<< Chapter < Page Chapter >> Page >

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

so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
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
anybody can imagine what will be happen after 100 years from now in nano tech world
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
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
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.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!

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
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'An interactive approach to signals and systems laboratory' conversation and receive update notifications?