The zeros of the transfer function
$H(z)$ of a linear-phase filter lie in specific configurations.
We can write the symmetry condition
$$h(n)=h(N-1-n)$$ in the
$Z$ domain. Taking the
$Z$ -transform of both sides gives
$H(z)=z^{-(N-1)}H(\frac{1}{z})$
Recall that we are assuming that
$h(n)$ is real-valued. If
${z}_{0}$ is a zero of
$H(z)$ ,
$$H({z}_{0})=0$$ then
$$H(\overline{{z}_{0}})=0$$ (Because the roots of a polynomial with real coefficients
exist in complex-conjugate pairs.)
Using the symmetry condition,
, it follows that
$$H({z}_{0})=z^{-(N-1)}H(\frac{1}{{z}_{0}})=0$$ and
$$H(\overline{{z}_{0}})=z^{-(N-1)}H(\frac{1}{\overline{{z}_{0}}})=0$$ or
$$H(\frac{1}{{z}_{0}})=H(\frac{1}{\overline{{z}_{0}}})=0$$
If
${z}_{0}$ is a zero of a (real-valued) linear-phase filter, then so
are
$\overline{{z}_{0}}$ ,
$\frac{1}{{z}_{0}}$ , and
$\frac{1}{\overline{{z}_{0}}}$ .
Zeros locations
It follows that
generic zeros of a linear-phase filter exist in sets of 4.
zeros on the unit circle (
${z}_{0}=e^{i{}_{0}}$ ) exist in sets of 2. (
${z}_{0}\neq (1)$ )
zeros on the real line (
${z}_{0}=a$ ) exist in sets of 2. (
${z}_{0}\neq (1)$ )
zeros at 1 and -1 do not imply the existence of zeros at
other specific points.
Zero locations: automatic zeros
The frequency response
${H}^{f}()$ of a Type II FIR filter always has a zero at
$=\pi $ :
$$h(n)$$
In this morden time nanotechnology used in many field .
1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc
2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc
3- Atomobile -MEMS, Coating on car etc.
and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change .
maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.