Software Radio Software Defined radio and Cognitive radio

PDA Architecture Domain
• In words, H states: “The analog signal in the time interval surrounding
the continuous point s(t) ∈ W corresponds to the discrete point x(i) ∈ S
at the sampling instant for N contiguous points.”
• The corresponding map G from S to W is not a digital to analog
converter.
• The map G answers the question “How do subsets of x(i) map to
subsets of s(t)?” This is answered in part by the Nyquist criterion.
• If a signal s(t) is sampled at least as fast as specified by the Nyquist
criterion, then the analog signal s(t) may be reconstructed uniquely from
the digital samples, x(i), e.g. using Fourier series.
• In addition, a received signal corresponds to some transmitted signal
modified by propagation, so G(x(i)) = Propagation(Nyquist(x(i))).
• G also is not a function. One need not be able to perform G on actual
signals. G is the set-theoretic map that specifies which members of S
correspond to which members of W.
• Thus, G and H are ontological statements about the structure of the
point sets s(t) and x(i).