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Since samples of the frequency response of an FIR filter can be calculated by taking the DFT of the impulse response h ( n ) , one could propose a filter design method consisting of taking the inverse DFT of samples of adesired frequency response. This can indeed be done and is called frequency sampling design . The resulting filter has a frequency response that exactly interpolates the given samples, but there is no explicit controlof the behavior between the samples [link] , [link] .

Three methods for frequency sampling design are:

  1. Take the inverse DFT (perhaps using the FFT) of equally spaced samples of thedesired frequency response. Care must be taken to use the correct phase response to obtain a real valued causal h ( n ) with reasonable behavior between sample response. This method works for general nonlinear phasedesign as well as for linear phase.
  2. Derive formulas for the inverse DFT which take the symmetries, phase, and causality into account. It is interesting to notice these analysis and designformulas turn out to be the discrete cosine and sine transforms and their inverses.
  3. Solve the set of simultaneous linear equations that result from calculating the sampledfrequency response from the impulse response. This method allows unevenly spaced samples of the desired frequency response but the resulting equationsmay be ill conditioned.

Frequency sampling filter design by inverse dft

The most direct frequency sampling design method is to simply take the inverse DFT of equally spaced samples of the desired complex frequencyresponse H d ( ω k ) . This is done by

h ( n ) = 1 N k = 0 N - 1 H d ( 2 π N k ) e j 2 π n k / N

where care must be taken to insure that the real and imaginary parts (or magnitude and phase) of H d ( ω k ) satisfy the symmetry conditions that give a real, causal h ( n ) . This method will allow a general complex H ( ω ) as well as a linear phase. In most cases, it is easier to specify proper and consistentsamples if it is the magnitude and phase that are set rather than the real and imaginary parts. For example, it is important that the desiredphase be consistent with the specified length being even or odd as is given in Equation 28 from FIR Digital Filters and Equation 24 from FIR Digital Filters .

Since the frequency sampling design method will always produce a filter with a frequency response that interpolates the specified samples, theresults of inappropriate phase specifications will show up as undesired behavior between the samples.

Frequency sampling filter design by formulas

When equally spaced samples of the desired frequency response are used, it is possible to derive formulas for the inverse DFT and, therefore,for the filter coefficients. This is because of the orthogonal basis function of the DFT. These formulas can incorporate the various constraints of a real h ( n ) and/or linear phase and eliminate the problems of inconsistency in specifying H ( ω k ) .

To develop explicit formulas for frequency-sampling design of linear-phase FIR filters, a direct use of the inverse DFT is most straightforward. When H ( ω ) has linear phase, [link] may be simplified using the formulas for the four types of linear-phase FIR filters.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Digital signal processing and digital filter design (draft). OpenStax CNX. Nov 17, 2012 Download for free at http://cnx.org/content/col10598/1.6
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