Frequency Response of FIR Filters

Properties of the Frequency ResponseExample: Difference Equation from• Suppose that• We immediately can write thatand• It could have been thatstarted in this formExample:hn yn He jˆHe jˆ• We need to convert the sine form back to complex exponentials• The impulse response is thus?– 2ˆHe jˆ = 1+ 4e j +=He jˆ=4e – j4ˆn + 4n – 2 + 4n – 4xn + 4xn–2 + 4xn–4 1 8e j2ˆ ----------------------------+ = + 2 –= 1+8e j2ˆcos2ˆ– e j2ˆ– 2j ˆ 2e jˆ 2= sin 2je j ˆ 2=He jˆ=– e jˆ 2–1 – e jˆ–e j2ˆe – jˆ 2– --------------------------------- 2j ECE 2610 Signals and Systems 6–15