Example: Find the Fourier transform of the triangle function (a-1r)) (-astsa) f (1) = (otherwise) From the functional form and from the graph of S (1), it is obvious that f(1) is piecewise smooth and that [ " |S(/)|dt converges to the value ak. f(t)

Q: (t+1, -1<t<0 0<t<1 14) Given a signal 1. a(t) = %3D 2 t. 1<t<2 0, otherwise Let X(@) denote the…

A: In this question,  Choose the correct option Find the value of Fourier transform X(0) using the…

Q: The discrete sequence of numbers x[n] =( 0, 1,-1, 0, 1,-1, 0, 1,-1, 0, 1,-1, 0, 1,-1) is recorded…

A: Discrete Fourier Transform (DFT) is the linear transformation of discrete finite duration sequence…

Q: Consider the following signal: cos(20Tt) te [-1,1] x(t) te [-2, –1) u (1, 2] 6. Assuming the signal…

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Q: B) Use the differentiation in time and differentiation in frequency properties to determine the…

A: Given,xt=12π e-t22 .....(1)or xt=Aoe-αt2 .....(2)By (1) and (2)Ao=12π, a=12xt=Aoe-αt2By definition…

Q: Determine the Fourier series representation of the following discrete time signal x(n) = {..... , 1,…

A: The time domain signals can be continuous or discrete. The time domain signals can be periodic as…

Q: 2. a) Find the frequency response of the causal LTI system whose difference equation is given below.…

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Q: B Use the scaling and real-signal frequency-translation properties to find the Fourier transform of…

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Q: Consider the function f(t) = 0.01e2t for 0 ≤t≤ π). (a) Sketch the even extension, feven, and the odd…

A: Given function f(t)= 0.01e2t for 0 ≤ t ≤ pi. The even and odd extensions of f(t) over the range -3pi…

Q: 1- By using exponential Fourier series, the average power of f(t)=cos(4nt)+2cos(2nt) is . 2- The…

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Q: Problem 1: Let x(t) = 1 + sin(Wot) + 2 cos(wot) + cos(2wot +) with wo as the fundamental frequency.…

A: Solution 1-

Q: Obtain the discrete Fourier transform (DFT) of the signal given as |n – N| x[n] = 0sn< 2N N 0,…

A: to obtain the discrete Fourier transform DFT of the signal given as- xn=1-n-NN0⩽n⩽2N0otherwise We…

Q: (A) A rectangular pulse x(t) of width t= 6 msec. and amplitude A=12 V is centered at the origin in…

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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: A bandpass signal is given by s(t) = 100sin(w.t + wmt) + 500coswet – 100sin(wat – wmt) where we = 2m…

A: Note: As per our policy, I have attempted the first three subquestions. Given data:…

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: Take v(n) = {1, 2, –1}. If vi(n) = v(n) – v(-n), find the Fourier transform (FT) of v, and v1. -Is…

A: Given :  Note: In the above mentioned questions are not  interlinked to each other, hence according…

Q: 2. Consider a linear, time-invariant, continuous-time system. a) Since the impulse response of the…

A: a) The impulse response of the system of the system is given as ht=δ(t)-δ(t-T) Therefore the…

Q: 1)For the discrete-time signal given as x [n] = [4,5,2,1,5,6,2,1], the Fast Fourier coefficients are…

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

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Q: determine the Fourier series expansion coefficients ġo, ản, bn and the Fourier transform equation…

A: Given : For the above given continuous periodic time domain signal x(t) they want to  know the…

Q: 1. Consider a function r(t) given by e-at, t> 0, -eat, t0 (a) (10 pt) Find the continuous-time…

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Q: A signal f(t) is defined as f(t) = [3 cos (2nt) + 5sin(2nt)]?. Is this a valid Fourier serie…

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Q: 2) If x[n] is input to a discrete time LTI system with impulse response h[n], find the Fourier…

A: For the given  x[n] = ∑δ(n-4k)k=-∞∞ h[n] = 10≤n≤2-1-2≤n≤-10otherwise  Fourier coefficient is…

Q: Consider the one-sided exponential function f(t) = Ae-at u(t), where u(t) is the unit step function,…

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

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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: .28 Consider a discrete-time LTI system with impulse response 1, 0 8[n - 4k], k=-o determine the…

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Q: (c) What does it mean for a system to be BIBO stable? Which region(s) of the z- plane correspond to…

A: BIBO STABLE: A system is said to be BIBO stable, for a given bounded input(finite amplitude signal)…

Q: 2. a) Find the frequency response of the causal LTI system whose difference equation is given below.…

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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: Derive the discrete-time Fourier transform (DTFT) of the signal [1, for 0<n< 4 x[n] = { and sketch…

A: Since you have posted a question with multiple sub-parts, we will solve the first part for you. If…

Q: Show that the trigonometric fourier series of a periodic signal f(t) containing fourier coefficient…

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Q: Find y(t) = x,(t) * x2(t), where x, (t) = e-tu(t), x2(t) = e-2'u(t), and ** denotes the convolution…

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Q: Given x(f) below, using Fourier transform find and plot X(w) x€) = rece{) t H cos(at) T where T T <t…

A: We need to find out Fourier transform of given signal

Q: Determine the discrete-time Fourier transform of the signal x[n] = (0.25)¹-¹u[n 1]. O a. X(w) = 1-4e…

A: In this question we need to choose a correct option

Q: (b) A periodic square wave (for example, a diffraction grating, electron density in a 1D crystal)…

A: A periodic square wave can be represented as a convolution between a square pulse and an array of δ…

Q: Question (3):. (i) (ii) Which is the fourier transform of the given time signal? -T Alternative I)…

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Q: 1. Consider the z-transform X(z) whose pole-zero plot is shown below. a) Determine the ROC if it is…

A: Given the pole-zero plot: a. We need to determine the ROC if it is known that Fourier Transform…

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

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Q: ind the Fourier series representation of the even extension of the function Then, find the value…

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Q: (b) x2(n) = -8(n)+8(n – 2). Calculate it in two ways, first directly, and second by relating it to…

A: We need to find out Fourier transform of given signal by direct formula and by shifting property .

Q: 2. Let s[n] be the input to each the three LTI systems with frequency responses shown below. Let c…

A: Let s[n] be the input to each of the three LTI systems with frequency response shown below. Let ck…

Q: Find the Fourier series coefficients of the discrete-time sequence x[n] = {...,1,0,0, -1,1,0,0,…

A: We need to find out the Fourier series coefficient , we will define given function for one period ,…

Q: For the discrete-time signal, In x[n] = )" Where In| is the absolute value of n, (a) Find the…

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Q: What are the 4-point Discrete Fourier Transform (DFT) coefficients of the sequence below? x [n] = δ…

A: What are the 4-point Discrete Fourier Transform (DFT) coefficients of the sequence below? x [n] = δ…

Q: A periodic signal with (N= 4) is given by (only one period is shown) 9 1 0 x (n ) = 3 Find the…

A: Discrete Fourier coefficients