2. Theoretical Basis

• 2.1. Upsampling
  • 2.1.1. "Fourier Zero Padding"
    • 2.1.1.1. Sinus cardinal interpolation
    • 2.1.1.2. Simple example
    • 2.1.1.3. Summary
  • 2.1.2. Tile processing of the large image
    • 2.1.2.1. The implicit edges discontinuities and their associated artifacts
    • 2.1.2.2. The possible solutions
      • 2.1.2.2.1. Margin the original data
      • 2.1.2.2.2. Mirroring the original data
      • 2.1.2.2.3. The periodic + smooth decomposition
    • 2.1.2.3. Conclusion : Sirius uses the p+s decomposition
  • 2.1.3. The discontinuous signals
    • 2.1.3.1. Illustrating the issue
    • 2.1.3.2. The windowing solution
  • 2.1.4. User kernel interpolator
    • 2.1.4.1. One can give Sirius his own low-pass filter
    • 2.1.4.2. The Sirius Filter must lie on the spatial domain
    • 2.1.4.3. The Sirius Filter must be sampled like the upsampled (targeted) signal
    • 2.1.4.4. The Sirius Filter is odd and a GDAL supported image format
    • 2.1.4.5. Sirius auto-shifts the Filter before its FT is computed
    • 2.1.4.6. Sirius can normalize the Filter
    • 2.1.4.7. When Sirius uses a Filter to upsample, the spectrum is periodized instead of zero padded
  • 2.1.5. Convolution near the data edges
    • 2.1.5.1. The real edges
    • 2.1.5.2. The virtual edges
    • 2.1.5.3. What Sirius proposes
  • 2.1.6. Float upsampling factor
• 2.2. Downsampling
  • 2.2.1. Anti-Aliasing process
  • 2.2.2. Non integer downsampling factor
• 2.3. References
• 2.4. Associated Python Code
  • 2.4.1. :mod:`conf`
    • 2.4.1.1. Module Contents
      • setupapp
  • 2.4.2. :mod:`simple_signal_proc`
    • 2.4.2.1. Module Contents
      • create_1D_rectn
      • sincx, dtype = None
      • create_1D_sincn, step = 1
      • create_1D_lanczosn, a = 3, step = 1
      • create_1D_miren
      • create_1D_triangle_signaln = 4, step = 1
      • create_1D_cosinen = 100, w = 1
      • create_1D_rampn = 100, step = 1
      • show_1Dsignal, title = "Figure"
      • mirrors, margin_factor = 2
      • zero_pads, margin_factor = 2, dtype = None
      • periodizes, margin_factor = 2, dtype = None
      • fft1D_zero_padtf, zoom_factor = 2
      • fft1D_periodizationtf, zoom_factor = 2
      • zoom_freq_zpdsignal, zoom_factor = 2
      • zoom_freq_img_periodizationsignal, zoom_factor = 2, user_kernel = None
      • interp1dsignal, zoom_factor
      • zoom_freq_img_perAndSmoothsignal, zoom_factor