DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

Figure 18.6 Vertical spatial
frequency domain
When spatial frequency is determined
analytically using the twodimensional
Fourier transform, the
result is plotted in the manner of
Figure 18.7, where low vertical
frequencies – that is, low y values –
are at the bottom. When spatial
frequency is computed numerically
using discrete transforms, such as
the 2-D discrete Fourier transform
(DFT), the fast Fourier transform
(FFT), or the discrete cosine transform
(DCT), the result is usually
presented in a matrix, where low
vertical frequencies are at the top.
1
0
0
1
Vertical displacement
(fraction of picture height)
graph, to the right, shows that all of the power of the
image is contained at coordinates [0, 3] of spatial
frequency. In an image where each image row takes
a constant value, all of the power is located on the
y-axis of spatial frequency.
If an image comprises rows with identical content, all of
the power will be concentrated on the horizontal axis
of spatial frequency. If the content of successive scans
lines varies slightly, the power will spread to nonzero
vertical frequencies. An image of diagonal bars would
occupy a single point in spatial frequency, displaced
from the x-axis and displaced from the y-axis.
The spatial frequency that corresponds to half the
vertical sampling rate depends on the number of
picture lines. A 480i system has approximately 480
picture lines: 480 samples occupy the height of the
picture, and the Nyquist frequency for vertical sampling
is 240 C/PH. No vertical frequency in excess of this can
be represented without aliasing.
In most images, successive rows and columns of
samples (of R’, G’, B’, or of luma) are very similar; low
frequencies predominate, and image power tends to
cluster toward spatial frequency coordinates [0, 0].
Figure 18.7 overleaf sketches the spatial frequency
spectrum of luma in a 480i system. If the unmodulated
NTSC color subcarrier were an image data signal, it
would take the indicated location. In composite NTSC,
chroma is modulated onto the subcarrier; the resulting
modulated chroma can be thought of as occupying a
CHAPTER 18 IMAGE DIGITIZATION AND RECONSTRUCTION 189
Vertical frequency, C/PH
3
0
0
Horizontal frequency, C/PW