Computer Vision Foundations · free preview

Signals and Linear Systems

Signals as sampled measurements, systems as maps on signals, and the discovery that most everyday image operations are linear and therefore matrices.

1. Signals and their samples

Signals and their samples

2. Systems map signals to signals

Systems map signals to signals

3. Linearity, and the quiz that surprises people

Linearity, and the quiz that surprises people

4. A linear system is a fully connected layer

A linear system is a fully connected layer

5. Which operations are linear

Which of the following image operations is linear, meaning it satisfies both f(ℓ1+ℓ2)=f(ℓ1)+f(ℓ2)f(\ell_1+\ell_2)=f(\ell_1)+f(\ell_2) and f(aℓ)=af(ℓ)f(a\ell)=af(\ell)?

6. Reading the general linear form

A linear system on discrete signals is written ℓout[n]=∑kh[n,k] ℓin[k]\ell_{\text{out}}[n] = \sum_k h[n,k]\,\ell_{\text{in}}[k]. What does the entry h[n,k]h[n,k] alone tell you?

7. The DC value

A four-sample signal has values ℓ=[1,2,3,6]\ell = [1, 2, 3, 6]. Compute its DC value μ=1N∑n=0N−1ℓ[n]\mu = \frac{1}{N}\sum_{n=0}^{N-1}\ell[n] and write it as a decimal.

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