# 6.1 Lab 6: analog-to-digital conversion, dtft and dft

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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.

## Analog and digital frequency

Digital frequency ( $\theta$ ) is related to analog frequency ( $f$ ) via the sampling frequency, that is, $\theta =\frac{2\pi f}{{f}_{s}}$ . Therefore, one can choose the sampling frequency ( ${f}_{s}$ ) to increase the digital or normalized frequency of an analog signal by lowering the number of samples.

## Aliasing

Set the sampling frequency to ${f}_{s}=\text{100}$ Hz and change the analog frequency of the signal. Observe the output for ${f}_{s}=\text{10}$ Hz and ${f}_{s}=\text{210}$ 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

How we are making nano material?
LITNING Reply
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LITNING Reply
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LITNING Reply
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LITNING
scanning tunneling microscope
Sahil
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Bob Reply
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Bob
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brayan
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Damian
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?
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biomolecules are e building blocks of every organics and inorganic materials.
Joe
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Damian Reply
research.net
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sciencedirect big data base
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Introduction about quantum dots in nanotechnology
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nano basically means 10^(-9). nanometer is a unit to measure length.
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Anassong
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Lily
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s. Reply
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NANO
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Lily
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Devang Reply
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s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
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CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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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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