Frequency Response of FIR Filters

Steady-State and Transient ResponseSteady-State and Transient Response• The frequency response definition relies on the fact that thesupport interval for the complex sinusoid input is – • In a computer simulation or in a real-time signal processingapplication, it is not practical to consider input signals whichbegin at –• Consider an input that begins at n = 0 using the unit stepfunction to turn on the inputwhereX=Ae jxn un and= Xe jˆ n un 1, n 00, otherwise(6.14)(6.15)• For an LTI FIR system, the convolution sum formula yieldsMyn b kXe jˆ n – k= un – k k = 0hk (6.16). . .0 Mun – kn 0kkECE 2610 Signals and Systems 6–10