# 0.6 Matrix implementation

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Handling multiple channels of data at once naturally yearns for an implementation utilizing matrix operations. While filtering one channel is a purely serial process, we can attempt to compute every channel's filtered output and the intermediate filter terms for a Direct Form-II implementationfor the next output in the following two matrix operations.

$\left[\begin{array}{c}{y}_{1}\\ ⋮\\ {y}_{N}\end{array}\right]={b}_{0}\left[\begin{array}{c}{x}_{1}\\ ⋮\\ {x}_{N}\end{array}\right]\phantom{\rule{0.166667em}{0ex}}+\phantom{\rule{0.166667em}{0ex}}\left[\begin{array}{c}{w}_{1}^{1}\\ ⋮\\ {w}_{N}^{1}\end{array}\right]$
$\left[\begin{array}{ccccccc}{b}_{1}^{1}& -{a}_{1}^{1}& {w}_{1}^{1}& \cdots & {b}_{N}^{1}& -{a}_{N}^{1}& {w}_{N}^{1}\\ {b}_{1}^{2}& -{a}_{1}^{2}& {w}_{1}^{2}& \cdots & {b}_{N}^{2}& -{a}_{N}^{2}& {w}_{N}^{2}\\ {b}_{1}^{3}& -{a}_{1}^{3}& {w}_{1}^{3}& \cdots & {b}_{N}^{3}& -{a}_{N}^{3}& {w}_{N}^{3}\\ {b}_{1}^{4}& -{a}_{1}^{4}& {w}_{1}^{4}& \cdots & {b}_{N}^{4}& -{a}_{N}^{4}& {w}_{N}^{4}\end{array}\right]\left[\begin{array}{c}{x}_{1}\\ {y}_{1}\\ 1\\ ⋮\\ {x}_{N}\\ {y}_{N}\\ 1\end{array}\right]=\left[\begin{array}{c}{\stackrel{^}{w}}_{1}^{1}\\ {\stackrel{^}{w}}_{1}^{2}\\ {\stackrel{^}{w}}_{1}^{3}\\ {\stackrel{^}{w}}_{1}^{4}\\ ⋮\\ {\stackrel{^}{w}}_{N}^{1}\\ {\stackrel{^}{w}}_{N}^{2}\\ {\stackrel{^}{w}}_{N}^{3}\\ {\stackrel{^}{w}}_{N}^{4}\end{array}\right]$

We implemented the above operations using the Basic Linear Algebra Subprograms (BLAS) Fortran Library due to its reputation as a very fast and stable linear albegra library.While the operations are simple mathematically, the filter implementation was the slowest taking almost 10 minutes to filter 60 million samples. The matrices and vectors are very large so they are not stored in cache resulting in the slow down. Additionally, the SSE3 intrinsics and O3compiler optimizations are rendered useless when using the Fortran library.

Here, the matrix operations should be outsourced to the GPU which is optimized for this very action. The GPU is responsible for rendering graphics which regularly involves updating many polyhedrons that really are just matrix operations at the core. However, the GPU would not directly follow the proposedprocedure. Instead, the GPU would hand off segments of the matrices to be multiplied to its shaders (modern GPU's have thousands of shaders). Each shader then tackles a very small number of multiplies and adds. This divide and conquer strategy is very fast but requires some involved programming.

find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
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Tamia
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Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
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algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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