# Translations:Frequency response of a digital system/1/en

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We recall that impulse response is the system’s response to a unit spike. Thus, the impulse response represents a transient that dies out over time for a stable system. On the other hand, the frequency response can be interpreted as a steady-state response of the system to signals, each with a pure frequency. Let the real variable denote frequency (in radians per second), and let be the discrete time spacing (in seconds). The function is a steady-state sinusoidal wave of pure frequency If we let this steady-state signal be the input to a unit-delay system *Z*, the steady-state output is the delayed signal . The frequency response is the ratio of the steady-state output to the steady-state input ; that is,