Subjects signals and systems

Exponential Signal

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

Exponential Signal


1. **Problem Statement:** We are given the exponential signal $$x(t) = 3e^t$$ and asked to draw its analog and digital forms. 2. **Understanding the Signal:** The signal is continuous-time and exponential, scaled by 3. The function grows exponentially as $$t$$ increases. 3. **Analog Form:** The analog form is the continuous curve of $$x(t) = 3e^t$$ for all real values of $$t$$. 4. **Digital Form:** The digital form samples the analog signal at discrete time points, for example at integer values of $$t$$. The digital signal is a sequence of points $$x[n] = 3e^n$$ where $$n$$ is an integer. 5. **Summary:** - Analog: continuous curve $$3e^t$$. - Digital: discrete points $$3e^n$$ for integer $$n$$. **Final answer:** The analog signal is $$x(t) = 3e^t$$ continuous over $$t\in\mathbb{R}$$, and the digital signal is the sequence $$x[n] = 3e^n$$ sampled at integer $$n$$.