2. A signal modeled using Fourier series is given by M x(0) = 1 + 2...

 

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2. A signal modeled using Fourier series is given by M x(0) = 1 + 2 (mm) 2A sin m=1 c) d) cos (Amnt) a) Identify the Fourier coefficients a and b b) Plot the signal x(t) for values of M = 10 and 100. Consider A=4, time interval t (-2, 2] and a sampling frequency F = 100 Hz. What signal is this? For each value of M, comment on the signal characteristics including the ability to approximate the signal. What is the fundamental frequency fo of the signal x(t) and what are its harmonics for M = 10? For M = 10, compute the magnitude of coefficients from the above equation and plot them against frequencies for fe [0, 20]. What are the major frequency components that you see? Note them. 3. a) Generate the signal x(t) for M = 10 from question 2b. Take the FFT and plot (using stem) the magnitude of Fourier coefficients from DC positive frequencies only. Use NFFT-length of signal x(t). Compare your FFT magnitude plot against the plot from question 2d. Do they look same or different? What are the major frequency components that you see? Note them. b) Now change NFFT to 128 and replot. What are the major frequency components that you see? Note them. c) Now change NFFT to 512 and replot. What are the major frequency components that you see? Note them. d) Can you explain what changed between FFT magnitude plots in questions 3a, 3b and 3c? 2. A signal modeled using Fourier series is given by M x(0) = 1 + 2 (mm) 2A sin m=1 c) d) cos (Amnt) a) Identify the Fourier coefficients a and b b) Plot the signal x(t) for values of M = 10 and 100. Consider A=4, time interval t (-2, 2] and a sampling frequency F = 100 Hz. What signal is this? For each value of M, comment on the signal characteristics including the ability to approximate the signal. What is the fundamental frequency fo of the signal x(t) and what are its harmonics for M = 10? For M = 10, compute the magnitude of coefficients from the above equation and plot them against frequencies for fe [0, 20]. What are the major frequency components that you see? Note them. 3. a) Generate the signal x(t) for M = 10 from question 2b. Take the FFT and plot (using stem) the magnitude of Fourier coefficients from DC positive frequencies only. Use NFFT-length of signal x(t). Compare your FFT magnitude plot against the plot from question 2d. Do they look same or different? What are the major frequency components that you see? Note them. b) Now change NFFT to 128 and replot. What are the major frequency components that you see? Note them. c) Now change NFFT to 512 and replot. What are the major frequency components that you see? Note them. d) Can you explain what changed between FFT magnitude plots in questions 3a, 3b and 3c?

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a To identify the Fourier coefficients a and b we need to determine the values of the coefficients in the Fourier series representation of the given s... View the full answer