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With this code, a time vector t is generated by taking a time interval of Delta for 8 seconds. Convolve the two input signals, x1 and x2, using the function conv. Compute the actual output y_ac using Equation (1). Measure the length of the time vector and input vectors by using the command length(t). The convolution output vector y has a different size (if two input vectors m and n are convolved, the output vector size is m+n-1). Thus, to keep the size the same, use a portion of the output corresponding to y(1:Lt) during the error calculation.

Use a waveform graph to show the waveforms. With the function Build Waveform (Functions → Programming → Waveforms → Build Waveforms) , one can show the waveforms across time. Connect the time interval Delta to the input dt of this function to display the waveforms along the time axis (in seconds).

Merge together and display the true and approximated outputs in the same graph using the function Merge Signal (Functions → Express → Sig Manip → Merge Signals) . Configure the properties of the waveform graph as shown in [link] .

Waveform Graph Properties Dialog Box

[link] illustrates the completed block diagram of the numerical convolution.

Block Diagram of the Convolution Example

[link] shows the corresponding front panel, which can be used to change parameters. Adjust the input exponent powers and approximation pulse-width Delta to see the effect on the MSE .

Front Panel of the Convolution Example

Convolution example 2

Next, consider the convolution of the two signals x ( t ) = exp ( 2t ) u ( t ) size 12{x \( t \) ="exp" \( - 2t \) u \( t \) } {} and h ( t ) = rect ( t 2 2 ) size 12{h \( t \) = ital "rect" \( { {t - 2} over {2} } \) } {} for , where u ( t ) size 12{u \( t \) } {} denotes a step function at time 0 and rect a rectangular function defined as

rect ( t ) = { 1 0 . 5 t < 0 . 5 0 otherwise size 12{ ital "rect" \( t \) = left lbrace matrix { 1 {} # - 0 "." 5<= t<0 "." 5 {} ## 0 {} # ital "otherwise"{}} right none } {}

Let Δ = 0 . 01 size 12{Δ=0 "." "01"} {} . [link] shows the block diagram for this second convolution example. Again, the .m file textual code is placed inside a LabVIEW MathScript node with the appropriate inputs and outputs.

Block Diagram for the Convolution of Two Signals

[link] illustrates the corresponding front panel where x ( t ) size 12{x \( t \) } {} , h ( t ) size 12{h \( t \) } {} and x ( t ) h ( t ) size 12{x \( t \) * h \( t \) } {} are plotted in different graphs. Convolution ( ) size 12{ \( * \) } {} and equal ( = ) size 12{ \( = \) } {} signs are placed between the graphs using the LabVIEW function Decorations .

Front Panel for the Convolution of Two Signals

Convolution example 3

In this third example, compute the convolution of the signals shown in [link] .

Signals x1(t) and x2(t)

[link] shows the block diagram for this third convolution example and [link] the corresponding front panel. The signals x1 ( t ) size 12{x1 \( t \) } {} , x2 ( t ) size 12{x2 \( t \) } {} and x1 ( t ) x2 ( t ) size 12{x1 \( t \) * x2 \( t \) } {} are displayed in different graphs.

Block Diagram for the Convolution of Two Signals

Front Panel for the Convolution of Two Signals

Convolution properties

In this part, examine the properties of convolution. [link] shows the block diagram to examine the properties and [link] and [link] the corresponding front panel. Both sides of equations are plotted in this front panel to verify the convolution properties. To display different convolution properties within a limited screen area, use a Tab Control (Controls Modern Containers Tab Control) in the front panel.

Front Panel of Convolution Properties
Block Diagram of Convolution Properties

Questions & Answers

Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
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
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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
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Source:  OpenStax, An interactive approach to signals and systems laboratory. OpenStax CNX. Sep 06, 2012 Download for free at http://cnx.org/content/col10667/1.14
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