TsAmE said:The system is time invariant and is non-linear, but I don't understand why it is causal and has memory.
Causality refers to the property of a system where the output of the system depends only on the current and past inputs. In other words, the output of a causal system cannot depend on future inputs. This is an important property in signal processing as it ensures that the system is predictable and can be analyzed using techniques such as convolution.
Causality is closely related to the stability of a system. A causal system is said to be stable if its output remains bounded for all bounded inputs. This means that the system will not produce infinite or oscillating outputs, which can lead to unpredictable behavior. In general, a causal system is more likely to be stable compared to a non-causal system.
Memory refers to the ability of a system to retain information about past inputs. A system with memory will produce an output that depends not only on the current input but also on previous inputs. The amount of memory a system has can vary, and it is an important factor in determining the complexity and performance of a system.
Memory and linearity are two important properties of a system that are closely related. A system is said to be linear if it follows the principle of superposition, where the output to a sum of inputs is equal to the sum of individual outputs. If a system has memory, it is more likely to be non-linear since the output will depend on the sequence of inputs, not just the sum of inputs.
The impulse response of a system is defined as the output of the system when the input is an impulse function. Causality and memory can be determined by analyzing the impulse response of a system. If the impulse response is zero for negative time, then the system is causal. If the impulse response is finite for all time, then the system has memory. By studying the impulse response, we can gain insights into the behavior and properties of a system.