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Sinusoidal <strong>Response</strong> <strong>of</strong> <strong>FIR</strong> Systems• The frequency response is a complex function <strong>of</strong> ˆgenerally viewed in either polar or rectangular formthat isHe jˆ He jˆ e j H ejˆ=(6.5)= ReHe jˆ+jImHe jˆ– The polar or magnitude and phase form is perhaps themost common• The polar form <strong>of</strong>fers the following interpretation <strong>of</strong>terms <strong>of</strong> xn , when the input is a complex sinusoidyn == e j H ejˆHe jˆ Ae j H ejˆHe jˆyn in(6.6)– Here we see that the input amplitude is multiplied by thefrequency response amplitude, and the input phase hasadded to it the frequency response phase– The output amplitude expression means that isalso termed the gain <strong>of</strong> an LTI systemAe j e jˆ n + jˆ n eHe jˆExample: = 11311 b k• The frequency response <strong>of</strong> this <strong>FIR</strong> filter is– b ke jˆ k=He jˆ=4k = 0–1 + e jˆ+ 3e – j2ˆ+ e – j3ˆ+e – j4ˆECE 2610 Signals and Systems 6–3
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