5. (20 points) Design a complementary filter by connecting a low pass filter (Filter 1) and a highpass filter (Filter 2) as shown below. Let hi(k) be the impulse response

of the LPF and h2(k)be the impulse response of the HPF. The output z(k) is the sum of outputs of Filter 1 and Filter 2. (a) Find the scaled impulse response hi(k) of the lowpass filter with the following specifications:cutoff frequency fc = 1520 Hz, sampling rate = fsampling = 10000 samples/s,number of taps = N = 11, window = Hamming window. List the values. (b) Find the scaled impulse response h2(k) of the highpass filter with the following specifications: cutoff frequency fc = 3320 Hz, sampling rate = fsampling = 10000 samples/s,number of taps = N = 11, window = Hamming window, algorithm = Complement method. List the values (c) Let x(k) = 4 cos(ak/2) u(k) + 3 cos(4rk/5) u(k). Find the output zi(k) of Filter 1 for0