1. Determine if the following system described by
sin is memoryless, causal, linear, time invariant and stable.

2. Determine the convolution of the two continuous-time functions given below:

3 cos 2t for all t

and e^t for t 0
for t 0

3. The system shown in Figure 1 is formed by connecting two systems in cascade. The impulse responses of the systems are given by and respectively and

Find the impulse response of the rI overall system shown in Figure 2.

Determine if the overall system is BIBO stable.

<img src='./qimages/15598-3.jpg'>

4. Figure 3 shows the periodic rectangular waveform. Obtain its Fourier series representation.

<img src='./qimages/15598-4.jpg'>

Derive the Fourier transform for Signum function.

Discuss the properties of Fourier transform.

6. The frequency response of a causal LTI filter is as shown in Figure 4. Find the filtered output signal for the input signals
sin

<img src='./qimages/15598-6.jpg'>

7. Find the Z-transform of the following sequence:



n 0
4
5

Determine whether or not the signal given below is periodic and determine the fundamental period, if the signal is periodic

sin 0·2n)

Find the even part of the following signal:


9. Write short notes on any two of the following:

Properties of Z-transform

Applications of Z-transform

Properties of non-linear systems