By Bers L.

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**Extra resources for Riemann surfaces **

**Example text**

Here again, the values of the samples are enough to define the signal completely. This similarity is a consequence of the duality between the time and frequency domains and the fact that both the Fourier series expansion and reconstruction from samples are orthogonal expansions, one in terms of the exponential signals and the other in terms of the sinc functions. This fact will be further explored in the problems. 5 BANDPASS SIGNALS In this section, we examine time domain and frequency domain characteristics of a class of signals frequently encountered in communication system analysis.

2 on page 27. Solution We follow the preceding steps. 3 13:6 Power and Energy 41 1 ohm resistor. The energy content of a signal x(t), denoted by E x , is defined as ∞ Ex = −∞ |x(t)|2 dt and the power content of a signal is Px = lim T →∞ + T2 1 T − T2 |x(t)|2 dt A signal is energy-type if E x < ∞ and is power-type if 0 < Px < ∞. A signal cannot be both power- and energy-type because for energy-type signals Px = 0 and for power-type signals E x = ∞. A signal can be neither energy-type nor power-type.

This is what we expect because a periodic signal consists of a sum of sinusoidal (or exponential) signals, and therefore the power is concentrated at discrete frequencies (the harmonics). 13) To find the power content of a periodic signal, we have to integrate this relation over the whole frequency spectrum. 6). If this periodic signal passes through an LTI system with frequency response H ( f ), the output will be periodic, and the power spectral density of the output can be obtained by employing the relation between the power spectral densities of the input and the output of a filter.

### Riemann surfaces by Bers L.

by James

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