Figure P10.24 shows a digital filter designed using the frequency-sampling method....

Figure P10.24 shows a digital filter designed using the frequency-sampling method.

Figure P10.24

(a) Sketch a z-plane pole-zero plot for this filter.

(b) Is the filter lowpass, highpass, or bandpass?

(c) Determine the magnitude response at the frequencies for k =0,1,2,3,4,5,6. (d) Use the results of part (c) to sketch the magnitude response for 0 ≤ ω ≤π and confirm your answer to part (b).