DigitalVideoAndHDTVAlgorithmsAndInterfaces.pdf

125 ns, 45° at 1 MHz
125 ns, 90° at 2 MHz
Figure 16.21 Linear phase
function is forced to zero. That position needs to be far
enough from the center tap that the filter’s highfrequency
response is small enough to be negligible for
the application.
Signal processing accommodates the use of impulse
responses having negative values, and negative coefficients
are common in digital signal processing. But
image capture and image display involve sensing and
generating light, which cannot have negative power, so
negative weights cannot always be realized. If you study
the transform pairs on page 151 you will see that your
ability to tailor the frequency response of a filter is
severely limited when you cannot use negative weights.
Impulse response is generally directly evident in the
design of an FIR digital filter. Although it is possible to
implement a boxcar filter directly in the analog domain,
analog filters rarely implement temporal weighting
directly, and the implementation of an analog filter
generally bears a nonobvious relationship to its impulse
response. Analog filters are best described in terms of
Laplace transforms, not Fourier transforms. Impulse
responses of analog filters are rarely considered directly
in the design process. Despite the major conceptual
and implementation differences, analog filters and FIR
filters – and IIR filters, to be described – are all characterized
by their frequency response.
Phase response (group delay)
Until now I have described the magnitude frequency
response of filters. Phase frequency response – often
called phase response – is also important. Consider
a symmetrical FIR filter having 15 taps. No matter what
the input signal, the output will have an effective delay
of 8 sample periods, corresponding to the central
sample of the filter’s impulse response. The time delay
of an FIR filter is constant, independent of frequency.
Consider a sine wave at 1 MHz, and a second sine wave
at 1 MHz but delayed 125 ns. The situation is sketched
in Figure 16.21 in the margin. The 125 ns delay could
be expressed as a phase shift of 45° at 1 MHz. However,
if the time delay remains constant and the frequency
CHAPTER 16 FILTERING AND SAMPLING 159