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Determine z-transform of the following x(n)={1,2,3,4,5,0,7}
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Solution:

x(0)=4x(1)=5x(2)=0x(3)=7x(1)=3x(2)=2x(3)=1

x(z)=n=x(n)zn=3n=3x(n)zn

=x(3)z+3+x(z)z+2+x(1)z+1+x(0)z0+x(1)z1+x(2)z2+x(3)z3

=1z+3+2z+2+3z+1+4+5z1+0zz+7z3

=z3+2z2+3z+4+5z+7z3x(z)=z3+2z2+3z+4+5/z+7/z3

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