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Index - Nomenclature Global Notation There are several...

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957 Nomenclature Global Notation There are several variables that occur with great frequency throughout the text. These variables are: t continuous time units are seconds (sec) ϖ (continuous) frequency units are radians/second (rad/sec) (discrete) frequency units are radians (rad) f (continuous) frequency units are hertz (Hz) If the units on these variables are not shown, they are the units shown above. Selected Notation The following list contains selected notation used throughout the text. This list is organized chapter by chapter with the notation shown when it first appears. Continuous-Time Signals and Systems Chapter 2 δ ( t ) unit impulse function Definition 2.2.1 u s ( t ) unit step function Definition 2.2.3 r p ( t ) unit ramp function Definition 2.2.4 Π ( t ) unit pulse function Definition 2.2.5 Λ ( t ) unit triangle function Definition 2.2.6 ln( ) t natural logarithm Definition 2.2.8 log( t ) logarithm base 10 Definition 2.2.9 Sa( t ) Sa function Definition 2.2.11 sinc( t ) sinc function Definition 2.2.11 n discrete-time function Definition 2.3.1 κ fixed integer Definition 2.3.1 δ ( n ) discrete unit impulse function Definition 2.3.3 u s ( n ) unit step function Definition 2.3.5 Sa( n ) discrete Sa function Definition 2.3.7 sinc( n ) discrete sinc function Definition 2.3.7 Π κ ( n ) unit pulse function Definition 2.3.8
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958 Nomenclature Chapter 3 s complex number Definition 3.1.1 σ real part of a complex number Definition 3.1.2 j ϖ imaginary part of a complex number Definition 3.1.2 ρ magnitude of a complex number Definition 3.1.7 θ phase of a complex number Definition 3.1.7 s complex conjugate Definition 3.1.12 s -plane copy of the set of complex numbers Definition 3.1.13 RHP, LHP right-and left-half plane Definition 3.1.14 n order of a rational function Definition 3.2.5 ϖ n natural frequency (3.2.8), Definition 6.4.1 ζ damping ratio (3.2.10), Definition 6.4.1 Chapter 5 and 6 x ( t ) a signal, input signal to a system Definition 5.1.1 H [ ] abstract notation for a system (6.1.1) y ( t ) a signal, output signal of a system (6.1.1) h ( t ) impulse response function Definition 6.2.1 Chapter 7 T 0 period of a periodic signal Definition 7.1.1 dt T 0 integration over any interval of length T 0 (7.3.2) F {} Fourier transform of x ( t ) Definition 7.4.1 Chapter 8 E x energy of a signal x ( t ) Definition 8.2.1 P x power in the signal x ( t ) Definition 8.2.2 D x energy spectral density of x ( t ) Definition 8.3.2 S x power spectral density of x ( t ) Definition 8.4.2 BL bandlimit of a signal Definition 8.3.4 B bandwidth of a signal Definition 8.3.5 Chapter 9 L {} Laplace transform of x ( t ) Definition 9.1.1 s Laplace transform variable Definition 9.1.1 Chapter 10 H ( s ) Laplace transfer function of a system Definition 10.1.3 a ( s ) denominator of H ( s ) (10.1.18) b ( s ) numerator of H ( s ) (10.1.18)
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Nomenclature 959 n order of the transfer function Definition 10.1.5 A, B, C, D state space representation Definition 10.5.8 Chapter 12 h h 1 2 convolution of two systems (12.1.25) H ( ϖ ) Fourier transfer function Definition 12.4.1 Chapter 14 dB decibel Definition 14.3.5 β bandwidth of a system Definition 14.5.3 Discrete-Time Signals and Systems
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