Eric Dubois
Multidimensional Signal and Color Image Processing Using Lattices

Chapter 10 Analysis and Design of Multidimensional FIR Filters

MATLAB code for figures and examples

  • Example 10.1 — Fig. 10.2-10.4 Frequency response of a moving average filter with L = 2 and Gaussian filter. Result when applied to image Barbara.
    • MATLAB script: mdsp_web_design_FIRfilt_design_examp.m
    • Fig. 10.2 (a) Moving average filter, contour plot. Output preview: fig10.2a.png
    • Fig. 10.2 (b) Moving average filter, perspective plot. Output preview: fig10.2b.png
    • Fig. 10.3 (a) Gaussian filter, contour plot. Output preview: fig10.3a.png
    • Fig. 10.3 (b) Gaussian filter, perspective plot. Output preview: fig10.3b.png
    • Fig. 10.4 (a) Barbara image filtered with moving average filter. Output preview: fig10.4a.jpg
    • Fig. 10.4 (b) Barbara image filtered with Gaussian filter. Output preview: fig10.4b.jpg
  • Example 10.2 — Fig. 10.5-10.7 Frequency response of Gaussian band-stop filter with center frequency (150, -86) c/ph. Applied to image Barbara.
  • Example 10.3 — Fig. 10.8-10.12 Filter a halftone image with a multi-band-stop filter. Input image, output image and spectra; points of the halftone interference pattern within one unit cell of the reciprocal lattice
  • Fig. 10.13 Radial profile of three circularly symmetric ideal responses with 3dB radial frequency cutoff of 0.125 c/px.
  • Fig. 10.14 Boundaries of polygonal pass and stop bands of an example ideal lowpass frequency response; perspective view of the ideal frequency response with planar transition band.
  • Fig. 10.15, 10.16 Frequency response of approximation to ideal circularly symmetric lowpass filter with -3dB point at radial frequency 0.125 c/px using the window method. Set L and W as indicated in the figure caption; result of filtering the Barbara image with this filter.
    • MATLAB script: mdsp_web_design_circular_window_FIR.m
    • Fig. 10.15 (a) Size 13 x 13 (W = 0:171) contour plot. Output preview: fig10.15a.png
    • Fig. 10.15 (b) Size 13 x 13 (W = 0:171) perspective plot. Output preview: fig10.15b.png
    • Fig. 10.15 (c) Size 21 x 21 (W = 0:1498) contour plot. Output preview: fig10.15c.png
    • Fig. 10.15 (d) Size 21 x 21 (W = 0:1498) perspective plot. Output preview: fig10.15d.png
    • Fig. 10.15 (e) Size 41 x 41 (W = 0:1366) contour plot. Output preview: fig10.15e.png
    • Fig. 10.15 (f) Size 41 x 41 (W = 0:1366) perspective plot. Output preview: fig10.15f.png
    • Fig. 10.16 (a) Barbara image filtered with 13 x 13 filter. Output preview: fig10.16a.jpg
    • Fig. 10.16 (b) Barbara image filtered with 41 x 41 filter. Output preview: fig10.16b.jpg
  • Example 10.4 — Fig. 10.17 Least pth design for low-pass filter with polygonal specifications shown in Fig. 10.14.
  • Example 10.5 — Fig. 10.18, 10.19 Low-pass filter for halftone suppression; filtered image with and without equality constraints on the frequency response. Must uncomment filter_design_zp_con (line 29) or filter_design_zp_unc (line 30) depending on which is desired.