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The amplitude response

If the real and imaginary parts of H f are given by

H f
the magnitude and phase are defined as H f 2 2 p so that
H f H f p
With this definition, H f is never negative and p is usually discontinuous, but it can be very helpful to write H f as
H f A
where A can be positive and negative, and continuous. A is called the amplitude response . illustrates the difference between H f and A .

A linear-phase phase filter is one for which the continuous phase is linear. H f A with M B We assume in the following that the impulse response h n is real-valued.

Why linear-phase?

If a discrete-time cosine signal x 1 n 1 n 1 is processed through a discrete-time filter with frequency response H f A then the output signal is given by y 1 n A 1 1 n 1 1 or y 1 n A 1 1 n 1 1 1 The LTI system has the effect of scaling the cosine signal and delaying it by 1 1 .

When does the system delay cosine signals with different frequencies by the same amount?

  • constant
  • K
  • The phase is linear.
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The function is called the phase delay . A linear phase filter therefore has constant phase delay.

Why linear-phase: example

Consider a discrete-time filter described by the difference equation

y n -0.1821 x n 0.7865 x n 1 0.6804 x n 2 x n 3 0.6804 y n 1 0.7865 y n 2 0.1821 y n 3
When 1 0.31 , then the delay is 1 1 2.45 . The delay is illustrated in :

Notice that the delay is fractional --- the discrete-time samples are not exactly reproduced in the output.The fractional delay can be interpreted in this case as a delay of the underlying continuous-time cosine signal.

Why linear-phase: example (2)

Consider the same system given on the previous slide, but let us change the frequency of the cosine signal.

When 2 0.47 , then the delay is 2 2 0.14 .

For this example, the delay depends on the frequency, because this system does not have linear phase.

Why linear-phase: more

From the previous slides, we see that a filter will delay different frequency components of a signal by the same amountif the filter has linear phase (constant phase delay).

In addition, when a narrow band signal (as in AM modulation) goes through a filter, the envelop will be delayed by the group delay or envelop delay of the filter. The amount by which the envelop is delayed isindependent of the carrier frequency only if the filter has linear phase.

Also, in applications like image processing, filters with non-linear phase can introduce artifacts that are visuallyannoying.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Intro to digital signal processing. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10203/1.4
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