Fal!2001 16.3121-4 So how can we use this result? Fix the size wcl2= 1 of the input, and see how large we can make the output Since we are working at a single frequency, we just analyze the relation ze=Guc,Gu≡G(s=ju) Define the maximum and minimum amplifications as 0≡maNx.‖zcll g≡min.‖ll Then we have that (let q=min(p, m)) qp≥mtal 0p<m“wide Can use O and g to determine the possible amplification and atten uation of the input signals Since G(s) changes with frequency, so will o and gFall 2001 16.31 21—4 • So how can we use this result? — Fix the size kwck2 = 1 of the input, and see how large we can make the output. — Since we are working at a single frequency, we just analyze the relation zc = Gwwc, Gw ≡ G(s = jω) • Define the maximum and minimum amplifications as: σ ≡ max kzck2 kwck2=1 σ ≡ min kzck2 kwck2=1 • Then we have that (let q = min(p, m)) σ = ½ σ1 σq p ≥ m “tall” σ = 0 p < m “wide” • Can use σ and σ to determine the possible amplification and atten￾uation of the input signals. • Since G(s) changes with frequency, so will σ and σ