Section 3.1 Norms and System Gains Frequently Used Signal Norms 1-norm.The 1-norm of r(t)is the integral of its absolute value: r()=Ir(e)l de 2-norm.The 2-norm of r(t)is 11/2 Ir(()d Suppose that r(t)is the current through a 10 resistor.The instantaneous power equals r(t)2 and the energy equals lr(t)2 oo-norm.The oo-norm of r(t)is the least upper bound of its absolute value: lr(t)川o:=supr(t)l 4口，+@，4定4=定0C Zhang.W.D..CRC Press.2011 Version 1.0 4/69Section 3.1 Norms and System Gains Frequently Used Signal Norms 1-norm. The 1-norm of r(t) is the integral of its absolute value: kr(t)k1 := Z ∞ −∞ |r(t)| dt 2-norm. The 2-norm of r(t) is kr(t)k2 := Z ∞ −∞ r 2 (t) dt1/2 Suppose that r(t) is the current through a 1Ω resistor. The instantaneous power equals r(t) 2 and the energy equals kr(t)k 2 2 ∞-norm. The ∞-norm of r(t) is the least upper bound of its absolute value: kr(t)k∞ := sup t |r(t)| Zhang, W.D., CRC Press, 2011 Version 1.0 4/69