# 1.3 Discrete vs analog

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When comparing analog vs discrete time, we find that there are many similarities. Often we only need to substitute the variblet with n and integration with summation. Still there are some important differences that we need to know.As the complex exponential signal is truly central to signal processing we will study that in more detail.

## Analog

The complex exponential function is defined: $x(t)=e^{it}$ . If(rad/second) is increased the rate of oscillation will increase continuously. The complex exponential function is also periodic for any value of. In figure we have plotted $e^{i\pi t}$ and $e^{i\times 3\pi t}$ (the real parts only). In we see that the red plot, corresponding to a higher value of, has a higher rate of oscillation.

## Discrete time

The discrete time complex exponential function is defined: $x(n)=e^{in}$ .

If we increase(rad/sample) the rate of oscillation will increase and decrease periodically.The reason is: $e^{i(+2\pi k)n}=e^{in}e^{i\times 2\pi kn}=e^{in}$ , where $n,k\in \mathbb{Z}$ .

This implies that the complex exponential with digital angular frequencyis identical to a complex exponential with ${}_{1}=+2\pi$ , see

The rate of oscillation will increase until $=\pi$ , then it decreases and repeats after 2. In we see that as we increase the angular frequency towardsthe rate of oscillation increases. If you download the Matlab files included at theend of this module you can adjust the parameters and see that the rate of oscillation will decrease when exceeding(but less than 2).
We need to consider discrete time exponentials at an (digital angular) frequency interval of 2only.
Low (digital angular) frequencies will correspond tonear even multiplies of. High (digital angular) frequencies will correspond tonear odd multiplies of.

## Matlab files

Take a look at

• Introduction
• Discrete time signals
• Analog signals
• Frequency definitions and periodicity
• Energy&Power
• Exercises
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how do they get the third part x = (32)5/4
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
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or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
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Kristine 2*2*2=8
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is it 3×y ?
J, combine like terms 7x-4y
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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?
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China
Cied
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I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
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Porter
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Cesar
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Uday
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Stotaw
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Azam
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Azam
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Azam
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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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