Computer Vision Foundations · free preview

Convolution in Action

Delta kernels as shifts and copies, the box kernel as defocus, and probing an unknown system with an impulse to read off its kernel.

1. The impulse and its shifted friends

The impulse and its shifted friends

2. The box kernel is defocus

The box kernel is defocus

3. Probing a system with an impulse

Probing a system with an impulse

4. Rooms, claps and echoes

Rooms, claps and echoes

5. What a shifted impulse does

A filter is defined by the kernel h[n]=δ[n−3]h[n] = \delta[n-3], an impulse with value 1 at index 3 and 0 elsewhere. What is the output for an arbitrary input ℓin\ell_{\text{in}}?

6. Reading an impulse response

You clap once in an unfamiliar hall and the recording shows a strong arrival at time 0, a weaker arrival at 40 ms and a still weaker one at 80 ms. Assuming the hall is linear and translation-invariant, what have you measured?

7. Energy of a signal

A short signal has values [3,4][3, 4]. Compute its energy E=∑n∣ℓ[n]∣2E = \sum_n |\ell[n]|^2 and write the result.

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