Frequency

Question 1

Basis for vector space of dimension n

Answer 1

N vectors are independent

N vectors span the vector space

Question 2

Orthonormal basis vectors

Answer 2

All bias vectors are if length 1
All pairs of basis vectors are orthogonal
Expansion is only down by projection

Question 3

If a neighborhood N has large dot product with a basis vector (image), then

Answer 3

N is similar to that basis vector image

Question 4

Feel-Chen basis

Answer 4

Vectors to represent

Gradient, ripple, line, Laplacian, and constant features

Question 5

Fourier series

Answer 5

Any univariate function can be rewritten as a weighted sum of wines and cosines of different frequencies

Question 6

Discrete Fourier transform

Answer 6

NxN spatial samples to F(u,v) array of coefficients for frequency representation

Question 7

Inverse DFT

Answer 7

Frequency representation to spatial samples

Question 8

Why do we use Fourier basis

Answer 8

Removes high frequency noise
Extract texture features
Image compression