Lecture 25
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sinusoidal
XD(w ) = cos (won)
N- =÷e- +g-
e-icw-w.in
1- e-JCW- wo)N I e-Jcwtwo)N
+£- 1-e-i(w-wo) I-e-JCWtwo)
→ (w – Wo)N/z eéicw- Wo) 42
ejcw- Wo)N1z
– ICW – Wo) Nlz
ICW Wo) 112
e-Jcwtwo)N/z ejcw-w.IM/z-e-J(w-wo)N1z–ze-#-wzeJ(w-wo)Yz-e-jC)w4-z
,géj(w – Wo)”¥SinÑ”””-
sinkw-w.IN/z] centered
e-icwtwo )^¥
Sin /(wtwo) 42]
Periodic since
Éto / Xdcw) /
[(w – no)kz] /
“/ sin [(wtwo) 2]
this approaches two impulses .
to o u r problem of spectral analysis :
n o t -14¥
If✗(n)isa sum ofseveralsinusoids, have
and can estimate M, Ii, andAias:
M = number of peaks on
( location of ith peak)/
If have two Ii
distinguish
peaks , we might
that the main lobes not rerlap :
h i -1 – 2¥ >
@, – d.)T > 4¥
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