Q1:
y [n]=x [n] - x[n-4]
a) Determine and plot magnitude response
b) Determine and plot phase response [0, π]
c) Find he output for input x[n] = cos((πn)/4).
d) Discuss possible applications for this filter.
Q2:
Explain how the linear convolution of two finie discrete-time signals can be computed using the period convolution. Illustrate the procedure with an example.
What are the advantage of the approach in part (a)?
Q3:
A sound wave x(t) is given
x(t)=sin (10 πt)+ sin (20 πt)+ sin (60 πt)+ sin(90 πt)
The signal is profiteeredwith an antiasing filter due sampled at a rate of 40 KHz. The resulting samples are reconstructed using an idea reconstructed.
Determine the output y(t) due compare it to the audible part (the part can be heard) of x (t).
a) There is on profiteering.
The filter is an idea filter with a cut off frequency of 20 KHz.
What are the drawbacks of the solution in part (a) and (b)
Q4:
Show how the two-dimensional (2D). Discrete Fourier Transform (DFT) of digital image f(x,y) of size M×N can be obtained using one-dimensional DFTtransforms.
Use part (a) to compute the 2D DFT of the 4×4 image
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Q5:
A casual LTID system is given by the equation
y [n]- 0.25 y [n-1]= -0.25 x [n]+ x [n-1]
a) Determine the transfer function of the system.
b) Sketch the poles and zeros of the transfer function in the complex plane. Is the system BIBO stable?
c) Determine and plot the amplitude response of the system.
d) Find the system response to the input (-2)n u[n]