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Digital transformation of the sampling rate of signals, or signal processing with different sampling rates in the system.


  1. CD to DAT format change, for example.
  2. oversampling converters; which reduce performance requirements onanti-aliasing or reconstruction filters
  3. bandwidth of individual channels is much less than theoverall bandwidth
  4. Eyes and ears are not as sensitive to errors in higher frequencybands, so many coding schemes split signals into different frequency bands and quantize higher-frequency bands withmuch less precision.

Outline of multirate dsp material

  1. General Rate-changing System
  2. Integer-factor Interpolation and Decimation and Rational-factor Rate Changing
  3. Efficient Multirate Filter Structures
  4. Optimal Filter Design for Multirate Systems
  5. Multi-stage Multirate Systems
  6. Oversampling D/As
  7. Perfect-Reconstruction Filter Banks and Quadrature Mirror Filters

General rate-changing procedure

This procedure is motivated by an analog-based method: one conceptually simple method to change the sampling rate is tosimply convert a digital signal to an analog signal and resample it! ( [link] )

H aa Ω 1 Ω T 1 0 h aa t T 1 t T 1 t Recall the ideal D/A:
x a t n x 0 n t n T 0 T 0 t n T 0 T 0
The problems with this scheme are:
  1. A/D, D/A,filters cost money
  2. imperfections in these devices introduce errors

Digital implementation of rate-changing according to this formula has three problems:

  1. Infinite sum: The solution is to truncate. Consider sinc t 0 for t t 1 , t t 2 : Then m T 1 n T 0 t 1 and m T 1 n T 0 t 2 which implies N 1 m T 1 t 2 T 0 N 2 m T 1 t 1 T 0 x 1 m n N 1 N 2 x 0 n sinc T m T 1 n T 0
    This is essentially lowpass filter design using a boxcar window: other finite-length filter design methods could beused for this.
  2. Lack of causality : The solution is to delay by N samples. The mathematics of the analog portions of this system can be implemented digitally.
    x 1 m t m T 1 h aa t x a t τ n x 0 n m T 1 τ n T 0 T 0 m T 1 τ n T 0 T 0 τ T 1 τ T 1
    x 1 m T T 0 T 1 n x 0 n T m T 1 n T 0 T m T 1 n T 0 n x 0 n sinc T m T 1 n T 0
    So we have an all-digital formula for exact digital-to-digital rate changing!
  3. Cost of computing sinc T m T 1 n T 0 : The solution is to precompute the table of sinc t values. However, if T 1 T 0 is not a rational fraction, an infinite number of samples will be needed, so some approximation will have tobe tolerated.
    Rate transformation of any rate to any other rate can be accomplished digitally with arbitrary precision (if somedelay is acceptable). This method is used in practice in many cases. We will examine a number of special cases andcomputational improvements, but in some sense everything that follows are details; the above idea is the centralidea in multirate signal processing.

Useful references for the traditional material (everything except PRFBs) are Crochiere and Rabiner, 1981 and Crochiere and Rabiner, 1983 . A more recent tutorial is Vaidyanathan ; see also Rioul and Vetterli . References to most of the original papers can be found in these tutorials.

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.
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Source:  OpenStax, Digital signal processing: a user's guide. OpenStax CNX. Aug 29, 2006 Download for free at http://cnx.org/content/col10372/1.2
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