# 2.1 Dsp00104-sampled time series  (Page 4/10)

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The two sinusoids above the center had higher frequencies than the sinusoid in the center, with the sinusoid at the top having the highest frequency. For afixed sampling frequency, the sinusoids above the center had fewer samples per cycle than the sinusoid in the center. The sinusoid at the top had the fewestnumber of samples per cycle.

The two sinusoids below the center had lower frequencies, than the sinusoid in the center, with the sinusoid at the bottom having the lowest frequency. Thetwo sinusoids below the center had more samples per cycle than the sinusoid in the center. The sinusoid at the bottom had the most samples per cycle.

## The number of samples per cycle is important

In the final analysis, what really counts is not the number of samples per second of the sampling frequency, or the number of cycles per second of thesignal frequency. What really counts is the number of samples per cycle of the highest frequency component. This value is established by the combination of the signal frequency and the samplingfrequency.

## The values between the samples

Because the plots in Figure 1 are pure sinusoids, I can mathematically determine the values between the samples. However, if there had been theslightest amount of random noise superimposed on the sinusoids, (which is the more realistic situation), I would have no way of knowing the values between the samples. Thus, all of the information that I have about these five signalsis contained in the heights of the vertical bars shown in Figure 1 .

## Estimating the values in between the samples

As mentioned earlier, we often find ourselves estimating the values in between the samples. One way to do this is shown in Figure 2 , which shows a different graphical treatment for the same five sinusoids.

Figure 2. Rectangular representations of samples from five sinusoids.

Figure 2 represents each of the sample values as a rectangle. In effect, this treatment estimates that there is no change in the value of the analog signalfor half a sample interval after the sample is taken. Then the value of the analog signal jumps to the value of the next sample.

## A more common representation

Now consider the graphical treatment for the same five sinusoids shown in Figure 3 .

Figure 3. Trapezoidal representations of samples from five sinusoids.

Figure 3 shows a more common representation of the data. Figure 3 treats each sample as a trapezoid consisting of a rectangle and a right triangle. Thetriangle sets atop the rectangle and connects each sample value to the next with a straight line.

## The most common representation

Now consider the most common representation of the sampled data, as shown in Figure 4 .

Figure 4. Most common representations of samples from five sinusoids.

Figure 4 shows the most common representation of the sampled data. Figure 4 is the same as Figure 3 except that the vertical lines that identify the sides of the trapezoids have been omitted. In Figure 4 , each sample value is connected to the next sample value with a straight-line segment.

can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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