Lab 1 Discrete-Time Fourier Transform (DTFT) In this lab,you will investigate the Matlab implementation of the DTFT.You may use the following Matlab functions: zeros(),ones(,exp(),cos(),abs(,angle(,plotO,subplot(),title(,xlabel(,ylabel(),figure(,stem(,eye(), filter(). (1)Generate and plot the discrete-time signal x(n)=0.93”cos(0.14πn+π/3)，0≤n≤30 (2)Determine and plot the DTFT of the signal x(n）=0.89[u(n）-u(n-30)] (3)A linear and time-invariant system is described by the difference equation y(n)-0.65y(n-1)+0.35y(n-2)=ax(n)-bx(n-1)+cx(n-2)-dx(n-3)where abcd is equal to the last four digits of your student ID number. (i)Is the system BIBO-stable? (ii)Determine and sketch the impulse response h(n),0sns100,of the system.Determine the stability of the system by observing h(n) (iii)Determine and plot the output of the system y(n),0sn<200,if the input is x(n)=[d+ccos(0.27πn）+dsin(0.77πn]u(n）Lab 1 Discrete-Time Fourier Transform (DTFT) In this lab, you will investigate the Matlab implementation of the DTFT. You may use the following Matlab functions: zeros(), ones(), exp(), cos(), abs(), angle(), plot(), subplot(), title(), xlabel(), ylabel(), figure(), stem(), eye(), filter(). (1) Generate and plot the discrete-time signal ( ) 0 93 cos 0 14 3 0 30 ( ) n xn . . = πn + ≤≤ π , n (2) Determine and plot the DTFT of the signal ( ) 0 89 ( ) ( 30) n xn . un un = −−     (3) A linear and time-invariant system is described by the difference equation y n . y n . y n ax n bx n cx n dx n ( ) − −+ − = − −+ − − − 0 65 1 0 35 2 ( ) ( ) ( ) ( 1 2 3 ) ( ) ( ) where abcd is equal to the last four digits of your student ID number. (i) Is the system BIBO-stable? (ii) Determine and sketch the impulse response hn n ( ), 0 100 ≤ ≤ , of the system. Determine the stability of the system by observing h n( ) . (iii) Determine and plot the output of the system yn n ( ), 0 200 ≤ ≤ , if the input is xn d c . ( ) =+ +   cos 0 27 sin 0 77 ( πnd . ) ( πn un ) ( )  