mm}\) at \(e^{-2}\) at a distance of \(500 \mathrm{~m}\) from the laser. What is the
Find the output ray of the system shown as follows when the input ray is characterized by \(ho=0.1 \mathrm{~cm}\) and \(ho^{\prime}=-0.1 \mathrm{~cm}^{-2}\).assuming \(d_{1}=7 \mathrm{~cm}, d_{2}=5
Determine the minimum radius of curvature of the two mirrors to ensure the following cavity is stable: R = = R3 = R d2 d R = R d =00 R4=
Let(a) what is \(\boldsymbol{A}+\boldsymbol{B}\) ?(b) What is \(\boldsymbol{A}-\boldsymbol{B}\) ? 23 A and B 0 1 14 23 2 30 -125
Compute the determinant 12 1 2 10 |A|=239 4 5 11
Compute the determinant |A| = 1+2 +32 +41 +3 -2 +1 +2 +3 +2 +3 +4 -2 +40 +5
Compute the determinant |A|= 1+2 +32 +4 +7 +4-3 +10 +3 +2 +3 +4 -2 +40 +5
Show that the cofactor of each element ofis that element. A = + 1 -1321323 + + 1 + I 231323 WIN win 23 23 13
Show that the cofactor of an element of any row ofis the corresponding element of the same numbered column. -4-3-3 A = +10+1 +4 +3 +3
Find the inverse of A = 1+2 +4 +3 +2 +3 +6 +5 +2 +2 +5 +2 -3 +4 +5 +14 +14
Calculate the Fourier series coefficients Cn for the following periodic function: B u(x) a A b X
Calculate the Fourier series coefficients Cn for the function u(x) plotted as follows, but do so exploiting some of the properties contained in Eqs. (1.4)-(1.24) to provide a solution derived from
Calculate the Fourier series coefficients Cn for the function u(x) plotted as follows, but do so exploiting some of the properties contained in Eqs. (1.4)-(1.24) to provide a solution derived from
Calculate the Fourier series coefficients \(C_{n}\) for \(u(x)=A(x) e^{i \varphi(x)}\). \(\varphi(x)=\varphi_{0}+10 \pi \frac{x}{b}\). The curve shown in the following figure is like the lower
LetProve that its Fourier transform is f(x) = e()
LetProve that its Fourier transform is 1 if |x| f(x) = rect 0 otherwise
LetWhat is its two-dimensional Fourier transform? f(x, y) = rect (1) rect (f).
LetWhat is its two-dimensional Fourier transform? f(x, y) = Circ(r) = circ function ={ 1 |r|= x + y 1 0 otherwise
Assume a card selected out of an ordinary deck of 52 cards. Letand A = {the card is a spade}
Let two items be chosen out of a lot of 12 items where 4 of them are defective. Assume and A = {both chosen items are defective} B = {both chosen items are not defective}. Compute P{A} and P{B}.
Given the problem laid out in Problem 1.19. Assume now thatWhat is the probability that event C occurs?Problem 1.19Let two items be chosen out of a lot of 12 items where 4 of them are defective.
Let a pair of fair dice be tossed. If the sum is 6 , what is the probability that one of the dice is a 2 ? In other words, we have and A = {sum is 6} Find P{B|A}. B = {a 2 appears on at least one
In a certain college, \(25 \%\) of the students fail in mathematics, \(15 \%\) of the students fail in chemistry, and \(10 \%\) of the students fail both in mathematics and chemistry. A student is
Let \(\boldsymbol{A}\) and \(\boldsymbol{B}\) be events with \(P\{\boldsymbol{A}\}=1 / 2, P\{\boldsymbol{B}\}=1 / 3\), and \(P\{\boldsymbol{A} \cap \boldsymbol{B}\}=\) \(1 / 4\). Find (a)
A lot contains 12 items of which 4 are defective. Three items are drawn at random from that lot one after another. Find the probability that all three are nondefective.
A card player is dealt 5 cards one right after another from an ordinary deck of 52 cards. What is the probability that they are all spades?
Let \(\varphi(t)\) be the standard normal distribution (i.e., mean equals zero and variance equals to unity)? Find \(\varphi(t)\) for(a) \(t=1.63\),(b) \(t=-0.75\) and \(t=-2.08\).
A fair die is tossed seven times. Let us assume that success occurs if a 5 or 6 appear. Let \(n=7, p=P\{5,6\}=\frac{1}{3}\), and \(q=1-p=\frac{2}{3}\).(a) What is the probability that a 5 or a 6
A fair coin is tossed six times. Let us assume that success is a heads. Let \(n=6\) and \(p=q=\frac{1}{2}\).(a) What is the probability that exactly two heads occur (i.e., \(k=2\) )?(b) What is the
For a Poisson distribution\[p(k, \lambda)=\frac{\lambda^{k}}{k !} e^{-\lambda}\]find(a) \(p(2,1)\),(b) \(p\left(3, \frac{1}{2}ight)\), and(c) \(p(2,7)\).
Suppose 300 misprints are randomly distributed throughout a book of 500 pages. Find the probability that a given page contains(a) exactly 2 misprints,(b) 2 or more misprints.
Suppose \(2 \%\) of the items made by a factory are defective. Find the probability that there are 3 defective items in a sample of 100 items.
Given\[X(\mathrm{~dB})=10 \log _{10} X\]derive an equation for \(X\) in terms of \(X(\mathrm{~dB})\).
Solve the following integral: Integrals running from \(-\infty\) to \(+\infty\) integrate over the parameters \(v\) and \(x\), while the integral with finite limits integrates over the parameter
Let us assume that the refractive index of the medium above the \((x\), y) plane is 1 and that the refractive index of the medium below the \((x\), \(y\) ) plane is \(n_{1} eq 1\). Also, let us
Computewith \(A=\frac{5}{2}, B=\frac{15}{2}, k=\frac{2 \pi}{5}, f(x)=x(x-5)^{2}\), and \(g(x)=\sin \left(\frac{\pi x}{30}ight)\). ] = A B 8(x) eikf(x) dx
We assume \(u(x)=0\) in \(|x| \geq \frac{P}{2}\). Hence, \(\tilde{u}(v)\) can be sampled at \(v_{n}=\) \(\frac{n}{p}\), which is enough to know, \(\tilde{u}(v)\) and \(u(x)\) complex. Refer to the
The Rayleigh Criterion for resolution states that two point sources are just resolved when the central maximum from one source falls on the first minimum of the diffraction pattern from the other
Two stars are a distance \(1.5 \times 10^{8} \mathrm{~km}\) apart. At what distance can they be resolved by the unaided eye? Assume that the refractive index and the lens aperture of the eye are 1.34
In Young's double-slit experiment, light intensity is a maximum when the two waves interfere constructively. This occurs whenwhere \(d\) is the separations of the slits, \(\lambda\) the wavelength of
Refer to the introduction to Problem 2.8 and the figure in Problem 2.9. Using the small angle approximation, develop an expression for wavelength used in this experiment. A pair of screens are placed
One end of a cylindrical glass rod of refractive index 1.5 is ground and polished to a hemispherical shape of radius \(R=20 \mathrm{~mm}\). A \(1 \mathrm{~mm}\) high, arrow-shaped object is located
What type of mirror is required to form an image on a wall \(3 \mathrm{~m}\), from the mirror, of a filament of a headlight lamp \(10 \mathrm{~cm}\) in front of the mirror? What is the height of the
Find the focal length and the positions of the focal points and principle points of a single thick lens shown in the following figure. The index of the lens is 1.5 , its axial thickness \(25
Ten-inch focal length lens forms an image of a telephone pole that is \(200 \mathrm{ft}\) away (from its first principal point). Where is the image located (a) with respect to the focal point of the
A 1 -in. cube is 20 in. away from the first principal point of a negative lens with a negative 5 -in. focal length. Where is the image and what are its height, width, and thickness?
Find the position and diameter of the Entrance and Exit Pupils of a \(100-\mathrm{mm}\) focal length lens with an aperture \(20 \mathrm{~mm}\) to the right of the lens. Assume that the lens and
What is irradiance \(2 \mathrm{~m}\) from a \(100 \mathrm{~W}\) light bulb? What is radiance of a typical \(100 \mathrm{~W}\) light bulb? Here assume that the filament area is \(1 \mathrm{~mm}^{2}\).
Your night light has a radiant flux of \(10 \mathrm{~W}\). What is the irradiance on your book you were reading that fell \(2 \mathrm{~m}\) from the light when you fell asleep (assuming the book is
A point source radiates \(10 \mathrm{~W} / \mathrm{sr}\) toward a \(10 \mathrm{~cm}\)-diameter lens. How much power is collected by the lens when its distance from the source is (a) \(3 \mathrm{~m}\)
Using the Stefan-Boltzmann law, compute the radiant exitance of a blackbody at \(T=27{ }^{\circ} \mathrm{C}\left(80.6^{\circ} \mathrm{F}ight)\). What are the maximum wavelength at this temperature
Using Planck's law, derive the Wien's law irradiance distribution used to create the curve in Figure 4.18. Irradiance H, (KW/(cm-m)) 5 4.5 4 3.5 3 2.5 2 0.5 10 Planck's law Wein's law Rayleigh-Jeans
What is the spectral radiant exitance of a \(5900 \mathrm{~K}\) blackbody in the region of \(0.5 \mu \mathrm{m}\) ? What is its radiance?
If you have a source at a temperature of \(1000 \mathrm{~K}\), and an emissivity of 0.93 , what is the radiant exitance of the source?
(a) What is the spectral radiant emittance of a \(1000 \mathrm{~K}\) blackbody in the region of \(2 \mu \mathrm{m}\) wavelength? (b) What is the radiance? (c) If an idealized band-pass filter only
What is the approximate wavelength that humans radiate at?

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