>>11356379>what even is this?signal processing
what does linearity mean?
given a function, two (vector) variables u and v , and scalars a and b, T is linear if
T(au + bv) = aT(u) + bT(v)
apply this definition to the different cases
y(x(t)) = 3x(t) - 5x(t-tau)
y(au(t) - bv(t)) = 3(au(t) - bv(t)) - 5(au(t-tau) + bv(t- tau))
= a(3u(t) - 5u(t-tau)) + b(3v(t) - 5v(t-tau))
= ay(u) + by(v)
which shows the last option is linear
from inspection, you should be able to pick out the non-linear case pretty fast
