In general, for
Strictly speaking, we say
is linear phase if
Why is this important? A linear phase response gives the
same time delay for
ALL frequencies ! (Remember the shift theorem.) This is
very desirable in many applications, particularly when theappearance of the time-domain waveform is of interest, such as
in an oscilloscope. (see
)
Restrictions on h(n) to get linear phase
For linear phase, we require the right side of
to be
. For
, we thus require
Thus
is a
necessary condition for
the right side of
to be real valued, for
.
For
, or
, we require
Usually, one is interested in filters with
real-valued coefficients, or see
and
.
(Symmetric Filters).
.
(Anti-Symmetric Filters).
. Filter design techniques are usually slightly different for
each of these four different filter types. We will study themost common case, symmetric-odd length, in detail, and often
leave the others for homework or tests or for when oneencounters them in practice. Even-symmetric filters are often
used; the anti-symmetric filters are rarely used in practice,except for special classes of filters, like differentiators or
Hilbert transformers, in which the desired response isanti-symmetric.
So far, we have satisfied the condition that
where
is
real-valued . However, we have
not assured that
is
non-negative . In general,
this makes the design techniques much more difficult, so mostFIR filter design methods actually design filters with
Generalized Linear Phase :
, where
is
real-valued , but possible negative.
is called the
amplitude of the frequency
response .
usually goes negative only in the stopband, and the
stopband phase response is generally unimportant.
where
Lowpass filter
Desired |h()|
DesiredH()
The slope of each line is
.
Actual |h()|
goes negative.
ActualH()
phase jumps due to periodicity of phase.
phase jumps due to sign change in
. Time-delay introduces generalized linear phase.
For odd-length FIR filters, a linear-phase design
procedure is equivalent to a zero-phase design procedurefollowed by an
-sample delay of the
impulse response . For
even-length filters, the delay is non-integer, and thelinear phase must be incorporated directly in the desired
response!
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
Got questions? Join the online conversation and get instant answers!
