<< Chapter < Page Chapter >> Page >

Response of discrete-time systems

This lab involves analyzing the response of discrete-time systems. Responses are calculated for three different kinds of inputs; impulse, step and sine. [link] shows the completed block diagram. Connect the input variable w to an Enum Control so that an input type (impulse, step or sine) can be selected. The response of this system to any discrete-time input x [ n ] size 12{x \[ n \] } {} can be written as

y [ n ] = i b i x [ n i ] + i a i y [ n i ] size 12{y \[ n \] = Sum cSub { size 8{i} } {b rSub { size 8{i} } x \[ n - i \]} + Sum cSub { size 8{i} } {a rSub { size 8{i} } y \[ n - i \] } } {}

For this example, consider five b’s and four a’s. The system output is displayed using a waveform graph.

Block Diagram of a Discrete-Time System

[link] shows the front panel of the above system. The front panel can be used to interactively select the input type and set the coefficients a and b. The system response for a particular type of input (impulse, step or sine) is shown in the waveform graph.

Front Panel of a Discrete-Time System

Square root

As another example of discrete-time systems, let us consider taking the square root of an integer number. Often computers and calculators compute the square root of a positive number A size 12{A} {} using the following recursive equation:

y [ n ] = 1 2 y [ n 1 ] + x [ n ] y [ n 1 ] size 12{y \[ n \] = { {1} over {2} } left (y \[ n - 1 \]+ { {x \[ n \] } over {y \[ n - 1 \]} } right )} {}

If the input x [ n ] size 12{x \[ n \] } {} to this equation is set as a step function of amplitude A, then y [ n ] size 12{y \[ n \] } {} converges to the square root of A after several iterations.

[link] shows the block diagram for a square root computation system. The number of iterations required to converge to the true value is shown in the output. The initial condition Initial value is set as a control. [link] shows the corresponding front panel.

Block Diagram of a Square Root Computation System

Front Panel of a Square Root Computation System

Analog and digital filtering

In this section, let us examine a basic analog and digital filtering example by implementing a lowpass and a highpass filter in the analog and digital domains, respectively. [link] shows the completed block diagram of the filtering system. For analog approximation of the signals, use a higher sampling rate (dw1=0.01). To detect whether the filtering is lowpass or highpass, use the Enum Control Analog filter type. Calculate the magnitude and phase response of these filters using equations provided in Chapter 7 for analog and digital filters. Set the values of R and C as controls, and display the responses using a Build Waveform function and a waveform graph.

Block Diagram of an Analog and Digital Filtering System

For the digital case, use a lower sampling rate (dw2=0.001). With the Enum controls Digital filter type 1 and Digital filter type 2, select lowpass or highpass and FIR or IIR filter type. Use a Build Waveform function and a waveform graph to display the magnitude and phase responses of the digital filters. [link] shows the front panel of this filtering system. For a better view of magnitude response of the digital filter, set the properties of the waveform graph as shown in [link] .

Front Panel of an Analog and Digital Filtering System

Graph properties of magnitude response of digital filter

Lab exercises

Bandpass and Bandstop Filters

Use the lowpass and highpass filters (both analog and digital) described in Analog and Digital Filtering section to construct bandpass and bandstop filters. The bandpass filter should be able to pass signals from 50 to 200 Hz and the bandstop filter should be able to stop signals from 150 to 400 Hz. Determine the values of R and C required for this analog filter design. Also, determine the values of the coefficients required for an equivalent IIR digital filter design.

Insert Solution Text Here

Noise Reduction

Use an analog lowpass filter to remove the high-frequency noise described in Noise Reduction example of Lab 5. Repeat using a digital lowpass filter.

Insert Solution Text Here

Frequency Division Multiplexing (FDM)

FDM is widely used in digital communication to simultaneously transmit multiple signals over a single wideband channel (for details, refer to [link] ). For FDM communication, individual signals are multiplied with different carriers to avoid overlaps in the frequency domain. Their time domain processing and corresponding frequency spectrums are shown in [link] . Build a VI to implement an FDM communication system for three signals x 1 ( t ) , x 2 ( t ) size 12{x rSub { size 8{1} } \( t \) ,x rSub { size 8{2} } \( t \) } {} and x 3 ( t ) size 12{x rSub { size 8{3} } \( t \) } {} . Use the files echo_1.wav and firetrucksiren.wav on the book website and a random noise with a frequency range of 20 Hz to 20 kHz to serve as these signals.

FDM Communication System

Insert Solution Text Here

FDM Detector

Build a VI to implement an FDM detector system for detecting the signal x 1 ( t ) size 12{x rSub { size 8{1} } \( t \) } {} as shown in [link] .

FDM Detector

Insert Solution Text Here

Questions & Answers

Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
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
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?