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# 4 we then obtain the frequency domain representation

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Unformatted text preview: Table 3.4 we observe that the DTFT of δ[n − 1] is e − jω and the DTFT of v[n − 1] is e − jωV (e jω ) 3 • Using the linearity property of Table 3.4 we then obtain the frequency-domain representation of d0v[n] + d1v[n − 1] = p0δ[ n] + p1δ[n − 1] as d0V (e jω ) + d1e − jωV (e jω ) = p0 + p1e − jω 4 • Solving the above equation we get p + p1e − jω V ( e jω ) = 0 d0 + d1e − jω Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra Energy Density Spectrum Energy Density Spectrum • The total energy of a finite-energy sequence g[n] is given by Eg = ∞ ∑ n = −∞ g[ n] • The quantity S gg (ω) = G (e jω ) 2 is called the energy density spectrum • The area under this curve in the range − π ≤ ω ≤ π divided by 2π is the energy of the sequence • From Parseval’s relation given in Table 3.4 we observe that Eg = ∞ ∑ n = −∞ g[ n] 2 = 1π jω 2 ) dω ∫ G (e 2π − π 5 2 6 Copyright © 2005, S. K. Mitra Copyright © 2005, S. K. Mitra 1 Band-limited Discrete-time BandDiscreteSi...
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