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F(t) and G(t) are the one-sided z-transforms of discrete time functions f(nt) and g(nt), the z-transform of ∑f(kt)g(nt-kt) is given by _____________
  • a)
    ∑f(nt)g(nt)z-n
  • b)
    ∑f(nt)g(nt)zn
  • c)
    ∑f(kt)g(nt-kt) z-n
  • d)
    ∑f(nt-kt)g(nt)z-n
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
F(t) and G(t) are the one-sided z-transforms of discrete time function...
F(nt) is given by F(z) = Z{f(nt)} and the z-transform of g(nt) is given by G(z) = Z{g(nt)}.
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Community Answer
F(t) and G(t) are the one-sided z-transforms of discrete time function...
Given that F (t) and G (t) are the one-sided z-transforms.
Also, f (nt) and g (nt) are discrete time functions, which means that property of Linearity, time shifting and time scaling will be similar to that of continuous Fourier transform. Since, for a continuous Fourier transform, the value of ∑f(kt)g(nt-kt) is given by∑f(nt)g(nt)z-n.
∴ z-transform of ∑f(kt)g(nt-kt) is given by∑f(nt)g(nt)z-n.
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F(t) and G(t) are the one-sided z-transforms of discrete time functions f(nt) and g(nt), the z-transform of ∑f(kt)g(nt-kt) is given by _____________a)∑f(nt)g(nt)z-nb)∑f(nt)g(nt)znc)∑f(kt)g(nt-kt) z-nd)∑f(nt-kt)g(nt)z-nCorrect answer is option 'A'. Can you explain this answer?
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