DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

An electrical engineer may call
this simply frequency response.
The qualifier magnitude distinguishes
it from other functions
of frequency such as phase
frequency response.
Resolution 7
To avoid visible pixel structure in image display, some
overlap is necessary in the distributions of light
produced by neighboring display elements, as
I explained in Image structure, on page 43. Also, to
avoid spatial aliasing in image capture, some overlap is
necessary in the distribution of sensitivity across neighboring
sensor elements. Such overlap reduces sharpness.
In this chapter, I will explain resolution, which is
closely related to sharpness. Before introducing resolution,
I must introduce the concepts of magnitude
frequency response and bandwidth.
Magnitude frequency response and bandwidth
Rather than analyzing a spot of certain dimensions, we
analyze a group of closely spaced identical elements,
characterizing the spacing between the elements. This
allows mathematical analysis using transforms, particularly
the Fourier transform and the z-transform.
The top graph in Figure 7.1 overleaf shows a onedimensional
sine wave test signal “sweeping” from zero
frequency up to a high frequency. (This could be a onedimensional
function of time such as an audio waveform,
or the waveform of luma from one scan line of an
image.) A typical optical or electronic imaging system
involves temporal or spatial dispersion, which causes
the response of the system to diminish at high
frequency, as shown in the middle graph. The envelope
of that waveform – the system’s magnitude frequency
response – is shown at the bottom.
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