Question: A finite duration signal. x(t), is given as: x (t) e where -5 ms S t s

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Question: A finite duration signal. x(t), is given as: x (t) e where -5 ms S t s 5 ms. e) [10pts] From the samples xIn] reconstruct x(t) (i.e, xr(t)) by using zero-order hold interpolation Plot x,(t) with respect to t and comment on the results. Be sure to add a title and axis labels. Hint: The stairs function plots a staircase rendition of the analog signal, given its samples. [10pts] From the samples xIn reconstruct x(t) (i.e., xr(t)) by using first-order hold (FOH) interpolation: plot xr(t) with respect to t and comment on the results. Be suure to add a title and axis labels. Hint: The plot function depicts a linear interpolation between samples g) [15pts] By using the "sinc" interpolation formula given below, reconstruct xr(t) from the samples xIn]. MATLAB has the sinc function as sinc (x). Be sure to add a title and axis labels. Hint: You may use the interval for m given in (d). x(t) n ni

Explanation / Answer

% ANSWER FOR (e)

t=-5e-3:0.0001:5e-3; %TIME DEFINED BETWEEN -5ms to 5ms

x = exp(-1000*abs(t)); %the function defined with respect to time

stairs(t,x);title('x(t)using zero order hold interpolation'); %plotting the function in time domain using stairs function

xlabel('time t');ylabel('x(t)'); % x and y label definition

% answer for (f)

t=-5e-3:0.0001:5e-3; %TIME DEFINED BETWEEN -5ms to 5ms

x = exp(-1000*abs(t)); %the function defined with respect to time

plot(t,x);title('x(t)using first order hold interpolation'); %plotting the function in time domain by linear interpolation using plot function

xlabel('time t');ylabel('x(t)'); % x and y label definition

% answer for (g)

t=-5e-3:0.000001:5e-3; %TIME DEFINED BETWEEN -5ms to 5ms

x = exp(-1000*abs(t)); %the function defined with respect to time

fs=400; % sampling frequency of the signal

n=length(x); % length of the signal x

y=x.*sinc(fs*(t-(n/fs))); % the signal represented using sinc function

plot(t,y);title('resonstruction of x(t) using sinc function'); %plotting the function in time domain using plot function

xlabel('time t');ylabel('x(t)'); % x and y label definition

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