Sampling and Pcriodic Signals interpolation filter Hicn;l Figiirc 11.15: Spcctrniri of the sampled complex signal 11.40 'I'herr is no conjugate syrriinetrp licrt.. For the spparentlv s
Trang 1276 1 1 Sampling and Pcriodic Signals
interpolation filter H(icn;l)
Figiirc 11.15: Spcctrniri of the sampled complex signal
(11.40)
'I'herr is no conjugate syrriinetrp licrt eithcr, so thc corresponding impiilsc response
is tomplcs:
(11.41) Figure 11.16 h 1 i o ~ l s the real and iniagiiiarv parts ol / I ( , ) for "'cl = 4Aw
For the spparentlv simple case of a reid ban gn,il correct choice of- sample fiecluency is not a s simplr as for the coiiiplex band-pass s i p a l T l i ~ sp~('1 iimi
of tt real bad-pass signal is ihowii in Figure 11 17 The coiiditions ol conjugate
~j-mnwtry are hilfillecl in this case
Crilicnl sampling rcquirei a sample rate of
1 h w
f -.=- , I.e., wa = 2Aw ,
" I T x
In contrast to complex bancl-pass signals, in this C R S P , tr i t icd sarnplirig is oiily possibltx if WO mid A d have i i particular rrlattionship with each other Continuation
u~ in F'igure 11.17 can take exactly an even ririiribcr of half-bands of width AdL1
I iirii witlront gaps requirvs that,