Question
Download Solution PDFThe energy of the signal x(n) = (-0.4)n u(n) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Energy of signal is given by:
\(E = \sum_{n = -\infty} ^\infty|x(n)|^2\)
Calculation: We have x(n) = (-0.4)n 4(n)
\(E = \sum_{n = -\infty} ^\infty|(-0.4^n)u(n)|^2\)
\(E = \sum_{n = -\infty} ^\infty(-0.4)^{2n}~u(n)\)
\(E = \sum_{n = -\infty}^\infty (-0.4)^{2n}\)
E = 1 + 0.42 + 0.44 + ....
\(\rm E = \frac{1}{1\space-\space0.4^2} = \frac{1}{1 \space- \space 0.16}\)
\(\rm E = \frac{100}{84}\)
\(\rm E = \frac{25}{21} \space Joule\)
Last updated on Jul 2, 2025
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