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N. T Thao and M. Vertterli
invertible mapping
z(t)
, (xk)k~Z E L2(Z) where
xk = x(kT,),
1
under the condition that fa = ~ _ 2fro. Errors between the bandlimited analog signals are
measured using the canonical norm of s and can also be evaluated in the discrete-time
space/:2(Z) using its own canonical norm, thanks to the relation:
• f~ I~(t)l ~t = ~ I~kl ~
T8 R kEZ
Unfortunately, this framework cannot be used to study quantization because the quantized
version (ck)keZ of an element (Zk)keZ of s is not necessarily an element of s (or,
is not necessarily square summable). For example, using ...