DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

0
Horizontal displacement
(fraction of picture width)
Figure 18.5 Horizontal
spatial frequency domain
1
1
0
Spatial frequency domain
I explained in Image structure, on page 43, how a onedimensional
waveform in time transforms to a onedimensional
frequency spectrum. This concept can be
extended to two dimensions: The two dimensions of
space can be transformed into two-dimensional spatial
frequency. The content of an image can be expressed as
horizontal and vertical spatial frequency components.
Spatial frequency is plotted using cycles per picture
width (C/PW) as an x-coordinate, and cycles per picture
height (C/PH) as a y-coordinate. You can gain insight
into the operation of an imaging system by exploring its
spatial frequency response.
In the image at the top left of Figure 18.5 above, every
image row has identical content: 4 cycles of a sine
wave. Underneath the image, I sketch the time domain
waveform of every line. Since every line is identical, no
power is present in the vertical direction. Considered in
the spatial domain, this image contains power at
a single horizontal spatial frequency, 4 C/PW; there is
no power at any vertical spatial frequency. All of the
power of this image lies at spatial frequency [4, 0].
Figure 18.6 opposite shows an image comprising
a sinewave signal in the vertical direction. The height of
the picture contains 3 cycles. The spatial frequency
188 DIGITAL VIDEO AND HDTV ALGORITHMS AND INTERFACES
Vertical frequency, C/PH
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0
4
Horizontal frequency, C/PW