84.4 The Concept of Filtering Now, the frequency response of the FIR filter is given by H(e0)=[O]+h]le1o+h[2]e-20 =a(1+e-J20)+阝e-0 e/o +e yo 20 e0+阝e0 2 =(2coso+β)e-/0
§4.4 The Concept of Filtering • Now, the frequency response of the FIR filter is given by − − = + + 2 ( ) [0] [1] [2] j j j H e h h e h e − − = a + +b j j (1 e ) e 2 − − − + b + = a j j j j e e e e 2 2 − = a +b j (2 cos )e
84.4 The Concept of Filtering The magnitude and phase functions are Hel)=2 alcona+β 0(0) In order to block the low-frequency component, the magnitude function at o=0.1 should be equal to zero e. Likewise, to pass the high-frequency component, the magnitude function at o=0. 4 should be equal to one
§4.4 The Concept of Filtering • The magnitude and phase functions are |H(ej)|=2acos+b () = - • In order to block the low-frequency component, the magnitude function at = 0.1 should be equal to zero • Likewise, to pass the high-frequency component, the magnitude function at = 0.4 should be equal to one
84.4 The Concept of Filtering Thus the two conditions that must be satisfied are IH(e)|=20cos(0.1)+B=0 H(e0)|=ccos(0.4)+B=1 Solving the above two equations we get c=-6.76195 β=13456335
§4.4 The Concept of Filtering • Thus, the two conditions that must be satisfied are |H(ej0.1)|=2acos(0.1)+b = 0 |H(ej0.4)|=2acos(0.4)+b = 1 • Solving the above two equations we get a = -6.76195 b = 13.456335
84.4 The Concept of Filtering Thus the output-input relation of the FIR HIter is given by yn=-6.76195(xm+xn-2])+13456335x[n-2 where the input is x[n={cos(0.1n)+co(0.4n)}n a. Program 4 2 can be used to verify the Filtering action of the above system
§4.4 The Concept of Filtering • Thus the output-input relation of the FIR filter is given by y[n] = - 6.76195(x[n]+x[n-2])+13.456335x[n-2] where the input is x[n] = {cos(0.1n) + cos(0.4n)}[n] • Program 4_2 can be used to verify the filtering action of the above system
84.4 The Concept of Filtering Figure below shows the plots generated by running this program ynI “-- 0 0 20 100
§4.4 The Concept of Filtering • Figure below shows the plots generated by running this program