Question

Suppose, we let g(t) of problem 1 be periodic (i.e., g(t) is 9T (t) according to the notation using). To be precise let A 4Volts, let the pulse width T-0.1 seconds and let the 0.2 seconds. Find its continuous Fourier transform. Hint: gr. (t) is now that we are fundamental period To periodic and hence you can first find the Fourier series coefficients (C,) and relate those coefficients to the continuous Fourier transform of a periodic signal. Accurately sketch the spectrum of the signal from -30 to 30 Hz. In MATLAB, you can use the stem() function along with the optional argument to plot a sequence of arrows representative of dirac deltas. A -t ()=4 A, g(t) Arect 2 2 0, otherwise

Answer 1

4- o.D5 -o.oS stepl Eind Cn TD O-2 Cn ohre f1 o nuwot dt =5 H 4 .05 4 Jnwo (o65) -jnooTb 4 woxo.bS2Txe.e -jzn O-2 -jn 4 Tn Sine 4 Sin oo5 and Go 4 dt To 2TO7 O. 2 4 0-2 step2 J°Mup° F.S. representaeton Cn e Ting F- T. patr arfot T, SCf-nfo) Cn Sinf -n) 4 ()5 n--oo

Matlab code:

ftof.m MATLAB Drive 1 f=-30:5:30; 2 n=-6:6 3 G=(4./(pi.*n)).*sin(n.*pi./2); 4 stem (f,G); 5 hold on 6 syms x % To set dc value in G(f) 7 x = -1:0.1:1 8 y 9 idx 10 y (idx) 11 stem (x,y); 12 xlabel ('f') 13 ylabel ('G (f)') 14 title('fourier transform of g(t)') dirac (x) Inf; % find Inf 2; y = % set Inf to finite value

Result:

fourier trans form of g(t) 2 1.5 0.5 0.5 -30 30 20 10 -10 -20 f G(f)