Please ss for matlab codes A finite duration signal, x(t), is given as: x(r) = e
ID: 1996629 • Letter: P
Question
Please ss for matlab codes
A finite duration signal, x(t), is given as: x(r) = e^-1000|t| where -5 ms lessthanorequalto t lessthanorequalto 5 ms. a) Sketch x(t) with respect to t (time). Choose appropriate increment value for t on your plot. Be sure to add a title and axis labels. b) Calculate the Continuous-Time Fourier Transform of x(t) (i.e.. X(j omega)) by using the Fourier transform analysts equation. c) Sketch X(j omega) with respect to omega (frequency) in rad/s. Check if X(j omega) 0 for |omega| > 4000 pi. Be sure to add a title and axis labels. d) Sample x(t) at f_s = 1/T_s = 5000 samples/sec to obtain x[n] = x(nT_s) and plot it with respect to n {-25, -24, ..., 24, 25}. You may use MATLAB's stem function to plot x[n]. Please be careful about the axis ticks and labels and do not forget to add a title and axis labels. e) From the samples x[n], reconstruct x(t) (i.e.. x_r(t)) by using zero-order hold interpolation. Plot x_r(t) with respect to t and comment on the results. Be sure to add a title and axis labels. From the samples x[n], reconstruct x(t) (i.e., x_r(t)) by using first-order hold (FOH) interpolation, plot x_r(t) with respect to f and comment on the results. Be sure to add a title and axis labels. g) By using the "sine" interpolation formula given below, reconstruct x_r(r) from the samples x[n]. MATLAB has the sine function as sine (x). Be sure to add a title and axis labels. x(t) sigma_n=-n_1^n_1 x[n]sinc(f_s[t-n/f_s]) h) Did you encounter aliasing in (e-g)? Why? If not, which method in (e-g) is better to reconstruct x(t)? i) Now, change f_s = 1000 samples/sec and repeat (d-h). Comment on your results.Explanation / Answer
(1) t = -5e-3:0.0000001:5e-3;
x=exp(-1000*abs(t));
plot(t,x);
xlabel('t (time)');ylabel('X(t)');
(2) f=1./t;
ff=x.*exp((-i*2*pi)*f.*t);
F=integral(ff,-Inf,Inf);