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Discrete Fourier Transform

Source Code: /src/families/_1d/tests/dft/

The discrete Fourier transform transforms a sampling sequence into frequency space.

The test generates 128 samples and places them as black dots in a 1024x1 white image, and does a DFT of that image.

For randomized sampling types, it does this test several times and reports the minimum, the maximum, and the average. Deterministic sampling sequences just do a single run.

There is no difference in this test for progressive vs non progressive sequences since it only ever generates a single 128 length sequence per sequence type.

No windowing function is used, but in some cases (non torroidal sampling!), a windowing function may make sense.

Test Results

tests done:

• DFT

DFT

Blue Noise Sequences

BestCandidate (Progressive, Randomized)

BestCandidate5 (Progressive, Randomized)

BestCandidate10 (Progressive, Randomized)

Irrational Number Sampling

GoldenRatioZero (Progressive, Deterministic)

GoldenRatio (Progressive, Deterministic)

Pi (Progressive, Deterministic)

Sqrt2 (Progressive, Deterministic)

Low Discrepancy Sequences

Sobol (Progressive, Deterministic)

VanDerCorput2 (Progressive, Deterministic)

VanDerCorput3 (Progressive, Deterministic)

VanDerCorput5 (Progressive, Deterministic)

Regular Sampling

Regular (Not Progressive, Deterministic)

RegularCentered (Not Progressive, Deterministic)

RegularCenteredOffset (Not Progressive, Deterministic)

RegularJittered (Not Progressive, Randomized)

Uniform Random Number Sampling

UniformRandom (Progressive, Randomized)