Digital transformation of the sampling rate of signals, or
signal processing with different sampling rates in the system.
Applications
CD to DAT format change, for example.
oversampling
converters; which reduce performance requirements onanti-aliasing or reconstruction filters
bandwidth of individual channels is much less than theoverall bandwidth
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.
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] )
Digital implementation of rate-changing according to this
formula has three problems:
Infinite sum: The solution is to truncate. Consider
$sinc(t)\approx 0$ 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
$${N}_{1}=\lceil \frac{m{T}_{1}-{t}_{2}}{{T}_{0}}\rceil $$$${N}_{2}=\lfloor \frac{m{T}_{1}-{t}_{1}}{{T}_{0}}\rfloor $$$${x}_{1}(m)=\sum_{n={N}_{1}}^{{N}_{2}} {x}_{0}(n){sinc}_{{T}^{\prime}}(m{T}_{1}-n{T}_{0})$$
This is essentially lowpass filter design using a boxcar
window: other finite-length filter design methods could beused for this.
Lack of
causality : The solution is to delay by
$\max\{\left|N\right|\}$ samples. The mathematics of the analog portions
of this system can be implemented digitally.
So we have an all-digital formula for
exact digital-to-digital rate changing!
Cost of computing
${sinc}_{{T}^{\prime}}(m{T}_{1}-n{T}_{0})$ : The solution is to precompute the table of
$\mathrm{sinc}(t)$ values. However, if
$\frac{{T}_{1}}{{T}_{0}}$ 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 variations in raman spectra for nanomaterials
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
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?