6 suppose the impulse response h n of a linear time

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6. Suppose the impulse response, h [ n ], of a linear time-invariant system is equal to zero except in the interval N 0 n N 1 , and the input x [ n ] is equal to zero except for in the interval N 2 n N 3 . The resulting output of the system, y [ n ], is equal to zero except for an interval, N 4 n N 5 . a. Determine N 4 and N 5 in terms of N 0 ,N 1 , N 2 , and N 3 . b. If x [ n ] is zero, except for N consecutive points, and h [ n ] is zero except for M consecutive points, what is the maximum number of nonzero consecutive points in the output sequence, y [ n ]? Hint: draw pictures of arbitrary, finite-length, sequences x [ n ] (ex. { … 0, 1, … 1, 0, …}) and h [ n ] then use graphical convolution to determine where the convolution result is equal to zero.
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  • Spring '10
  • BROWN
  • Digital Signal Processing, LTI system theory, Impulse response, unit step functions, discrete delta functions

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