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This module is the recursive cosine generation lab.


In this laboratory you write a program that generates a cosine on the output of the D/A converter. After this laboratory you should:

  • Be able to work with transfer functions and difference equations.
  • Be able to get a Visual Basic program to communicate with your DSP program on the DSK board.


  • Chapter 4: Emmanuel Ifeachor and Barrie W. Jervis, Digital Signal Processing: A Practical Approach , Pearson Education Limited, England, 2002.
  • Chapter 13&14: Mrinal Mandal, Amir Asif, Continuous and Discrete Time Signals and Systems , Cambridge University Press, 2007.


In this lab you will be making a cosine function generator. This will require you to generate the values that go to the D/A converter in order to produce a cosine function. Since we are only concerned with the output, the input values will be ignored. You will need to determine the values of the cosine function necessary to produce it on the output.


  • In order to generate a cosine function we will generate the impulse response of a system that has the impulse response
h ( n ) = cos ( αn ) u ( n ) size 12{h \( n \) ="cos" \( αn \) u \( n \) } {}
  • For the given impulse response find the following:
  1. Transfer function of the system. Look it up in a ZT table.
  2. Direct Form II structure of the system.
  3. Pole/zero diagram of the system. Assume α = π/4 for the example diagram.
  4. Difference equation of the system.
  • Calculate h (0), h (1), and h (2) assuming the input is an impulse x ( n ) = δ( n ). Simplify the h (2) term.
  • Show how you will recursively determine the impulse response of this system.
  • Suppose the sample rate of the system is 8000 Hz and we want to generate a cosine with a frequency of 500 Hz, what should α be to implement this cosine function?
  • In MATLAB, write a program that will recursively determine the impulse response of this system with sample rate 8000Hz and cosine of 400 Hz. Put the data into an array and plot the impulse response. Generate 100 points. Compare the recursively generated values to the direct calculation of the cosine function.
  • Modify the while loop Write a program in C that will recursively determine the impulse response of this system.
  1. The recursive portion should be in an infinite while loop and the data should not go into an array but in a single variable.
  2. All of the variables should be of type double .
  3. In your program you will need to include the header file math.h .
  4. The data we are generating is for the D/A converter. The D/A converter accepts Int16 type data which has the limits of [-32768, 32767]. Since the impulse response has the limits [-1, 1]you will need to multiply the result by a number to scale the value up to a level that will work with the D/A converter without overflowing. Use the value 32000.0 . The statement will be something like (Int16)(32000.0*y) .
  5. To calculate π , use the following statement:


Part 1

  • Use the sample I/O program for the DSK and generate a 400 Hz cosine sampled at 8000 Hz using the recursive program you developed.
  • Change the frequency of the cosine to at least 2 other values from about 50 Hz to 4000 Hz and record the results.
  • What happens when you change the frequency of the cosine to 5000 Hz? Explain what you see.

Questions & Answers

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
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
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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.
Do you know which machine is used to that process?
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.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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