Answer Happy

(Difficulty: ★) Consider 2D filters with the following impulse responses: f₁ 4 f3 = 1 || 19 0000 0 0 0 1 0 0 0 1 1 1 0 0 0 1 00 00000 2468 00000 0 1 1 1 0 0 1 1 10 0 1 1 1 0 0 000 0 f4 1 13 00 1 00 300 00 00 5 00 003 0 0 00100 00000 1 0 1 0 1 1 0 1 010 1 0 1 0 1 000 0 Using the separability property where appropriate, write the minimum total number of arithmetic operations (number of additions and multiplications summed together) per sample needed to filter a 2D image with each of the given filters. Assume that the size of the filtered 2D image is N × N, where N is very large. Write the minimum number of arithmetic operations separated by a space, from the one corresponding to the filter f₁ to the one corresponding to f4. For example, if f₁ required 1 addition and 1 multiplication per sample, ƒ2 2 additions and 2 multiplications per sample, f3 3 additions and 3 multiplications per sample, and f4 4 additions and 4 multiplications per sample, the correct answer would be: