9.3 • DIGITAL SIGNAL FILTERS 391
(b} y[n] = x[n]- x[n-l]+x[n- 2) will "zero-out" x[n] = cos( in} and x[n] =
sin( in).
(c) y[n] = x[n]+v'2x[n- l l+x[n- 2) wUI "zero-out" x[n] = cos(^3 ;n) and x(n] =
sin(3;n).
(d} y[n) = x[n)+v'Jx[n- l )+x[n- 2) will "zero-out" x[n) = cos(^56 " n) and x(n) =
sin(^5 ; n).
(e) y(n] = x(n]-v'3x(n-l)+x(n-2] will "zero-out" x (n) = cos(~n} and x[n] =
sin(~n).
- Given the recursion formula y(n] = x (nl + x[n - I I + x(n - 2].
(a) Calculate the amplitude response A(0.10) , AG), A<2:n, and A(2.10).
(b) Discuss what happens to the filtered signal for the input x [n) = cos(O.lOn}
+ sin(2.10n).
- Given the recursion formula y(n) = x[n) + v'2x(n - l] + x[n - 2j.
(a) Calculate the amplitude response A(0.10), A(~), A(3r>, and A(2.40).
(b) Discuss what happens to the filtered signal for the input x[n] = cos(O.lOn)
+ sin(2.40n}.
- Given the recursion formula. y[n) = x (n) - x(n - ll + x[n -2).
(a) Calculate the amplitude response A(0.10), A(j), A(l.00), and A(2;).
(b) Discuss what happens to the filtered signal for the input x[n) = cos(O.lOn)
+ sin(LOOn}.
- Given the recursion formula y(n) = x[n] + h !n - 11 - ~y{n -2].
(a) Calculate the amplitude response A(O}, A(i), A(2;), and A(1r).
(b) Discuss what happens to the filtered signal for the input x[n] =cos( fn)
+ sin(2; n).
- Given t he recursion formula y[n] = x(n] + ~v'3y[n - 1] - ~y[n - 2].
(a) Calculate the amplitude response A(~), A(J}), A(~), and A(2;>.
(b} Discuss what happens to t he filtered signal for the input x(n] = cos(~n)
+ si n(2; n).
- The single-pole low-pMS filter is y(n] = K x [n ) + (1 - K)y(n - 1), where constant
K is between 0 and 1.
(a} Use K = ~ to find A(B), A(O}, A(f ), A(~), and A(1r).
(b) Use K =to to find A(9), A(O), A(t), A(~), and A(1r).
(c) Use K = ft to find A(9), A(O), A(i), A(~), and A(1r).
- Use t he recursion formula. y[n) = ~x[n) + ~y[n - l ] in Exercise 7(a).
