[Exercises]
[Workspace]
Purpose:
The purpose of this lab is to demonstrate the separability of
the DFT.
Activities:
-
Create a small white box 4 x 16 centered in a 128 square black
background using the operators Constant and Pad. Display it.
-
Glyphs:Input/Output:Generate Data:Constant
-
Constant parameters:
Width: 4,
Height: 16,
Real Constant Level: 1
-
Glyphs:Data Manip:Size & Region Operators:Pad
-
Pad parameters:
Padded Width : 128,
Padded Height: 128,
Width Offset : 62,
Height Offset: 56
-
Glyphs:Visualization:Non-Interactive Display:Display Image
-
First take the DFT of the lines of the image, using the FFT
operator set up to operate only in the width dimension. Display it.
-
Glyphs:Arithmetic:Linear Transforms:FFT
-
FFT Parameters:
Direction : Forward,
Shifting : Centered (DC at N/2),
Scaling : Unity Scaling,
Transform Dimensions: Width
-
Glyphs:Visualization:Non-Interactive Display:Display Image
-
Take the DFT of the columns of the previous DFT, using the FFT
operator set up to operate only in the height dimension. Display it.
-
Glyphs:Arithmetic:Linear Transforms:FFT
-
FFT Parameters:
Direction : Forward,
Shifting : Centered (DC at N/2),
Scaling : Unity Scaling,
Transform Dimensions: Height
-
Glyphs:Visualization:Non-Interactive Display:Display Image
-
Compute a 2D DFT on the original image, this time with both the
width and height dimensions on the FFT operator selected.
-
Glyphs:Arithmetic:Linear Transforms:FFT
-
FFT Parameters:
Direction : Forward,
Shifting : Centered (DC at N/2),
Scaling : Unity Scaling,
Transform Dimensions: Width and Height
-
Glyphs:Visualization:Non-Interactive Display:Display Image
-
Compare the results from the two-step DFT, performed in Steps B and
C, with the result from Step D. Use operator Compare Objects to
compare the data.
-
Glyphs:Data Manip:Analysis & Information:Compare Objects
-
Open the Compare Objects pane and unselect the "Run Silently"
option. When the face appears under the Compare Objects glyph, click
on it to open the information window.
Exercises
-
Perform the inverse DFT using the principle of the separable
transform.
Khoros Workspace
Execute the visual program c5s2dft-2d-from-1d.wk
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