Use the Fourier transform to find the output y(n) when the input is x(n) = (.5)nu(n) for the following systems:
Use the Fourier transform to find the output y(n) when the input is x(n) = (.5)nu(n) for the following systems:
3. (20 points) Use the Fourier transform method to find the output ytn) when the input is xn)-m)+n-4) for the following system hin) (0.7) u(n) 4 (20 points)
Given LTI system with following input response (can use properties of the Fourier transform like, sinc(x) = sin(πx)/πx ): h(t) = 8/π sinc(8t/π) where input x(t) of the LTI system is the following continuous-time signal x(t) = cos(t) cos(8t) a) find the Fourier transform of x(t) b) find the Fourier transform of h(t) c) Is this LTI system BIBO stable? Prove d) find the output y(t) of the LTI system
The relation between input and output is from the Fourier transform ofthe system given asFind the pulse response \(h\) [n] using.$$ y[n]-5 y[n-1]+6 y[n-2]=2 x[n]-4 x[n-1] $$
Problem 5: Use the duality property of the Fourier transform to find the Fourier transform of x(t) = sinc(Wt).
Problem 5: Use the duality property of the Fourier transform to find the Fourier transform of x(t) = sinc(Wt). Please solve clearly, not copy paste old solutions.
Please solve using the Discrete-Time Fourier Transform: Given a filter described by the difference equation y[n] = x[n] + 2x[n - 1] + x[n - 3] where x[n] is the input signal and y[n] is the output signal. a) Find H[n] the impulse response of the filter. b) Plot the impulse response c) Find the value of H( Ω) for the following values of Ω = 0, pi, pi/2, and pi/4
Given the following difference equation that describes the input output relationship, (a) Express Y(z), the z-transform of the output, in terms of X(z), the z-transform of the input. (b) Find the system function H(z). (c) Identify the zeros and poles. Sketch the zero-pole plot. (d) For an input rn]- cos (n), find the output yn] (e) Use the zero-pole plot to explain what you obtain in d)
Consider a first-order system with input x(t) and output y(t). Let the time constant be the part of your birth date in the format of day, month (ddmm) in microseconds. Complete the following steps: 1. Write the differential equation representing the system. 2. Derive the transfer function H(s). A Note: Label all graphs appropriately. ddmm 3. Use H(s) with MATLAB to complete the following actions: • Find the poles are zeros. • Find the step response. • Find the impulse...
Problem 3: Let x(n) be an arbitrary signal, not necessarily real valued, with Fourier transform X (w). Express the Fourier transforms of the following signals in terms of X() (C) y(n) = x(n)-x(n-1) (d) v(n) -00x(k) (e) y(n)=x(2n) (f) y n even n odd , x(n/2), (n) 0 Problem 4: etermine the signal x(n) if its Fourier transform is as given in Fig. P4.12. X(a) 0 10 10 10 X(o) 0 X(a) Figure P4.12
Problem 3: Let x(n) be an...
Consider three systems with the following input-output
relationships
6. Consider three systems with the following input-output relationships: { 4 0, odd System 1: y[n n even r[n] 10ar(n 2]3r[n - 1 System 2: yn + + System 3: yn x[3n] The interconnection diagram is at follows: System 1 System 2 System 3 Find the input-output relationship of the interconnected system. State the properties of the system (linear, stable, time invariant, memoryless, and causal).
6. Consider three systems with the following...