CS 450 Sampling and Reconstruction 1
Sampling
Continuous
f(t)
t
Discrete
f(t)
t
CS 450 Sampling and Reconstruction 2
Sampling
Sampling a continuous function fto produce a discrete function ˆ
f
ˆ
f[n]=f(n∆t)
is just multiplying it by a comb:
ˆ
f=fcombh
where h=∆t
CS 450 Sampling and Reconstruction 3
Sampling In The Spatial Domain - Graphical Example
Continuous
f(t)
t
Sampling Comb
t
f(t)
Discrete
f(t)
t
CS 450 Sampling and Reconstruction 4
Sampling In The Frequency Domain
Sampling (multiplication by a combh)
ˆ
f=fcombh
is convolution in the frequency domain with the transform of a comb:
ˆ
F=F∗comb1/h
Convolution of a function and a comb causes a copy of the function to
“stick” to each tooth of the comb, and all of them add together.
CS 450 Sampling and Reconstruction 5
Sampling In The Frequency Domain - Graphical Example
Spectrum
s
F(s)
Comb’s Spectrum
s
F(s)
Spectrum of the Discrete Signal
s
F(s)
