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Unformatted text preview: For x ( t ) = ∑ ∞ k =-∞ δ ( t-kT ), we have a k = 1 T for all k . Fourier Series Properties: In the following table, assume that both x ( t ) and y ( t ) have fundamental period T . Signal Fourier Series Coe±cients x ( t ) a k y ( t ) b k Ax ( t ) + By ( t ) Aa k + Bb k x ( t-t ) a k e-jkω t x (-t ) a-k x * ( t ) a *-k x ( t ) y ( t ) ∑ ∞ l =-∞ a l b k-l y ( t ) = dx ( t ) dt b k = jkω a k Parseval’s relation for Fourier series: 1 T i T | x ( t ) | 2 dt = ∑ k | a k | 2...
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This note was uploaded on 08/06/2008 for the course ECE 130A taught by Professor Madhow during the Fall '07 term at UCSB.
- Fall '07