C H A P T E R 2

SIGNALS AND SIGNAL SPACE

Figure 2.1 Examples of signals: (a) signal with finite energy;(b) signal with finite power.

Figure 2.2 Signal for Example 2.1.

Figure 2.3 (a) Continuous time and (b) discrete time signals.

Figure 2.4 Examples of signals: (a) analog and continuous time; (b) digital and continuous time;(c) analog and discrete time; (d) digital and discrete time.

Figure 2.5 Periodic signal of period T0.

Figure 2.6 Time shifting a signal.

Figure 2.7 Time scaling a signal.

Figure 2.8 Examples of time compression and time expansion of signals.

Figure 2.9 Time inversion (reflection) of a signal.

Figure 2.10 Example of time inversion.

Figure 2.11 (a) Unit impulse and (b) its approximation.

Figure 2.12 (a) Unit step function u(t). (b) Causal exponential e−atu(t).

Figure 2.13 Component (projection) of a vector along another vector.

Figure 2.14 Approximations of a vector in terms of another vector.

Figure 2.15 Approximation of square signal in terms of a single sinusoid.

Figure 2.16 Signals for Example 2.6.

Figure 2.17 Physical explanation of the auto-correlation function.

Figure 2.18 Representation of a vector in three-dimensional space.

Figure 2.19 (a, b) Periodic signal and (c, d) its Fourier spectra.

Figure 2.20 (a) Square pulse periodic signal and (b) its Fourier spectrum.

Figure 2.21 Bipolar square pulse periodic signal.

Figure 2.22 (a) Impulse train and (b) its Fourier spectrum.

Figure 2.23 Exponential Fourier spectra for the signal in Fig. 2.19a.

Figure 2.24 (a) Unit length complex variable with positive frequency (rotating counterclockwise)and (b) unit length complex variable with negative frequency (rotating clockwise).