During lab 4, we have seen numerical implementation of FourierSeries for periodic signals. As first part of this assignment, youneed to write a Matlab function that would take an arrayrepresenting a single period of a signal (x), corresponding timearray (t), and return the Fourier Series coefficients (Ck) inexponential form. The function should also be able to take two (2)optional input arguments: number of Fourier coefficients (Nk) andplot option (p). Use the template ‘fourier_series_exp.m’ for thisproblem.

(Template \"fourier_series_exp.m\")

function [Ck]=fourier_series_exp(x,t,Nk,p)

% Ck = exponential fourier series cofficient
% x = single period of a signal
% t = time corrosponding to 'x'
% Nk = (optional input) number of exponential terms
% p = plotting option ; p=0, no plots, p = 1 plot Ck vs k andreconstructed signal
% dT = t(2)-t(1) = temporal resolution of signal (x)
% T = peiod of signal 'x'
% w0= angular frequency of signal 'x'

dT=t(2)-t(1);
T= dT*length(t);
w0=2*pi/T;   

% Check the number of inputs, 'nargin' returns number of inputarguments
if nargin <2
error('Not enough input argument!')
elseif nargin == 2
Nk=101; % you can set any default value you like
p=0; % not plots
elseif nargin ==3
p=0; % not plots
end
k=-floor(Nk/2):floor(Nk/2); % if Nk=11, k=-5:5; if Nk=12,k=-6:6

%% evaluate Ck
%
% % % write this code segment
%
%% plot spectrum and reconstructed signal   
if p==1
% plot abs(Ck) vs k and angle(Ck) vs k
%
% % % write this code segment
%
  
% plot 3 cycles of the signal 'x' and the reconstructedsignal
%
% % % write this code segment
%
end

end