54) Find a signal with -transform .

55) Find the -transform of . Find the transfer function and impluse response of a filter such that .

56) Find the impulse response, transfer function, and frequency response of the following filters. Then plot their amplitude and phase responses. (Feel free to use Matlab for the plots.)

57) Find the amplitude response of the filter with transfer function . (Your answer should be evidently real.) Sketch the graph.

58) Find the transfer function of a filter such that kills the 400 Hz component of a signal sampled at 1000 Hz. Find such an whose frequency response is real and even.