Frequency response is the analysis of the response of systemswhen subjected to a sinusoidal change in input. When a linear system is subjected to a sinusoidal input, its ultimate response is also a sustained sinusoidal wave, with the same frequency. The figure below compares the output response of a system (solid line) with a sinusoidal input (dashed line) disturbing the system

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The output y[n] of a frequency-selective LTI discrete-time system with a frequency response exhibits some delay relative to the input x[n] caused by the nonzero phase response of the system

BIBO Stability Condition - A discrete-time LTI system is BIBO stable if the output sequence {y[n]} remains bounded for any bounded input sequence{x[n]}