The impulse response of a linear system is . If the input to the system is , write two…

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(a) The impulse response of a linear system is . If the input to the system is , write two
possible expressions for the output of the system in terms of .
(b) A linear system has an impulse response . is a right handed sequence.
i.e. . Using the answer to (a) show that the system is a causal system.
(c) Show that a linear system is BIBO stable if ? , where is the impulse response of the
system.
2.
(a) (i) What is the relationship between DTFT (Discrete Fourier Transform) and the z- Transform?
(ii)
1. Sketch .
2. Find the z- transform ( ) of .
3. Find the DTFT ( ) of
4. Sketch ( ) . Indicate all the important values on your diagram.
(b) The impulse response of a low-pass filter is given by . A new filter is designed with the
the impulse response ( )
(i) Find the frequency response ( ) of the new filter.
(ii) Show that filter given in (i) is a high pass filter.

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