Question 1 Let f(r) be the 27-periodic function defined by x € [0, 7) -x- 2 rE (-7, 0). 1+1 f(x) = Then, the Fourier series of f (A) converges to -1/2 in r = 0 (B) converges to 1 in r = 0 (C) does not converge pointwise in all points where f is discontinuous (D) does not converge in r = T/2

Q: 3. Let D, be the Fourier coefficients of periodic signal f (t). (a) When H, is the Fourier…

A: (a). Linearity property of Fourier series: Given information:

Q: Q4: For the periodic function whose definition in one period is: 0 <x <n (x, f(x) = {n. n <x< 2n)…

A: Given Given function is  f(x)=xπ0&lt;x&lt;ππ&lt;x&lt;2π

Q: 4.7. For each of the following Fourier transforms, use Fourier transform properties (Table 4.1) to…

A:

Q: Ques2: Evaluate the Fourier series for a periodic signal given by a ramp signal, x(t) = t for 0 < t…

A: We will calculate exponential series coefficient, we know direct formula for that .

Q: Suppose that we are given the following information about a signal x[n]: 1. x[n] is a real signal.…

A: By using the properties of Discrete Time Fourier Series....

Q: A periodic function f(x) is defined as 2, -1<x<0, f(x)=- [3x, 0<x<1. f(x+2) = f(x) Based on the…

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Q: A half-range periodic function f(x) is defined by { 0 < x < T, TT < x < 2n. T - x, f(x) 0, i. Sketch…

A: A function defined only in the half of the range (i.e., 0 to L) instead of full range (-L to L) is…

Q: 3. (a) Find the Fourier series of the triangular wave function defined by flx) = |x| for -1 <x<l and…

A: "According to the company's policy we will provide solution of the first part of the question if you…

Q: The discrete time periodic signal x(n)={2,1,-4,2} has the Fourier coefficients given as Cx =…

A:

Q: 3.10. Let x[n] be a real and odd periodic signal with period N = 7 and Fourier coefficients ak.…

A:

Q: Problem (6) A discrete-time periodic signal x[n] is real valued and has a fundamental period N= 5.…

A: Given a discrete-time periodic signal x(n) is real valued and has a fundamental period N=5. Given…

Q: 2) A discrete-time periodic signal x[n] is real valued and has a fundamental period N = 5. The non-…

A: x(n) is expressed in the given form as shown below

Q: Question 6. Given, the following function |-2x, -zs1<0 S(1)=- | 2.x, Ost<z -St<0 , and f(t+4x)=f(t)…

A: We need to draw and find out whether the given signal is odd or even and we need to find out Fourier…

Q: A periodic signal x(t) is given as following. a) Find the fourier series components via complex…

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Q: Q1 Find the Fourier series expansion for the periodic function f(1) if in one period f(1) A f (t) =…

A: We need to find out Fourier series coefficient of given signal .

Q: At a point where the spatial gradient of the temperature is equal to zero, Fourier's law implies…

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Q: 180 The output of a system is y(t) = 3x(t-2). where x(t-1) is the input. The system impulse response…

A: In this question , we have to find out impulse response of system..

Q: Problem 4 Consider a continuous-time LTI system whose frequency response H(jw) is shown graphically…

A: a)

Q: Suppose we are given the following information about a signal x(t): • x(t) is real and odd x(t) is…

A:

Q: (A) A rectangular pulse x(t) of width t= 8 msec. and amplitude A=10 V is centered at the origin in…

A: As per our company guidelines we are supposed to answer only first 3 subpart kindly repost other…

Q: Given a zero-centered hat function of height 3 volts and width 20.0 ms, determine the Fourier…

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Q: Sketch the wave form defined by: 1+ , when -n <x<0 f(x) = ,when 0 <x <n Determine the Fourier series…

A: Function fx is a repeating composite of two lines in the defined time intervals, one line has…

Q: [Part C-C3 (A) A rectangular pulse x(t) of width t= 8 msec. and amplitude A=10 V is centered at the…

A: Given :    Amplitude of the signal A = 10 V    Width of the signal T = 8 m Sec.   Here first of all…

Q: Question 1 Consider the following Fourier series: 8 s(t) = (-2) 1 (sin (2tnft)) n=1 where, n is an…

A: Given: Consider the following Fourier series: st=-8π2∑n=1∞1n2sin2πnft where n is an odd integer and…

Q: Exercise 1: (iii) Determine TF [g (t)]. 6) Show that TF [f (t - a)] = e-2nva TE (f (t)] where aeR *.…

A: Given: h(t)=0, -∞&lt;t&lt;0t2-t+0.25, 0≤t&lt;10, 1≤t&lt;∞ i) We need to plot h(t) ii) We need to…

Q: Express the Fourier series expansion up to the second harmonic for a periodic function, f(t) which…

A:

Q: Problem (6) A discrete-time periodic signal x[n] is real valued and has a fundamental period N= 5.…

A: The discrete-time signal, with the fundamental period N=5, is given as:…

Q: A continuous-time periodic signal x(t) is a real valued has the fundamental period To is equal to 8…

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Q: Let x() be a periodic signal of period T and C =k 0. Let y(t)= x(t)cos(v,t),W. Then, the complex…

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Q: The Fourier series coefficient for the periodic signal x(t) = sin?t %3D A. 8lk – 1] +8[k] +78[k+ 1]…

A: In the Given expression Find the coefficient of the Fourier series.

Q: A half-range periodic function f(x) is defined by {" *- r, 0, 0 < x < 7, * <x< 2n. f(1) = %3D i.…

A: A half range periodic function is one that is defined just in half of the range (i.e., 0 to L)…

Q: Question 2 The complex Fourier series coefficients of a Discrete-Time periodic signal x[n], with…

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Q: Exactly one period of x (t) is given by u (t + c) + Au (t + d)- Au (t- d)- u (t- c) for It| <c,…

A: x(t)=u (t+c)+A u(t+d)-A u(t-d)-u (t-c)subtituing the given valus we have,x(t)=u (t+8)+8 u(t+2)-8…

Q: Q4. Define Fourier Integral. Find the Fourier cosine integral represantation of the function Sk if…

A: We can use an extension of f(x) to R in order to obtain the Fourier cosine integral of f(x).…

Q: 2) Consider a periodic signal f(t), with period T, that has a value of T/2t in the interval -t A)…

A: The signal shown in the question is an even function. The Fourier series of an even function contain…

Q: The periodic function f (x) of period 2n is given by 0<x < T TI < x < 2n f(x): a) Sketch the graph…

A: Given: A periodic function of the fundamental period T=2π is given as fx=x, 0&lt;x&lt;πx+π,…

Q: T/2, and T = 2n. Using Fourier series, derive an expression for the voltage across the inductor in…

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Q: Given an even symmetric periodic signal with a period T, its trigonometric Fourier series…

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Q: Find the trigonometric Fourier series of a periodic signal x(t) defined by x(t) = 12, -7 <t <T and…

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Q: -1 3. a) f(t)\ . f(t) = ao + a, cos nwt + b, sin not ao. an ve b, b) f(t) r) = C,+ C, cos( C, cos(…

A: Here first of all we have calculated the fourier transform of the given continues time periodic…

Q: 3. (a) Show that the Fourier series for f(x) = x², –T < x < n, is n-1 Cos(nx) 4(-1)"-1 n2 n=1 (b)…

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Q: Q1) Choose the correct answer (s) 1. Which of the following is an even function of t.? (a) 12 (b)t…

A: given here some multiple choice question and asked find the correct answer for those questions.…

Q: Consider the following continuous time system that sums two input signal z1(t) and z2(t) with aj and…

A: Any continuous time periodic signals can be represented as an infinite sum of sine and cosine…

Q: f(x)=[-k,  -2<x<0 and k, 0<x<2]  Find the Fourier series expansion of the periodic function.

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Q: A periodic waveform #(t) with period T = 4 sec is defined over one period by the equa- tion 2(t) =…

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Q: Q1- Find the Fourier Coefficients using Fourier series x (n) = {..., -1, 2, 1, 2, -1, 0,-1, 2, 1, 2,…

A: We know the Fourier series coefficient formula , we will use that formula to calculate Fourier…

Q: A function y=Rx) is defined by Domain ,: xe (,+){±2,±6,±10,±14,..} (3 if - 2< x<0 S(x)=? 3-x if 0<x…

A:

Q: The discrete time periodic signal x(n)={2,1,-4,2} has the Fourier coefficients given as…

A: Given: A discrete-time signal xn=2,1,-4,2 with period N = 4 has Fourier coefficients as…

Q: B- Let f(t) be the 2n- periodic function defined over the interval (-t, A) by: [o if -n <t < 0 f(t)…

A:

Q: Find the discrete time Fourier coefficients of the following periodic signal; x[n] = cos^2((T/8)n) O…

A: Discrete time fourier series

Dielectric Breakdown

A dielectric is a material with low electrical conductivity and so is classified as an insulator. Dielectric materials are used to block the flow of electricity through them, allowing them to behave as an insulators. They can also be used to store electric charge or improve capacitance.Dielectrics have no free electrons for conduction because electrons are tightly bound to the nucleus. Because dielectrics contain a small number of electrons for electrical conductivity, they have a dipole. The two primary roles of dielectrics in electrical devices are insulation and electrical energy storage. An electric field polarizes the dielectric, and the polarization of the molecules allows dielectric materials to store charge.