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Find Z-Transform of f(k) = e-2ksinh4k , k 0 Find inverse Z-Transform of -1T-2 <Iz 5 markS ii) 2 2 (+2z Solve any three Q4A] 15 marks Is the following function even or odd? Find its Fourier seri...
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,...
2) (15 marks) Consider the function ffo E [0,1 (a) Construct the even extension of f and find its...
2) (15 marks) Consider the function ffo E [0,1 (a) Construct the even extension of f and find its Fourier series. You may use MuPAD to check your calculations, but you will have to show your working for computing each integral to get any marks. (b) Construct the odd extension of f and find its Fourier series. You may use MuPAD to check your calculations, but you will have to show your working for computing each integral to get any...
Question 3 Fourier transform] Find the Fourier transform of the following functions. (i) f(z) = H...
Question 3 Fourier transform] Find the Fourier transform of the following functions. (i) f(z) = H (t-k)e-4. (ii) f(x) = 5e-4H21 (im)(xe 0, otherwise. IV) f(x) = Fourier transform
Question 3 Fourier transform] Find the Fourier transform of the following functions. (i) f(z) = H (t-k)e-4. (ii) f(x) = 5e-4H21 (im)(xe 0, otherwise. IV) f(x) = Fourier transform
Find the Inverse Fourier transform of: Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t) = 143w e-11ιω Question 13 (2 marks) Attempt 1 F(u...
Find the Inverse Fourier transform of:
Your answer should be expressed as a function of t
using the correct syntax.
Inverse F.T. is f(t) =
143w e-11ιω Question 13 (2 marks) Attempt 1 F(u)=# Find the Inverse Fourier transform of: e-11u Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped
143w e-11ιω
Question 13 (2 marks) Attempt 1 F(u)=# Find the Inverse Fourier transform of: e-11u Your answer should be...
Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier...
Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier Sine and Fourier Cosine series, respectively. periodic extension, 0< x < X f(x) = -< x< 2 2
Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier Sine and Fourier Cosine series, respectively. periodic extension, 0
Find the Inverse Fourier transform of: Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t) = sin (20u)e-7ίω F(u) Question 14 (2 marks) Attem...
Find the Inverse Fourier transform of:
Your answer should be expressed as a function of t
using the correct syntax.
Inverse F.T. is f(t) =
sin (20u)e-7ίω F(u) Question 14 (2 marks) Attempt 1 14 Find the Inverse Fourier transform of F(u)-sin(2Oue-Tu Your answer should be expressed as a function of t using the correct syntax. 20 inverse FT. is f(t) = Skipped
sin (20u)e-7ίω F(u)
Question 14 (2 marks) Attempt 1 14 Find the Inverse Fourier transform of F(u)-sin(2Oue-Tu...
Question 13 (2 marks) Attempt 1 ,2/144-aw Find the Inverse Fourier transform of: Te-v F(u)--3 Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skippe...
Question 13 (2 marks) Attempt 1 ,2/144-aw Find the Inverse Fourier transform of: Te-v F(u)--3 Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped a Screen Shot 2019-05-17 at 2.07.40 AM Search Question 14 (2 marks) Attempt 1 Find the inverse Fourier transform of: F(w-5 π w sgn(w) e-Tw Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped Question 15...
Fourier Series. Thank you in advance. Q 2(a) [6 Marks] (i) Sketch 3 successive cycles of the periodic function g(t):[4 marks) g() gt3). (ii) Is g(t)an even or odd function of? [2 marks] [14 Marks] (i...
Fourier Series. Thank you in advance.
Q 2(a) [6 Marks] (i) Sketch 3 successive cycles of the periodic function g(t):[4 marks) g() gt3). (ii) Is g(t)an even or odd function of? [2 marks] [14 Marks] (i) Show that the Fourier series coefficients of gl), as defined in part 2(a), may Q 2(b) [11 marks]: be written as follows 0, EVEN (ii) Obtain a value for the constant [3 marks] [5 Marks Q 2(c) What is the power, or mean-squared value,...
Consider the function 0<x<π/2. z, f(x) = (a) Sketch the odd and even periodic extension of f(x) for-3π 〈 x 〈 3π...
Consider the function 0<x<π/2. z, f(x) = (a) Sketch the odd and even periodic extension of f(x) for-3π 〈 x 〈 3π. (b) Find the Fourier cosine series of the even periodic extension of f(x)
Consider the function 0
Q3: 5 marks (A) Expand f(z) (2-1)(2-3) in a Laurent series valid for (i) Iz -...
Q3: 5 marks (A) Expand f(z) (2-1)(2-3) in a Laurent series valid for (i) Iz - 11 < 2, and (ii) Iz - 31 < 2. 1.5 marks each part (B) Use Laurent series to find the residue of f(2)= e (x - 2)-2 at its pole z = 2. 2 marks
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,...
2) (15 marks) Consider the function ffo E [0,1 (a) Construct the even extension of f and find its Fourier series. You may use MuPAD to check your calculations, but you will have to show your working for computing each integral to get any marks. (b) Construct the odd extension of f and find its Fourier series. You may use MuPAD to check your calculations, but you will have to show your working for computing each integral to get any...
Question 3 Fourier transform] Find the Fourier transform of the following functions. (i) f(z) = H (t-k)e-4. (ii) f(x) = 5e-4H21 (im)(xe 0, otherwise. IV) f(x) = Fourier transform
Question 3 Fourier transform] Find the Fourier transform of the following functions. (i) f(z) = H (t-k)e-4. (ii) f(x) = 5e-4H21 (im)(xe 0, otherwise. IV) f(x) = Fourier transform
Find the Inverse Fourier transform of:
Your answer should be expressed as a function of t
using the correct syntax.
Inverse F.T. is f(t) =
143w e-11ιω Question 13 (2 marks) Attempt 1 F(u)=# Find the Inverse Fourier transform of: e-11u Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped
143w e-11ιω
Question 13 (2 marks) Attempt 1 F(u)=# Find the Inverse Fourier transform of: e-11u Your answer should be...
Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier Sine and Fourier Cosine series, respectively. periodic extension, 0< x < X f(x) = -< x< 2 2
Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier Sine and Fourier Cosine series, respectively. periodic extension, 0
Find the Inverse Fourier transform of:
Your answer should be expressed as a function of t
using the correct syntax.
Inverse F.T. is f(t) =
sin (20u)e-7ίω F(u) Question 14 (2 marks) Attempt 1 14 Find the Inverse Fourier transform of F(u)-sin(2Oue-Tu Your answer should be expressed as a function of t using the correct syntax. 20 inverse FT. is f(t) = Skipped
sin (20u)e-7ίω F(u)
Question 14 (2 marks) Attempt 1 14 Find the Inverse Fourier transform of F(u)-sin(2Oue-Tu...
Question 13 (2 marks) Attempt 1 ,2/144-aw Find the Inverse Fourier transform of: Te-v F(u)--3 Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped a Screen Shot 2019-05-17 at 2.07.40 AM Search Question 14 (2 marks) Attempt 1 Find the inverse Fourier transform of: F(w-5 π w sgn(w) e-Tw Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped Question 15...
Fourier Series. Thank you in advance.
Q 2(a) [6 Marks] (i) Sketch 3 successive cycles of the periodic function g(t):[4 marks) g() gt3). (ii) Is g(t)an even or odd function of? [2 marks] [14 Marks] (i) Show that the Fourier series coefficients of gl), as defined in part 2(a), may Q 2(b) [11 marks]: be written as follows 0, EVEN (ii) Obtain a value for the constant [3 marks] [5 Marks Q 2(c) What is the power, or mean-squared value,...
Consider the function 0<x<π/2. z, f(x) = (a) Sketch the odd and even periodic extension of f(x) for-3π 〈 x 〈 3π. (b) Find the Fourier cosine series of the even periodic extension of f(x)
Consider the function 0
Q3: 5 marks (A) Expand f(z) (2-1)(2-3) in a Laurent series valid for (i) Iz - 11 < 2, and (ii) Iz - 31 < 2. 1.5 marks each part (B) Use Laurent series to find the residue of f(2)= e (x - 2)-2 at its pole z = 2. 2 marks
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