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EL 611 HW 6 Soln

# EL 611 HW 6 Soln - 1 The output is given by the convolution...

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1) The output is given by the convolution sum a)  k k n x k h n y ) ( ) ( ) ( . If ) ( n h and ) ( n x are both real then it is obvious that ) ( n y will also be real. b) Note that, since ) ( n h is real we can take the conjugate of the convolution sum equation above to get  k k n x k h n y ) ( ) ( ) ( which shows that if the input is ) ( n x the output is ) ( n y . c) Again, since ) ( n h is real we can use the two summation equations above to get    k k k k n x k n x k h k n x k h k n x k h n y n y 2 ) ( ) ( ) ( 2 ) ( ) ( ) ( ) ( 2 ) ( ) ( or, equivalently,  k k n x k h n y ) ( Re ) ( ) ( Re Which is the same as ) ( Re ) ( ) ( Re k n x k h n y . This means that if the input is ) ( Re n x the output is ) ( Re n y . For the imaginary part result, recall that j n x n x n x 2 ) ( * ) ( ) ( Im

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EL 611 HW 6 Soln - 1 The output is given by the convolution...

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