Image Processing Toolbox User's Guide |

**Windowing Method**

The windowing method involves multiplying the ideal impulse response with a window function to generate a corresponding filter, which tapers the ideal impulse response. Like the frequency sampling method, the windowing method produces a filter whose frequency response approximates a desired frequency response. The windowing method, however, tends to produce better results than the frequency sampling method.

The toolbox provides two functions for window-based filter design, `fwind1`

and `fwind2`

. `fwind1`

designs a two-dimensional filter by using a two-dimensional window that it creates from one or two one-dimensional windows that you specify. `fwind2`

designs a two-dimensional filter by using a specified two-dimensional window directly.

`fwind1`

supports two different methods for making the two-dimensional windows it uses:

- Transforming a single one-dimensional window to create a two-dimensional window that is nearly circularly symmetric, by using a process similar to rotation
- Creating a rectangular, separable window from two one-dimensional windows, by computing their outer product

The example below uses `fwind1`

to create an 11-by-11 filter from the desired frequency response `Hd`

. Here, the `hamming`

function from the Signal Processing Toolbox is used to create a one-dimensional window, which `fwind1`

then extends to a two-dimensional window.

Hd = zeros(11,11); Hd(4:8,4:8) = 1; [f1,f2] = freqspace(11,'meshgrid'); mesh(f1,f2,Hd), axis([-1 1 -1 1 0 1.2]), colormap(jet(64)) h = fwind1(Hd,hamming(11)); figure, freqz2(h,[32 32]), axis([-1 1 -1 1 0 1.2])

**Desired Two-Dimensional Frequency Response (left) and Actual
Two-Dimensional Frequency Response (right)
**

Frequency Sampling Method | Creating the Desired Frequency Response Matrix |

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