<< Chapter < Page Chapter >> Page >

Thus, the impulse response describes how a system behaves directly in time, while the frequency responsedescribes how it behaves in frequency. The two descriptions are intimately related because the frequency response is theFourier transform of the impulse response. This will be used repeatedly in [link] to design filters for the manipulation (augmentation or removal)of specified frequencies.

In Exercise  [link] , a system was defined to have an impulse response that is a sinc function.The Fourier transform of a sinc function in time is a rect function in frequency [link] . Hence, the frequency response of the system is a rectangle that passes all frequencies below f c = 1 / T and removes all frequencies above (i.e., the system is a lowpass filter).

M atlab can help to visualize the relationship between the impulse response and the frequency response.For instance, the system in convolex.m is defined via its impulse response, which is a decaying exponential. [link] shows its output when the input is a simple sum of delta functions, andExercise  [link] explores the output when the input is a white noise. In freqresp.m , the behavior of this system is explained by looking at its frequency response.

Ts=1/100; time=10;             % sampling interval and total time t=0:Ts:time;                   % create time vectorh=exp(-t);                     % define impulse response plotspec(h,Ts)                 % find and plot frequency response
freqresp.m numerical example of impulse and frequency response (download file)

The output of freqresp.m is shown in [link] . The frequency response of the system (which is just the magnitude spectrum ofthe impulse response) is found using plotspec.m . In this case, the frequency response amplifies low frequenciesand attenuates other frequencies more as the frequency increases. This explains, for instance, why the output of theconvolution in Exercise  [link] contained (primarily) lower frequencies, as evidenced by the slower undulations in time.

The action of a system in time is defined by its impulse response (in the top plot). The action of the system in frequency is defined by its frequency response (in the bottom plot), a kind of lowpass filter.
The action of a system in time is defined by its impulse response (in the top plot). The action of the system in frequencyis defined by its frequency response (in the bottom plot), a kind of lowpass filter.

Suppose a system has an impulse response that is a sinc function. Using freqresp.m , find the frequency response of the system. What kind of filter does this represent?Hint: center the sinc in time; for instance, use h=sinc(10*(t-time/2)) .

Suppose a system has an impulse response that is a sin function. Using freqresp.m , find the frequency response of the system. What kind of filter does this represent?Can you predict the relationship between the frequency of the sine wave and the location of the peaks in the spectrum?Hint: try h=sin(25*t) .

Create a simulation (analogous to convolex.m ) that inputs white noise into a system with impulse responsethat is a sinc function (as in Exercise  [link] ). Calculate the spectra of the input and outputusing plotspec.m . Verify that the system behaves as suggested by thefrequency response in Exercise  [link] .

Create a simulation (analogous to convolex.m ) that inputs white noise into a system with impulse responsethat is a sin function (as in Exercise  [link] ). Calculate the spectra of the input and outputusing plotspec.m . Verify that the system behaves as suggested by thefrequency response in Exercise  [link] .

Questions & Answers

what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
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
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
Good
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Software receiver design. OpenStax CNX. Aug 13, 2013 Download for free at http://cnx.org/content/col11510/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Software receiver design' conversation and receive update notifications?

Ask