Q1. Consider a system in the Fig 1,
Fig 1
a) Sketch ( ) for | | ≥ 9 for the following values of
i)
=
ii)
=2
iii)
=3
iv)
=5
b) For which of the preceding values of
is ( ) identical?
Q2.In
In the system shown in the Fig 2, ( ),, is sampled with a periodic impulse train,
and a reconstructed signal ( ) is obtained from the samples by low pass filtering.
Fig 2
The sampling period is 1 ms, and ( ) is a sinusoidal signal of the form ( ) =
cos (2
+ ).. For each of the following choices of and , determine ( ).
Q3.Figure 3,, gives a system in which the sampling signal is an impulse train with
alternating sign. The Fourier transform of the input signal is as indicated in the figure.
Fig 3
a) For Δ < /(2
b) For Δ < /(2
c) For Δ < /(2
),, sketch the Fourier transform of ( ) and ( ).
),, determine a system that will recover ( ) from ( ).
),, determine a system that will recover ( ) from ( ) .
Q4. A signal ( ) = sin (
+ ) is the input to an LTI system having a frequency
response (
).. If the output of the system is ( − ),, then what is the most
general form of phase of (
).
Q5. A five-point sequence [ ] is given as
[−3] = 1, [−2] = 1, [−1] = 0, [0] = 5, [1] = 1
Let (
) denote the DTFT of [ ]. Find the value of