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Table 2 Expressions of the uncertainty principles for the M th-order LPFT

From: Systematic analysis of uncertainty principles of the local polynomial Fourier transform

Type of uncertainty principle

Uncertainty product

1. Global uncertainty principle

T LPP 2 B LPP 2 ≥1

2. Local duration-conditional standarddeviation

σ ω | t 2 T t 2 ≥ 1 4

3. Local bandwidth-conditional standarddeviation

σ t | ω 2 B ω 2 ≥ 1 4

4. Conditional standard deviations in timeand frequency

σ t | ω 2 σ ω | t 2 > 1 4