Using the ekg simulator posted in elearning, generate 20 cycles of the ekg waveform (when displaying the original, noisy or filtered signals in time-domain, show only two or three cycles). (a) (10 points) display the original ekg signal both in time-domain and frequency-domain. (b) (10 points) add the following two noises to the original signal: - a 60 hz noise (with an amplitude of 1). - an additive white gaussian noise (awgn), i. e. independent and identically-distributed (i. i.d.) gaussian random variables with = 0 and = 2. display the noisy signal both in time-domain and frequency-domain. (c) (20 points) analyze the spectra of the original and noisy signals and design a suitable filter to extract the ekg signal from the noisy signal. display the filter’s response. display the filtered signal both in time-domain and frequencydomain.