Using Matlab,

An N-sample moving average low-pass FIR filter is given by, y[n] = 1/N sigma^N - 1_i = 0 x[n - i], where the value of N required to obtain a certain cut-off frequency depends on the sampling rate, F_S. The following {F_S, N} combinations yield somewhat comparable gain characteristics with omega_C = 100 Hz. The higher the value of F_S, the better the representation you get of the analog signal when performing analog-to-digital conversion (ADC). More importantly, you can avoid aliasing if there are frequencies higher than F_S/2. However, the processing speed of your computer imposes a restriction on how fast you can sample and process the data in real-time. Write a Matlab code to find the maximum F_S you can use to implement this low-pass digital filter with cut-off frequency of 100 Hz when: (a) The output is computed one sample at a time. (b) The output is computed every T_C ms (using "conv" or "filter"), where T_C