Please show the step to solve theoretical solution. Compare the theoretical solution and sci lab simulation and state th
Posted: Sat Nov 27, 2021 10:32 am
Please show the step to solve theoretical solution. Compare the
theoretical solution and sci lab simulation and state the
conclusion.
Mathematically write the Fourier series coefficient of a periodic signal x(t) = sin (at). • Show detail theoretical solutions on a separate sheet. You must apply EXPONENTIAL Fourier Series approach to find the coefficient Dk and sketch (by hand) the magnitude spectra plot of Dk vs k. (for -5>k>5) • Compare the above theoretical results with the simulation plot obtained by running the following source codes using SCILAB. • Write a comment and conclusion based on the finding.
Use SCILAB to plot the Fourier Series Coefficient of a periodic signal x(t) = sin (tt). Source Code [/To represent a function in exponential Fourier series //Continuous Time Fourier Series Coefficient of a periodic signal x(t) = sin (nt) clc close clear V=1 t0 =1,T=1, w0 =2*3.14/T,P=1 t=0:0.01:3 f=V*abs( sin (%pi *t)) //The Exponential Fourier series coefficient disp('The Exponential Fourier series coefficient are for n=-5 to 5') a=1 for n=-5:5 fr=f.* cos(%pi *n*t/T) Fr(a)= inttrap (t,fr) fi=f* sin(%pi *n*t/T) Fi(a)= inttrap (t,fi) mag (a)=abs(Fr(a)+%i*Fi(a)) disp (Fr(a) -%i*Fi(a))) x(1,size (t,2))=0 x=x+((Fr(a))-%i*Fi(a)).*( cos(%pi *n*t/T)+%i* sin %pi *n*t/T)) a=a+1 end n=-5:5 subplot (2,1,1), plot2d (t,f, style =5) // Rectified sine function Plot xlabel ("t", "fontsize", 2); vlabel ("sin (Trt)","fontsize", 3, "color", "blue"); title ('NAME and ID Number') subplot (2,1,2),plot2d3 (n,mag,12, rect=[-11,0,11,1], style =4) //Plot of the magnitude of the Fourier coefficient xlabel ("k","fontsize", 2); ylabel ("|Dk]","fontsize",4,"color","red"); Legends ([ "Sin (TTT) ";"Exponential Fourier Coefficient Dk" ],[5,4], withbox =%f, opt="ur")
theoretical solution and sci lab simulation and state the
conclusion.
- Please Show The Step To Solve Theoretical Solution Compare The Theoretical Solution And Sci Lab Simulation And State Th 1 (42.6 KiB) Viewed 58 times
- Please Show The Step To Solve Theoretical Solution Compare The Theoretical Solution And Sci Lab Simulation And State Th 2 (73.57 KiB) Viewed 58 times
Use SCILAB to plot the Fourier Series Coefficient of a periodic signal x(t) = sin (tt). Source Code [/To represent a function in exponential Fourier series //Continuous Time Fourier Series Coefficient of a periodic signal x(t) = sin (nt) clc close clear V=1 t0 =1,T=1, w0 =2*3.14/T,P=1 t=0:0.01:3 f=V*abs( sin (%pi *t)) //The Exponential Fourier series coefficient disp('The Exponential Fourier series coefficient are for n=-5 to 5') a=1 for n=-5:5 fr=f.* cos(%pi *n*t/T) Fr(a)= inttrap (t,fr) fi=f* sin(%pi *n*t/T) Fi(a)= inttrap (t,fi) mag (a)=abs(Fr(a)+%i*Fi(a)) disp (Fr(a) -%i*Fi(a))) x(1,size (t,2))=0 x=x+((Fr(a))-%i*Fi(a)).*( cos(%pi *n*t/T)+%i* sin %pi *n*t/T)) a=a+1 end n=-5:5 subplot (2,1,1), plot2d (t,f, style =5) // Rectified sine function Plot xlabel ("t", "fontsize", 2); vlabel ("sin (Trt)","fontsize", 3, "color", "blue"); title ('NAME and ID Number') subplot (2,1,2),plot2d3 (n,mag,12, rect=[-11,0,11,1], style =4) //Plot of the magnitude of the Fourier coefficient xlabel ("k","fontsize", 2); ylabel ("|Dk]","fontsize",4,"color","red"); Legends ([ "Sin (TTT) ";"Exponential Fourier Coefficient Dk" ],[5,4], withbox =%f, opt="ur")