Find the Fourier series and plot the magnitude and phase of the Fourier Series for the...

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Find the Fourier series and plot the magnitude and phase of the Fourier Series for the following signals: a) x(t) = sint b) x(t) = cos(2t +) c) x(t) == sin(t) + sin(3t+1)+cos (5t) b) 2 -To 2. For each signal, find the Fourier transform, X(), and then plot X(0)| a) |x(t) 0 x(1) fin To 0 To To x(0= x() 2 t 270 47 7 3. Given two inputs signal x(t) and y(t) to a modulator circuit as follows: x(t)=20 cos (100t), y(t)= 20 sin (100t) Sketch the frequency spectrum (magnitude and phase) for x(t) and y(t). EBGE3101: Signals and Systems 4. Given x(t)=10 sin t. Find the Fourier Transform for x(2(t-1)). 5. Find the frequency response and impulse response of then system with input x(t) = etu(t) and output y(t) = e-3tu(t). 6. The system is described by dy dy +4 -+ 3y(t): dt dt dx = + 2x (t) dt a) Find the frequency response and impulse response of the system using Fourier Transform. b) Find the output y(ft) when the input x(t)-e-*u(t). 7. An input signal is given as x(t) = g1(t)g2(t), where g1(t) = 5cos (2000nt) and g2(t) = 2cos (4000mt). Determine: a) Fourier transform of x (t). b) The output signal, x(t) if H (f) is defined as: H(f) = 4 -1000 f 1000 elsewhere Find the Fourier series and plot the magnitude and phase of the Fourier Series for the following signals: a) x(t) = sint b) x(t) = cos(2t +) c) x(t) == sin(t) + sin(3t+1)+cos (5t) b) 2 -To 2. For each signal, find the Fourier transform, X(), and then plot X(0)| a) |x(t) 0 x(1) fin To 0 To To x(0= x() 2 t 270 47 7 3. Given two inputs signal x(t) and y(t) to a modulator circuit as follows: x(t)=20 cos (100t), y(t)= 20 sin (100t) Sketch the frequency spectrum (magnitude and phase) for x(t) and y(t). EBGE3101: Signals and Systems 4. Given x(t)=10 sin t. Find the Fourier Transform for x(2(t-1)). 5. Find the frequency response and impulse response of then system with input x(t) = etu(t) and output y(t) = e-3tu(t). 6. The system is described by dy dy +4 -+ 3y(t): dt dt dx = + 2x (t) dt a) Find the frequency response and impulse response of the system using Fourier Transform. b) Find the output y(ft) when the input x(t)-e-*u(t). 7. An input signal is given as x(t) = g1(t)g2(t), where g1(t) = 5cos (2000nt) and g2(t) = 2cos (4000mt). Determine: a) Fourier transform of x (t). b) The output signal, x(t) if H (f) is defined as: H(f) = 4 -1000 f 1000 elsewhere

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