EXAMPLE a()=co(2m*5)0≤t≤1,f=5 Sampling frequency: &Hz Reconstruct frequency f=8-5=3Hz
x t t t f Hz a ( ) = cos(2 5 ),0 1, = 5 f ' = 8 − 5 = 3Hz Reconstruct frequency: EXAMPLE Sampling frequency:8Hz
Ideal reconstruction system Convert from Ideal reconstruction sequence to filter xInli impulse train,(D) H, (in) Sampling period T Figure 4.10(a)mathematic model for ideal D/C x(j2)=X,(92)H(j)=Xc(Q) TQ2<Q2 Hr(八2) l019>
Figure 4.10(a) mathematic model for ideal D/C c c r r s r c T H j X j X j H j X j = = = | | | | 0 ( ) ( ) ( ) ( ) ( )
X,(92)=X,(jQ)H(Q h, (=IFT(H, (Q2))=_H, (jS)e/"dQ Te dQ 丌 sin(Q2 t) sin( t/T nt/T nt/T x(0=x0)+()=∑(-m)m/D nt/T sin( rt/T' xnS(t-nr)* xn sin[ (t-nT)/TI ideal reconstruction in nt/T ∑ 丌(t-nT)/T time domain c(x) 0.8
ideal reconstruction in time domain sinc(x) t T t T t T t h t IFT H j H j e d Te d X j X j H j c j t j t r r r r s r C C / sin( / ) / sin( ) 2 1 ( ) 2 1 ( ) { ( )} ( ) ( ) ( ) = = = = = = − − − x x c x t nT T t nT T x n t T t T x n t nT t T t T x t x t h t x n t nT n n n r s r sin( ) sin ( ) ( )/ sin[ ( )/ ] ] [ ] / sin( / ) [ ][ ( ) / sin( / ) ( ) ( ) ( ) [ [ ] ( )] = − − = − = = = − =− =− =−
EXAMPLE Figure 4.9
Figure 4.9 EXAMPLE
understand aliasing from time EXAMPLE domain interpolation
EXAMPLE understand aliasing from time - domain interpolation