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Digital filtering is not simply converting from analog to digital filters; it is a fundamentally different way of thinkingabout the topic of signal processing, and many of the ideas and limitations of the analog methodhave no counterpart in digital form

—R. W. Hamming, Digital Filters , 3d ed., Prentice Hall 1989

Once the received signal is sampled, the real story of the digital receiver begins.

An analog bandpass filter at the front end of the receiver removes extraneous signals (for instance, it removes televisionfrequency signals from a radio receiver) but some portion of the signal from otherFDM users may remain. While it would be conceptually possible to remove all but the desired user at the start,accurate retunable analog filters are complicated and expensive to implement. Digital filters, on the other hand, are easy to design,inexpensive (once the appropriate DSP hardware is present) and easy to retune.The job of cleaning up out-of-band interferences left over by the analog BPF can be left to the digital portion ofthe receiver.

Of course, there are many other uses for digital filters in the receiver, and this chapter focuses on how to “build” digital filters.The discussion begins by considering the digital impulse response and the related notion of discrete-time convolution.Conceptually, this closely parallels the discussion of linear systems in Chapter [link] . The meaning of the DFT (discrete Fourier transform) closely parallels the meaning ofthe Fourier transform, and several examples encourage fluency in the spectral analysis of discrete data signals. The finalsection on practical filtering shows how to design digital filters with (more or less) any desired frequency responseby using special M atlab commands.

Discrete time and discrete frequency

The study of discrete-time (digital) signals and systems parallels that of continuous-time (analog) signals and systems.Many digital processes are fundamentally simpler than their analog counterparts, though there are a few subtletiesunique to discrete-time implementations. This section begins with a brief overview and comparison, and then proceedsto discuss the DFT, which is the discrete counterpart of the Fourier transform.

Just as the impulse function δ ( t ) plays a key role in defining signals and systems in continuous time,the discrete pulse

δ [ k ] = 1 k = 0 0 k 0

can be used to decompose discrete signals and to characterize discrete-time systems. The pulse in discrete time is considerably more straightforward thanthe implicit definition of the continuous-time impulse function in [link] and [link] . Any discrete-time signal can be written as a linear combination of discrete impulses.For instance, if the signal w [ k ] is the repeating pattern { - 1 , 1 , 2 , 1 , - 1 , 1 , 2 , 1 , ... } , it can be written

w [ k ] = - δ [ k ] + δ [ k - 1 ] + 2 δ [ k - 2 ] + δ [ k - 3 ] - δ [ k - 4 ] + δ [ k - 5 ] + 2 δ [ k - 6 ] + δ [ k - 7 ] ...

In general, the discrete time signal w [ k ] can be written

w [ k ] = j = - w [ j ] δ [ k - j ] .

This is the discrete analog of the sifting property [link] ; simply replace the integral with a sum, and replace δ ( t ) with δ [ k ] .

Like their continuous-time counterparts, discrete-time systems map input signals into output signals.Discrete-time LTI (linear time-invariant) systemsare characterized by an impulse response h [ k ] , which is the output of the system when the input is an impulse,though, of course, [link] is used instead of [link] . When an input x [ k ] is more complicated than a single pulse, the output y [ k ] can be calculated by summing all the responses to all the individual terms, and this leadsdirectly to the definition of discrete-time convolution:

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
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Adin Reply
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what school?
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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.
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Damian Reply
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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.
what is biological synthesis of nanoparticles
Sanket Reply
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Source:  OpenStax, Software receiver design. OpenStax CNX. Aug 13, 2013 Download for free at http://cnx.org/content/col11510/1.3
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