A voltage signal has root-mean-square value over

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Linear algebra and vector spaces · Linear algebra and vector spaces

Conditions of Validity, Ch Inner products, orthogonality and the adjoint

Problem

A voltage signal f(t)f(t) has root-mean-square value 3.0 V3.0\,\text{V} over 0≤t≤2 s0 \le t \le 2\,\text{s}, and a second signal g(t)g(t) has root-mean-square value 1.5 V1.5\,\text{V} over the same interval. Both are real-valued. Using the inner product ⟨f,g⟩=∫02f(t)g(t) dt\langle f,g\rangle = \int_0^2 f(t)g(t)\,\mathrm{d}t, estimate the largest magnitude that ⟨f,g⟩\langle f,g\rangle can possibly take, and decide whether a claimed measurement of ⟨f,g⟩=10 V2 s\langle f,g\rangle = 10\,\text{V}^2\,\text{s} could be correct.

Browse the problem library