a) Using Octave, prepare and test the set of programming statements to generate two different Sine waves (x1(n) and x2(n)).
b) Process these two sinewaves through a linear system with the following definition:
y(n) = (-3*x(n))/8;
Demonstrate, through example, that for your two Sine waves, the result of processing sum of your two sine waves, x1(n) + x2(n) by linear system y(n) is same output as sum of the two outputs, y applied to x1(n) added to y applied to x2(n).
You must provide plots of x1, x2, and x1+x2. Additionally you must provide plots of y1, (i.e., y applied to x1) and y2 (y applied to x2). At last, you must show in the plot that y1+y2 is the same as y(x1+x2).
Generate various sine waves using different sample rates or oscillations but the net result must show that your system is linear.
Describe why your system is a linear system.
c) Prepare a block diagram for time-invariant linear system that performs a 5-point moving average. Using Octave, then prepare and test Impulse response which tests your 5-point moving average system. Plot both input and the output for the Impulse and the attached dataset (for5avg.m).
You must include a separate Octave m file for each of the problems for this set. Name one your namehw1a.m and the other yournamehw1b.m. These m files must be fully tested and run perfectly from start to finish. The m files would include plotting routines but you must also include a word document which includes your output, explanations, block diagram and other information from both parts of this assignment. If you prefer to use LaTeX, a freely downloadable tool that many researchers prefer to Word, you are welcome to do so, so long as you send me the .pdf output.
Your plots must be neat, properly labelled, with axis information, legends and titles as suitable. Your code (m file) must include inline comments which explains your code and include header information including author, date and descriptions. Your word document must be named yournamehw1.doc (or yournamehw1.docx)