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FIR Filter Designs for Sampling Rate Conversion 499
FIR Interpolator
x(n)
↑I
v(m)
FIR LPF
H(ω)
y(m)
Rate: F x IF x IF x
FIGURE 9.18
An FIR integer interpolator
only one of D outputs is required [see the discussion following (9.44) on
page 496]. We will first discuss integer interpolators, followed by integer
decimators and then the rational resamplers. The main emphasis will be
on the specifications of these FIR lowpass filters, since the design problem
has already been considered in Chapter 7.
9.5.1 FIR INTEGER INTERPOLATION
Replacing the ideal filter of the system given on page 489 with an FIR
filter, we obtain the system shown in Figure 9.18. The relevant equation
that relates the Fourier transforms V (ω) and X(ω) is(9.28), repeated
here for convenience.
V (ω) =X(ωI) (9.48)
Considering the frequency compression by I and the required amplitude
scale factor of I, the ideal lowpass filter was determined in (9.30) and
(9.33) to be
{
I, |ω|