Question

For the following DT system, determine the following: hi[n] = [n] 1 h2[n] = 128[n – 1] T y hin] ha[n] a. The difference equation in delay form. (Hint: Lecture 9 notes may help too) b. Find the DT frequency response of the system using the eigenfunction as the input.

Answer 1

Solution:- Given. h. (n= sin han] = to Sin-1] d ar thing ha (n] From peoperties properties of OFFT HiCam = 1 binasin) DTET JW (-1) h2 cm)- za 6(71) د (علی) را - Le 12 DTFT The two

From the fig ulewy x(ein) قلعه Hiles) = X(w) 1. in eth 12 (سالم) ju x Cejay It th yceu)= H (eda), ex (ein). is the transfer function It Hi Cew) Ela(w) Transfer function # Cew) @ Difference equation = ? from above egn ywno 1. The difference equation function. DTFT response eigen jono Solution: function a(n)= e Let the ilp eigen Х 12 eu Y(u) Celing "Cew) By taking inverse DTFT we no y(n-1] = a[n] get Hea) = yen-no) y[M]+ Yn] + 2 yen - 1] = a[n] for imput : From Tramsfer function output 4(en)

4 Cew) (ona) IIW Taking inverse DTFT we e get Baum :: -aan xCeów). 8.C, sino ain-Do) ejuno Excew :. From the properties given you are yen)= (-1) -no) anno) of Giono. € . For on eigen function input output yen)= Ch 0-no ucn-no).