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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

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, 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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