For each of the systems please show a system diagram and plots of the impulse response

4 Difference Equations In this section, we will study the effect of two discrete-time filters. The first filter, y-S1 obeys the difference equatiorn and the second filter, y = S2 , obeys the difference equation y(n)- ^y(n -1) +x(n) Write Matlab functions to implement each of these filters. Then use these functions to calculate the impulse response of each of the following 5 systems: S1, S2, S1(S2) (i.e., the series connection with Si following S2), S2(S1) (i.e., the series connection with S2 following Si), and S1 S2. Note: In Matlab, when implementing a difference equation using a loop structure, it is very good practice to pre-define your output vector before entering into the loop. Otherwise, Matlab has to resize the output vector at each iteration. For example, say you are using a FOR loop to filter the signal x(n), yielding an output y(n). You can pre-define the output vector by issuing the command y - zeros(1,N) before entering the loop, where N is the final length of y. For long signals, this speeds up the computation dramatically INLAB REPORT: For each of the five systems, draw and submit a system diagram (use only delays, multi- plications and additions as in Fig. 1). Also submit plots of each impulse response. Discuss ur observations 4 Difference Equations In this section, we will study the effect of two discrete-time filters. The first filter, y-S1 obeys the difference equatiorn and the second filter, y = S2 , obeys the difference equation y(n)- ^y(n -1) +x(n) Write Matlab functions to implement each of these filters. Then use these functions to calculate the impulse response of each of the following 5 systems: S1, S2, S1(S2) (i.e., the series connection with Si following S2), S2(S1) (i.e., the series connection with S2 following Si), and S1 S2. Note: In Matlab, when implementing a difference equation using a loop structure, it is very good practice to pre-define your output vector before entering into the loop. Otherwise, Matlab has to resize the output vector at each iteration. For example, say you are using a FOR loop to filter the signal x(n), yielding an output y(n). You can pre-define the output vector by issuing the command y - zeros(1,N) before entering the loop, where N is the final length of y. For long signals, this speeds up the computation dramatically INLAB REPORT: For each of the five systems, draw and submit a system diagram (use only delays, multi- plications and additions as in Fig. 1). Also submit plots of each impulse response. Discuss ur observations