Proj1 - -x n-2 3 Let x 1 n = n u n 10-u n-20 x 2 n = cos(0...

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EECS 152A, CSE 135A: Digital Signal Processing Computer Project #1 Due Oct. 5 in class Write MATLAB programs for the following projects. Include a copy of your programs in your report along with the requested results (numbers, figures, etc.). 1. Let x ( n ) = { 1 , - 2 , 4 , 6 , - 5 , 8 , 10 } , x ( - 4) = 1 , x ( - 3) = - 2 , x ( - 2) = 4 , x ( - 1) = 6 , x (0) = - 5 , x (1) = 8 , x (2) = 10. Generate and plot the samples of the following sequences. x 1 ( n ) = 3 x ( n + 2) + x ( n - 4) - 2 x ( n ) x 2 ( n ) = 2 e 0 . 5 n x ( n ) + cos(0 . 1 πn ) x ( n + 2) for - 10 n 10 . Hint: You need to think about how to add two sequences starting from different indexes. You may use the ‘stemplot’ function, provided in the website. 2. Randomly pick two sequences x ( n ), y ( n ) (any distribution and length) and numerically show which one of the following systems is linear. T 1 [ x ( n )] = 2 x ( n ) T 2 [ x ( n )] = x ( n ) 2 + 2
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Unformatted text preview: -x ( n-2) 3. Let x 1 ( n ) = n [ u ( n + 10)-u ( n-20)] , x 2 ( n ) = cos(0 . 1 πn )[ u ( n )-u ( n-30)] , x 3 ( n ) = (1 . 2) n [ u ( n + 5)-u ( n-10)] . Check the following properties of linear convolution: • Commutation: x 1 ( n ) * x 2 ( n ) = x 2 ( n ) * x 1 ( n ) • Association: x 1 ( n ) * ( x 2 ( n ) * x 3 ( n )) = ( x 1 ( n ) * x 2 ( n )) * x 3 ( n )) • Distribution: x 1 ( n ) * ( x 2 ( n )+ x 3 ( n )) = ( x 1 ( n ) * x 2 ( n ))+( x 1 ( n ) * x 3 ( n )) Hint: You may use the conv m function, provided in the website. 4. Let x ( n ) = (0 . 8) n u ( n ). Determine the first 50 samples of y ( n ) = x ( n ) * x ( n ), i.e., n = 1 , 2 ,..., 50. 1...
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