it is a fourier transform question in Turkish language ve 2. rect(t) = 51,-1/2 st 5...
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal x(t) is X(f) - rect(f/ 2), find the Fourier Transform of the following signals using properties of the Fourier Transform: (a) d(t) -x(t - 2) (d) h(t) = t x( t ) (e) p(t) = x( 2 t ) (f) g(t)-x( t ) cos(2π) (g) s(t) = x2(t ) (h)p()-x(1)* x(t) (convolution)
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal...
Problem 4 (25 Points) Obtain the Fourier transform of f(t), where f(t) = rect(2 ) cos(0.5t - 471) + recte le using relevant Fourier transform pairs and Fourier transform properties from the tables.
Fourier transfroms
Obtain the Fourier transform of (a) (t)-eu(2 -t). (b) f2(t)e rect (t) = te-(t+1)a(t-1) (2-jt) +9
how to derive the underlying signal x(t) using the
definition of the Inverse Fourier transform
Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)
Inverse Fourier Transforms by Definition Plot the following spectra and using the definition of the inverse Fourier transform, derive the underlying signal z(t). 1. Fał(w) w rect(w/wo) 2. Ffa) cos(w) rect (w/T)
Problem 5. (Properties of Fourier transform) Consider a continuous time signal x(1) with the following Fourier transform: X(jw) = J 1 - if we l-207, 207] if|wl > 207 (3) Let y(t) = x(26) cos? (507). Sketch Y (w), i.e., the Fourier transform of y(t). (Note that 2 1 + cos(20) cos? (0) = 2
7. The signal x(t) shown below is modulated (multiplied) by cos(10nt). Find the Fourier transform of x(t)cos(10nt) and neatly sketch the magnitude? Useful transform pairs. rect (9) = t sinc (); «(t)cos (Wgt) }(x(w+wo) + X(w – wo)); «(t – to) ~X(w)e-juto (10 points) x(+) 1 t
Question 1 (10 points) Determine Fourier Transform of f(t) = u(t – 2) + 6(t – 6)? e-12w + e-jow (ies + 70(w))er2we=you Giv - 70()e=12W +e=you Gius + 78(w))e=124 +e-sou Question 2 (10 points) Using the convolution property of Fourier Transform to find the following convolution: sinc(t) * sinc (4t) [Hint: sinc(t) én rect(w/2)] π sinc (2t) 2 TT 8 sinc(t)sinc(2t) TT sinc(4t) TT sinc(t)
Bonus Question: Determine the Fourier Transform using the Fourier Transform integral for x(t) and then answer (b). (a) x(t) = 8(t) -e-tu(t) (b) Plot the magnitude of the Fourier Spectrum. 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) =...
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 .
3. If x(t) has the Fourier transform j2π f + 10 Find the Fourier transform of the following signals Hint: use the properties of Fourier transform) a. v(t)-x(1):cos(10π t) d. v(t)X(t) e. v()-e"x(t-1)