Question

PROBLEM 1.1 Consider the two pyramid-like signals below (courtesy Prof. Magnus Egerstedt). (a) The pyramid-like signal on the left can be written as A[u(t-1 ) _ u(t-2)] + B(u(t-2)-u(t-3)] + C[u(t-3)-u(t-4)] r(t) _ Find the values of the constants A, B, C, D, and E (b) The pyramid-like signal on the left can be written as r(t) = Flu(t-1) _ u(1-6)] + Glu(t-2)-u(t-5)] + Hla(t-3)-u(t-4)]. Find the values of the constants F, G, and H (c) The pyramid-like signal on the left can be written as Find the values of the constants J, K, L, M, N, and P (d) The pyramid-like signal on the right can be written as The R term and the S term can be thought of as ramp functions, one starting at1 and another starting at -4. Note that we cannot just chose R and S to have the same value with different signs; in addition to producing the downward ramp, the " term must also be able to counteract the "S" ter Find the values of the constants Q, R, and S (e) The pyramid-like signal on the right can be written as r(t) = [u(t-a)-u(t-β))(t-p) + [a(t-1)-u(t-K)(e-t). Find the values of, β, p, γ, K, and ξ.

Answer 1

LLI 4 ブ3C4 344) -t スH) (1+1+リ-3 4

a CA 14) 1 13 S 3 a 56 4- 412