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Simplification using the differential

Simplification using the differential. If Then Therefore. Example. Rectangular pulse ( π(t)). Inverse transforms: V( ω) v(t). Reverse transform convert a spectrum to the pulse which contains it. Example: low-pass filter. Example:. What spectrum does a sinc-shaped pulse have?.

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Simplification using the differential

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  1. Simplification using the differential • If • Then • Therefore from: John Pearson, Basic Communication Theory

  2. Example • Rectangular pulse (π(t)) from: John Pearson, Basic Communication Theory

  3. Inverse transforms: V(ω) v(t) • Reverse transform convert a spectrum to the pulse which contains it. Example: low-pass filter from: John Pearson, Basic Communication Theory

  4. Example: • What spectrum does a sinc-shaped pulse have? from: John Pearson, Basic Communication Theory

  5. Power and energy spectra • A periodic signal power signal • A non-periodic pulse signal energy signal • Parseval’s theorem • Power signals Energy signal from: John Pearson, Basic Communication Theory

  6. Examples: • square pulse train a0= V0/2, an=0, bn={ 0 --- even n 2V0/nπ --- odd n P≅0.50 V02 • Half sine pulse train P = 0.2499V02 from: John Pearson, Basic Communication Theory

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