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(a) Given the following signals: z(t) = { ={ex? exp(-kt) t> 0 0 t<0 sin(Ot) g(t)...
(a) Given the following signals: z(t) = { ={ex? exp(-kt) t> 0 0 t<0 sin(Ot) g(t) = **(t) art (i) Explain what the symbol * means in this context and write down the expression for the function y(t). (ii) Compute the energy of the signal x(t) in the time domain. (iii) Using the formulae 1 F[2(t)]() = k + 2ris F(II(t)](s) = sinc(s) It > 1/2 II(t) It < 1/2 sin(TTS) sinc(s) ITS compute the energy of the signal y(t)...
where M=7 322-M2 4) Find the inverse - transform of F(z) = (2-1)(2-2M)' (15 marks) 0...
where M=7
322-M2 4) Find the inverse - transform of F(z) = (2-1)(2-2M)' (15 marks) 0 t<-M/2 M <t< - 5) Show that the Fourier transform of function f(t) sin 7 s (10 marks) au 6) Show that u = ln(x2 + xy + y2) satisfies the partial differential equation x x ди +y 2. (7 marks) au 7) Solve the partial differential equation = e-cos(x) where at du x = 0, at =tet ax at and t = 0,...
I really need help with Part B of this question Problem 2: a) If F(a) is...
I really need help with Part B of this question
Problem 2: a) If F(a) is the Fourier transform (FT) of a function qx), show that the inverse FT of ewb F(a) is q -b), with b a constant. This is the shift theorem for Fourier transforms. Hint: Y ou will need the orthogonality relation: where y-y) is the Dirac delta function] [ Joeo(y-y')dus2πδ(y-y'), b) Solve the diffusion equation with convection: vetneuzkat.aax au(x,t) аги, ди with-c < 鱸8: and ux,0)-far)....
Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t)...
Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = ) Using the convolution property of Fourier Transform to find the following convolution: sinc(t) * sinc (4t) [Hint: sinc(t) or rect(w/2)] TC .
1.12. The Fourier transform of a signal x(t) is defined by X(f) = sincf, where the sinc func- tion is as defined in Equ...
1.12. The Fourier transform of a signal x(t) is defined by X(f) = sincf, where the sinc func- tion is as defined in Equation (1.39). Find the autocorrelation function, R.(T), of the signal x(t).
1.12. The Fourier transform of a signal x(t) is defined by X(f) = sincf, where the sinc func- tion is as defined in Equation (1.39). Find the autocorrelation function, R.(T), of the signal x(t).
2cost,tl s 1 2 lt > 2 (a) The Fourier transform of the function: f(t)=(cost, 1 < is 0, 3 cos(w+5)...
1)
do both a & b subparts thank u
2cost,tl s 1 2 lt > 2 (a) The Fourier transform of the function: f(t)=(cost, 1 < is 0, 3 cos(w+5) (b) The inverse Fourier transform of the function F (w)22 is
2cost,tl s 1 2 lt > 2 (a) The Fourier transform of the function: f(t)=(cost, 1
Exercises: u used to the instructor b the end of next lab. 20 102 Plot the f(t)-sinc(20r) cos(300...
Exercises: u used to the instructor b the end of next lab. 20 102 Plot the f(t)-sinc(20r) cos(300t)sinc (10t) cos(100t) Use the fast Fourier transform to find the magnitude and phase spectrum of the signal and plot over an appropriate range. Use appropriate values for the time interval and the sampling interval. Note that in Matlab sinc(x)-, so we need to divide the argument by n to make it match the given function. Le, sinc(20t/pi) Hint: Use the parameters from...
Problem 3, (25 pts) Consider the integral y(t)x(t) dr where x(t)-ult +1)-u(t -1) Find the Fourier...
Problem 3, (25 pts) Consider the integral y(t)x(t) dr where x(t)-ult +1)-u(t -1) Find the Fourier transform Y(au) by using the differentiation and the integrati domain properties. Reduce your answer t o the simplest form possible as a function of sinc(u). sin(θ)sene-o siren Formulas: sine(θ)
Problem 3. 0 Figure 2 Given: f(t) = { 2.5, -1.5 <=<= 1.5 f(t) = {...
Problem 3. 0 Figure 2 Given: f(t) = { 2.5, -1.5 <=<= 1.5 f(t) = { 0 otherwise See figure(2) above. A) Find the Fourier transform for f( (see figure 2) and sketch its waveform. B) Determine the values of the first three frequency terms (w1, W2, W3) where F(w) = 0. C) Given x(t) = 1.58(-0.8) edt Determine whether or not Fourier transform exists for x(t). If yes, find the Fourier transfe not explain why it does not. Problem...
..3-1 In Fig. P1.3-1, the signal fi(t) = f(-). Express signals fa(t), f(t), fu(t), and f(t)...
..3-1 In Fig. P1.3-1, the signal fi(t) = f(-). Express signals fa(t), f(t), fu(t), and f(t) in terms of signals f(t), fi(t), and their time-shifted, time-scaled or time-inverted versions. For instance f2(t) = f(t-T) + fit - T). f (1) f (1) 1,(0) f(t) 0 - 0 1 Fig. P1.3-1
(a) Given the following signals: z(t) = { ={ex? exp(-kt) t> 0 0 t<0 sin(Ot) g(t) = **(t) art (i) Explain what the symbol * means in this context and write down the expression for the function y(t). (ii) Compute the energy of the signal x(t) in the time domain. (iii) Using the formulae 1 F[2(t)]() = k + 2ris F(II(t)](s) = sinc(s) It > 1/2 II(t) It < 1/2 sin(TTS) sinc(s) ITS compute the energy of the signal y(t)...
where M=7
322-M2 4) Find the inverse - transform of F(z) = (2-1)(2-2M)' (15 marks) 0 t<-M/2 M <t< - 5) Show that the Fourier transform of function f(t) sin 7 s (10 marks) au 6) Show that u = ln(x2 + xy + y2) satisfies the partial differential equation x x ди +y 2. (7 marks) au 7) Solve the partial differential equation = e-cos(x) where at du x = 0, at =tet ax at and t = 0,...
I really need help with Part B of this question
Problem 2: a) If F(a) is the Fourier transform (FT) of a function qx), show that the inverse FT of ewb F(a) is q -b), with b a constant. This is the shift theorem for Fourier transforms. Hint: Y ou will need the orthogonality relation: where y-y) is the Dirac delta function] [ Joeo(y-y')dus2πδ(y-y'), b) Solve the diffusion equation with convection: vetneuzkat.aax au(x,t) аги, ди with-c < 鱸8: and ux,0)-far)....
Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = ) Using the convolution property of Fourier Transform to find the following convolution: sinc(t) * sinc (4t) [Hint: sinc(t) or rect(w/2)] TC .
1.12. The Fourier transform of a signal x(t) is defined by X(f) = sincf, where the sinc func- tion is as defined in Equation (1.39). Find the autocorrelation function, R.(T), of the signal x(t).
1.12. The Fourier transform of a signal x(t) is defined by X(f) = sincf, where the sinc func- tion is as defined in Equation (1.39). Find the autocorrelation function, R.(T), of the signal x(t).
1)
do both a & b subparts thank u
2cost,tl s 1 2 lt > 2 (a) The Fourier transform of the function: f(t)=(cost, 1 < is 0, 3 cos(w+5) (b) The inverse Fourier transform of the function F (w)22 is
2cost,tl s 1 2 lt > 2 (a) The Fourier transform of the function: f(t)=(cost, 1
Exercises: u used to the instructor b the end of next lab. 20 102 Plot the f(t)-sinc(20r) cos(300t)sinc (10t) cos(100t) Use the fast Fourier transform to find the magnitude and phase spectrum of the signal and plot over an appropriate range. Use appropriate values for the time interval and the sampling interval. Note that in Matlab sinc(x)-, so we need to divide the argument by n to make it match the given function. Le, sinc(20t/pi) Hint: Use the parameters from...
Problem 3, (25 pts) Consider the integral y(t)x(t) dr where x(t)-ult +1)-u(t -1) Find the Fourier transform Y(au) by using the differentiation and the integrati domain properties. Reduce your answer t o the simplest form possible as a function of sinc(u). sin(θ)sene-o siren Formulas: sine(θ)
Problem 3. 0 Figure 2 Given: f(t) = { 2.5, -1.5 <=<= 1.5 f(t) = { 0 otherwise See figure(2) above. A) Find the Fourier transform for f( (see figure 2) and sketch its waveform. B) Determine the values of the first three frequency terms (w1, W2, W3) where F(w) = 0. C) Given x(t) = 1.58(-0.8) edt Determine whether or not Fourier transform exists for x(t). If yes, find the Fourier transfe not explain why it does not. Problem...
..3-1 In Fig. P1.3-1, the signal fi(t) = f(-). Express signals fa(t), f(t), fu(t), and f(t) in terms of signals f(t), fi(t), and their time-shifted, time-scaled or time-inverted versions. For instance f2(t) = f(t-T) + fit - T). f (1) f (1) 1,(0) f(t) 0 - 0 1 Fig. P1.3-1
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