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Sampling, aliasing, quantization and reconstruction

The example in this section addresses sampling, quantization, aliasing and signal reconstruction concepts. [link] shows the completed block diagram of this example, where the following four control parameters are linked to a LabVIEW MathScript node:

Amplitude – to control the amplitude of an input sine wave

Phase – to control the phase of the input signal

Frequency – to control the frequency of the input signal

Sampling frequency – to control the sampling rate of the corresponding discrete signal

Number of quantization levels – to control the number of quantization levels of the corresponding digital signal

To simulate the analog signal via a .m file, consider a very small value of time increment dt (dt = 0.001). To create a discrete signal, sample the analog signal at a rate controlled by the sampling frequency. To simulate the analog signal, use the textual statement xa=sin(2*pi*f*t) , where t is a vector with increment dt = 0.001. To simulate the discrete signal, use the textual statement xd=sin(2*pi*f*n) , where n is a vector with increment dn. The ratio dn/dt indicates the number of samples skipped during the sampling process. Again, the ratio of analog frequency to sampling frequency is known as digital or normalized frequency. To convert the discrete signal into a digital one, perform quantization using the LabVIEW MathScript function round . Set the number of quantization levels as a control.

To reconstruct the analog signal from the digital one, use a linear interpolation technique via the LabVIEW MathScript function interp 1 . The samples skipped during the sampling process can be recovered after the interpolation. Finally, display the Original signal and the Reconstructed signal in the same graph using the functions Build Waveform, Merge Signal and Waveform Graph. Discrete waveform, Digital waveform, Analog frequency, Digital frequency and Number of samples skipped in ADC are also included in the front panel, shown in [link] . Use this VI to examine proper signal sampling and reconstruction.

Block Diagram of Sampling, Aliasing, Quantization and Reconstruction

Front Panel of Sampling, Aliasing, Quantization and Reconstruction

Analog and digital frequency

Digital frequency ( θ size 12{θ} {} ) is related to analog frequency ( f size 12{f} {} ) via the sampling frequency, that is, θ = 2πf f s size 12{θ= { {2πf} over {f rSub { size 8{s} } } } } {} . Therefore, one can choose the sampling frequency ( f s size 12{f rSub { size 8{s} } } {} ) to increase the digital or normalized frequency of an analog signal by lowering the number of samples.


Set the sampling frequency to f s = 100 size 12{f rSub { size 8{s} } ="100"} {} Hz and change the analog frequency of the signal. Observe the output for f s = 10 size 12{f rSub { size 8{s} } ="10"} {} Hz and f s = 210 size 12{f rSub { size 8{s} } ="210"} {} Hz (See [link] and [link] ). The analog signals appear entirely different in these two cases but the discrete signals are similar. For the second case, the sampling frequency is less than twice that of the analog signal frequency. This violates the Nyquist sampling rate leading to aliasing, which means one does not know from which analog signal the digital signal is created. Note the value of digital frequency is 0.1 radians for the first case and 2.1 radians for the second case. To prevent any aliasing, keep the digital frequency less than 0.5 radians.

Questions & Answers

who was the first nanotechnologist
Lizzy Reply
technologist's thinker father is Richard Feynman but the literature first user scientist Nario Tagunichi.
Norio Taniguchi
I need help
@Richard Is that Richard Feynman
anyone have book of Abdel Salam Hamdy Makhlouf book in pdf Fundamentals of Nanoparticles: Classifications, Synthesis
Naeem Reply
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pedro Reply
It could change the whole space science.
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sibaram Reply
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hydrothermal synthesis
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Eke Reply
is this allso about nanoscale material
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Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
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where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
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..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
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.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
STM - Scanning Tunneling Microscope.
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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
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