3 What can you say about the periodicity of the output of an

3. What can you say about the periodicity of the output of an LTI system when its input is a periodic sequence of period N. Prove your answer.

Solution

output of the LTI sysytem is periodic when the periodic signal is applied.

As LTI sysytem refers to linerar time invarient sysytem.

A sysytem is linear when its output changes linearly with change in input i.e. it follows input signal with some variation in phase or amplitude that depends on nature of system but characterstic remain similar to input.

A system in time invarient when it doesnt vary with time i.e. system doent have any component which varies the output timely with respect to input.

SO by observing above two condition we can say that output will foolow linearly with respect to input.

Thus it will remain periodic.