Question No. 1 [15] Find out the Fourier series coefficients for the following signals as shown in Fig. 1. Also draw the magnitude and phase spectrum of the each of the following signals showing at least 3 non-zero coefficients on each side of zero. Comment on the nature of the coefficients (real, imaginary or complex). -20π -10π -I 10πT 20πT → Fig. 1

Need correctly in neat and clean handwritten solution.

Q8/ The Fourier Transform for the following function shown in Figure (2) is --? -4 4 a) 2 sinc(4w) b) 4 sinc(4w) c) 16 sinc(4w) d) 32 sinc(4w)

Fourier Expansions of Periodic Waveforms given in the Figures. Find it. Show on the amplitude-frequency axis. f=1/T 2nf=w a) b) f(t) T f(t) for -V T

- Define Fourier Series. Discuss an application of Fourier series. - What is the difference between odd and even function? Explain with example. -Obtain the Fourier coefficients of first four harmonics of the following periodic function: Assume any value for A, T1 and T2. SO A A -T2 -T1 0 T1 T2

a) Figure 4 below shows a rectangular pulse. i. Derive the Fourier transform for x(t) using integration. ii. Sketch X(@). Label all the important information on the sketching. i. Predict what happens to the DC level as the pulse gets broader while the peak amplitude is maintained at A. x(t) A Activate Window t T T Go to Settings to activ Figure 4 Windows.

Q2) Determine the Fourier Transform of the signal shown in figure. Gung -2 -1 2.

Assume that there is a Fourier series converging to the function f(t) defined by the graph below -3 a. Determine the period and the mathematical function of the f(t). b. Determine if the above function is an even or odd function c. Determine the coefficients in this Fourier series. d. Use Matlab to plot the fourier series function and overlay it to the the original function. Select the number of terms n corresponding to your last 2 digits of your NIM.

Do if you only know please and thank you

Draw the graph please