Steps
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Part a. Let x[n] represent the following discrete-time signal
x[n]=\cases{
0&for $n\lt0$\cr
a^0&for $n=0,1,2$\cr
a^1&for $n=3,4,5$\cr
a^2&for $n=6,7,8$\cr
\cdots\cr}
where a is a real number between 0 and 1,
as shown in the plot below.
Determine a closed form expression for X(\Omega), which is the discrete-time Fourier transform of x[n].
Part b. Let x(t) represent the following continuous-time signal
x(t)=\cases{
0&for $t\lt0$\cr
a^0&for $0\le t\lt3$\cr
a^1&for $3\le t\lt6$\cr
a^2&for $6\le t\lt9$\cr
\cdots\cr}
where a is a real number between 0 and 1,
as shown in the plot below.
Determine a closed-form expression for X(\omega), which is the continuous-time Fourier transform of x(t).
Please upload a single pdf file that contains your answers to all parts of this problem: No file selected
