Interpolation means increasing the sampling rate,
or filling in in-between samples. Equivalent to sampling abandlimited analog signal
times faster. For the ideal interpolator,
We wish to accomplish this digitally. Consider
[link] and
[link] .
The DTFT of
is
Since
is periodic with a period of
,
is periodic with a period of
(see
[link] ).
By inserting zero samples between the samples of
, we obtain a signal with a scaled frequency response
that simply replicates
times over a
interval!
Obviously, the desired
can be obtained simply by lowpass filtering
to remove the replicas.
Given
In practice, a finite-length lowpass filter is designed using
any of the methods studied so far (
[link] ).
Decimation: sampling rate reduction (by an integer factor m)
Let
(
[link] )
That is, keep only every
th
sample (
[link] )
In frequency (DTFT):
Now
for
as shown in homework #1, where
is the DFT of one period of the periodic sequence.
In this case,
for
and
.
so
i.e. , we get
digital
aliasing .(
[link] )
Usually, we prefer not to have aliasing, so the downsampler
is preceded by a lowpass filter to remove all frequencycomponents above
(
[link] ).
Rate-changing by a rational fraction l/m
This is easily accomplished by interpolating by a factor of
, then decimating by a factor
of
(
[link] ).
The two lowpass filters can be combined into one LP filterwith the lower cutoff,
Obviously, the computational complexity and simplicity of
implementation will depend on
:
will be easier to implement than
!
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
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Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,