Consider a signal, y(t) defined as, (-t+2, Osts1 t-1, y(t)= 1st32 t 5 3 3' |0, 2st55 otherwise The energy of the signal y(t) is E = 3 J. A periodic signal z(t) is defined as, 0st36 z(t) =. [v(t+6) for all t The power of w(t)= ÷z(21) is, (a) 1/24 J (b) 1/8 J (c) 1/16 J (d) 1/4 J

Q: Exercise 1: (iii) Determine TF [g (t)]. 6) Show that TF [f (t- a)] = e -j2rva TF [f (t)] where aER…

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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: 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: 1. Tracing the o utline or the ha art shape shown below results in a periodic signal which can…

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

Q: Consider a signal, y(t) defined as, (-t+2, 0st<1 t-1, 1sts2 y(t) ={ t 5 2st5 --+-. 3 3 0, otherwise…

A: W(t) = 12Z2t = 0.5 Y(2t) = 0.5 [∫01(-2t+2)dt + ∫12(2t-1)dt + ∫25(-2t3+53)dt

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 Fourier transform of x(t) = te-0.5tu(t) and sketch its magnitude and phase %3D spectrums.

A: In the question,  Find the Fourier transform of the x(t) signal.  Sketch the magnitude and phase…

Q: Question 1: Determine the causal signal x(n) if its z-transform X(z) if ROC is 0.8</z/<1.25.    A.…

A: 1. Option E 2.True Explanations are as below

Q: A. An FM signal has the form S(t) = 10 Cos (2 T fc t + 4 Sin (2 a fm t)) Where fc = 200 MHz, and fm…

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Q: Exercise 2-2: Find the Fourier Transform of y(t) = 100cos (20nt +T/3) %3D 1. First, write y(t) in…

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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: The message signal m(t) is a periodic signal given below in Fig A. Assume that it is a DSB-AM: x(t)…

A: Modulation is the process of appending the information contained in a message signal to a high…

Q: Q#5 A) What is the practical significance of ROC. Give an example where this is used in real life…

A: ROC of any Signal signifies that the converging nature of the Signal means means like taking tue…

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: b. A Communication Engineering comparing is analyzing vibration signals from one point to another as…

A: According to our expert policy only first three subparts are to be answered kindly repost the…

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. Consider the signal r(t) given below. t – 1, if 1<t < 2, if 2 <t < 3, r(t) = 0, 1, otherwise. For…

A: x (t) = t-1 if 1&lt; t&lt; 2 1    if 2&lt;t&lt;3 0     otherwise       lets first draw x (t)   a)…

Q: 3. Given the LTI system described by the following differential equation ay(t) + 3음y(t) + 5y(t) =D…

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

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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: 1.20. The Fourier transform X(w,, w2) of the sequence x(n,, n2) is given by X(w1, w2) = 3 + 2 cos w,…

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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: 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: Q2(a) For a Linear Time Invariant (LTI) system with an unit impulse response h(t) = 7e-3'u(t) and an…

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Q: Q.6 Consider the finite-duration signal f (t) given in Fig.3. (a) Evaluate the Fourier transform…

A: 1. Rectangular function xt=ArecttτXω=∫-∞∞Arecttτe-jωtdt=A  -τ2≤t≤τ20…

Q: Use the Fast Fourier Transform to find the DFT for the function f(t) = 3cos (at) + sin (at- x).…

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Q: 2. The signal s(t), where t is in seconds, has the (real-valued) Fourier transform S(jN), 2 SUN) =…

A: Given :

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: 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: 1 sin( 2t) Consider an LTI system S with impulse response h(t) = 2 t 1) Using the Fourier transform…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: An analogue, non-periodic signal f is given by Set, t1 (a) write your answer in the format Find the…

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Q: 6. Consider the RLC circuit given in the figure below. x(t) is the input voltage, the voltage y(t)…

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Q: (a) Determine whether the functions given can be represented by a Fourier series (i) x(t) : (ii)…

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Q: Consider a signal x (t) = cos(t), 0 <t 1, and zero otherwise. (a) Find its Fourier transform X (2).…

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Q: Q2) The input voltage (V.) to the circuit shown in fig.(2) has the following Fourier series…

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

Q: Suppose that X(W)is real but not even. Can we conclude whether X[n]must be or cannot be real ? Can…

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

Q: Suppose there is a sequence x[n] = [2, -1, 0, c, 1] where the value of c is unknown. X[k] is the DFT…

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Q: Signal Classification. Consider the signal T x(t) = 4 sin(t) +2, -0 <t <∞ %3D and t – 2 y(t) = 2…

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

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Q: A3. Show that for an even function, the Fourier coefficients are: (a) a, = | S(1) cos- dt, r = 1, 2,…

A: A3 The Fourier series of a periodic function  f(t) is given as:…

Q: For the following signals, x(t), use the Fourier Transform “Common Signals" Table and the…

A: Using the Fourier transform property, the Fourier transform of the rectangular signal is given by:…

Q: Using Fourier integral representation, show that 0, ifx 0 -o cos xw+w sin xw dw 1+w2

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Q: Question 8 Let f (0) = 0, and %3D f (x) ={ -1, r€ (-7,0) r € (0, 7) 1, Extend f to PC (27). (a)…

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Q: Figure Q3 shows one complete cycle of signal y(t): Calculate the fundamental period, T and angular…

A: Solution-a)- yt=cosωt+sinωtyt=cos-π3t+sinπ4tyt=-cosπ3t+sinπ4tω1=π3, f1=16,T1=6ω2=π4, f2=18, T2=8

Q: A periodic function, f(t) is given as t – 1, -2<t< – 1 0, t + 1, f(t + 4) -1<t<1 f(t) = 1<t<2 a)…

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Q: Q2) A signal m(t) has a Fourier transform 1. fi < Ifl < f2. fi = 1 kHz ; f2 = 10 kHz %3D M(f) 0.…

A: Communications

Q: a) Fourier transformation of a continuous-time function is given below. Using inverse fourier…

A: Part (a): The mathematical expression for the inverse Fourier transform is given by:…

Fourier Series

Most of the incidents studied in the field of Engineering and Science as a function of time. For example, current and voltage are in the alternating current circuit. These occasional activities can be analyzed in the activity components (fundamental frequency and harmonics) through a process called Fourier analysis.