Sampling and Interpolation

Question 1

Nyquist sampling
recovers completely the function if

Answer 1

𝑢max < 1/2𝑝

Question 2

How to get rid of moiré artifacts?

Answer 2

Convolute with low pass filter in real space before binning (or after sampling)

Multiplication in Fourier space does not help too much anymore

Question 3

Random sampling artifacts can be efficiently removed using

Answer 3

randomized aliasing artifacts appear “noise-like” and “incoherent”
l Can be efficiently removed using non-linear de-noising

Question 4

Almost all …. transforms
require interpolation

Answer 4

Almost all affine transforms (rotation, translation, scaling, shear etc)
require interpolation

Question 5

Whittaker–Shannon interpolation in literature (also called Fourier zero padding)

Answer 5

sinc function
= sin(pi x) / (pi x)

Question 6

Sinc interpolation can perfectly reconstruct a function from its samples if

Answer 6

• sampled at a rate higher than Shannon-Nyquist rate
• bandlimited up to Shannon-Nyquist frequency
• àno aliasing

Question 7

Use window function to truncate sinc: Widely used: sinc kernel with ……….. window

Answer 7

Widely used: sinc kernel with Lanczos window

The Lanczos window is the central of
a stretched sinc function

Question 8

Re-gridding
Change from polar to Cartesian co-ordinates
Linear, but not

Answer 8

Linear, but not translation invariant

Question 9

Aliasing in periodic structures can cause

Answer 9

Moiré artifacts

Question 10

Band limiting a signal may lead to

Answer 10

ringing artifacts

Question 11

Typical interpolation kernels include

Answer 11

nearest neighbor
linear
bi-cubic
higher B-spline interpolation

Question 12

Zero-padding in one domain equals

Answer 12

Zero-padding in one domain equals sinc interpolation in the Fourier pair