A. Determine the period of the sinusoid sequence from the plot and verify the result theoretically. Solution The graph shows 20 samples per periodof the cosine signal (sinusoidal), and plots it in a range 0-20, which means that just only a cycle is displayed. Mathematically x=cos∗0.1∗pi∗n 2∗pi∗f=0.1∗pi f=(1/10)∗(1/2)=1/20 T=1/f=20 b.Generate and display a sinusoid with 16 samples per period over two periods with the help of the above program Solution Graph of two periods with 16 signals per cycle each. By just counting the number of samples in each cycle, the period can be known from the graph. C. Using the previous program, display a discrete sinusoid from a sampled continuous sinusoid of 50 Hz frequency at a sampling rate of 400 Hz. D. Given the following sinusoid x(n) = cos(0.8*pi*n), find the expression of a discrete sinusoid identical (Alias)to x(n). Plot the sinusoids in Matlab to validate your expression 1.1 Composite signal (Periodicity) A. Write a program to plot 40 samples of this signal and deduce its period. B. Calculate the period of this signal and compare your results with that obtained from the plot Soln 6.6 1.3 Harmonic signals A. Display the fundamental, second and third harmonics. In each case determine the number of cycles and the period from the graphs. (Note: Cycles and period do not necessarily match) Soln: Fundamental frequency Number of cycles?Period ?from graph Number of cycles?Period ?calc N=period is 16 k/N=1/16 = is frequency in cycles/sample Second harmonics Number of cycles?Period ? Number of cycles?Period ?calc N=period is 16 k/N=3/16 = is frequency in cycles/sample Third harmonics Number of cycles?Period ?from graph Number of cycles?Period ?calc N=period is 16 k/N=4/16 = 0.25 is frequency in cycles/sample B. Calculate the frequency f (cycles per samples) and the period and compare with the results measured from the graphs. C. Explain how this behaviour compares with the analogue sinewaves.