Let ã[n] be a periodic sequence with period N = 10. The Fourier Transform of [n] is given by r=00 r=0 14T X (ejw) = E 46(w - 2πr) + Σ 36ω. - 2πr). N N r=-0 r=-0 Find ã[n].
Let ã[n] be a periodic sequence with period N = 10. The Fourier Transform of [n] is given by r=00 r=0 14T X (ejw) = E 46(w - 2πr) + Σ 36ω. - 2πr). N N r=-0 r=-0 Find ã[n].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let \(\tilde{x}[n]\) be a periodic sequence with period \(N = 10\). The Fourier Transform of \(\tilde{x}[n]\) is given by
\[
\tilde{X}(e^{j\omega}) = \sum_{r=-\infty}^{\infty} 4\delta\left(\omega - \frac{4\pi}{N} - 2\pi r\right) + \sum_{r=-\infty}^{\infty} 3\delta\left(\omega - \frac{14\pi}{N} - 2\pi r\right).
\]
Find \(\tilde{x}[n]\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe68f0066-db31-42e2-87ae-f5acbabd5711%2F2d48056d-1a72-487a-bc2f-7ccfb91ba884%2Fpxiwhnp_processed.png&w=3840&q=75)
Transcribed Image Text:Let \(\tilde{x}[n]\) be a periodic sequence with period \(N = 10\). The Fourier Transform of \(\tilde{x}[n]\) is given by
\[
\tilde{X}(e^{j\omega}) = \sum_{r=-\infty}^{\infty} 4\delta\left(\omega - \frac{4\pi}{N} - 2\pi r\right) + \sum_{r=-\infty}^{\infty} 3\delta\left(\omega - \frac{14\pi}{N} - 2\pi r\right).
\]
Find \(\tilde{x}[n]\).
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