Question

. Consider figure 4, is the given y (t) a differentiation of x (t)?

I got this question in quiz.

This interesting question is from Basic Operations on Signals in section Signals and Systems Basics of Signals and Systems

Answer 1

To determine if \( y(t) \) is the differentiation of \( x(t) \), you need to check if \( y(t) \) represents the derivative of \( x(t) \) with respect to time. In other words, \( y(t) = \frac{dx(t)}{dt} \).

To confirm this, observe the following characteristics:

1. **Shape Analysis**: If \( y(t) \) changes at points where \( x(t) \) has changes in slope, peaks, or other significant features, it may indicate differentiation. For example:

   - If \( x(t) \) has a ramp (linear increase), \( y(t) \) should be constant.

   - If \( x(t) \) has a sudden step change, \( y(t) \) would resemble an impulse (since the derivative of a step is an impulse).

2. **Amplitude Relationship**: Check if the amplitude of \( y(t) \) matches the rate of change in \( x(t) \) at corresponding points. Higher slopes in \( x(t) \) should correspond to larger values in \( y(t) \).

Without seeing Figure 4, this general approach should guide you. If \( y(t) \) indeed follows the pattern of the derivative of \( x(t) \), then \( y(t) \) would be the differentiation of \( x(t) \).