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Sampling Rate Conversion by a Rational Factor I/D 495
x (n)
−3
−2 −1 0
1 2 3
n
v(k)
I = 3
−9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9
k
w(k)
I = 3
−9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9
k
y(m)
−4 −3 −2 −1 0 1 2 3 4
m
D = 2
FIGURE 9.16 Examples of signals x(n), v(k), w(k), and y(m) in the sampling
rate converter of Figure 9.15 for I =3and D =2
Consequently, (9.41) can be expressed as
y(m) =
∞∑
n=−∞
(⌊ ⌋ ) mD
h[nI +((mD)) I ] x − n
I
(9.42)
These operations are shown in Figure 9.16 for I =3and D =2.
It is apparent from (9.41) and Figure 9.16 that the output y(m) is
obtained by passing the input sequence x(n) through a time-variant filter
with impulse response
g(n, m) =h[nI +((mD)) I ] −∞