kovachattack said:As t approaches zero, you get unbounded outputs from bounded inputs. So, it is unstable.
Also, please somebody correct me if I am wrong, but I believe y(t) = t x(t) does in fact have a bounded output for a bounded input. If you don't let x go to infinity, then y will also not go to infinity, and is therefore bounded and stable.
A signal is a physical quantity or variable that conveys information. In the context of signals and systems, it can be represented as a function of time or space.
Some common types of signals include continuous-time signals, discrete-time signals, periodic signals, and aperiodic signals. Continuous-time signals are defined over a continuous range of time, while discrete-time signals are defined only at discrete points in time.
The main properties of a system in signals and systems are linearity, time-invariance, causality, and stability. Linearity means that the output of the system is directly proportional to the input. Time-invariance means that the system's behavior does not change over time. Causality means that the output of the system depends only on the current and past inputs, not future inputs. Stability means that the system's output does not grow without bounds for a bounded input.
Signals and systems are closely related because signals are processed by systems. A system takes an input signal and produces an output signal based on its properties and characteristics. Understanding the properties of systems is essential in analyzing and designing systems for specific applications.
Studying system properties in signals and systems is crucial because it allows us to understand and predict the behavior of systems. It also enables us to analyze and design systems for various applications, such as communication, control, and signal processing. Knowing the properties of a system can also help us troubleshoot and optimize its performance.