Practice Problems

### Problem 1

Given a signal $x(t)$ as shown in Figure.Perform the following and plot $y(t)$.
1. $y(t)=x(3t-2)$
2. $y(t)=x(-3t+2)$
3. $y(t)=x(\frac{3t+4}{5})$

Solution:

1. The operations are performed as shown below-
2. The operations are performed as shown below-
3. The operations are performed as shown below-

### Problem 2

Let $x(t)$ be a signal with $x(t)=0$ when $t<3$.
1. $x(1-t)+x(2-t)$
2. $x(1-t)*x(2-t)$
3. $x(3t)$
4. $x(t/3)$

For each of these signals find the value of '$t$' such that the signal is guaranteed to be zero.

Solution:

The signal $x(t)$ is-
The signals $x(1-t)$,$x(2-t)$,$x(3t)$ and $x(t/3)$ are as shown below-

1. For $t>-1$ the signal is zero.
2. For $t>-2$ the signal is zero
3. For $t>1$ the signal is zero
4. For $t>9$ the signal is zero