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Multiply-add speed is important

Some DSP processes require extremely large numbers of multiply-add operations. In order to perform DSP in real time, the equipment used to performthe arithmetic must be extremely fast. That is where the special DSP chips, (which are designed to perform multiply-add operations at an extremely high rate of speed) earn their keep.

The net area under the curve

If you plot a time series as a curve on a graph, as shown in Figure 3 , the sum of the values that make up the time series is an estimate of the net areaunder the curve.

(Assuming that the horizontal axis represents a value of zero, the sample values above the axis contribute a positive value to the net area and thesample values below the curve contribute a negative value to the net area. In the case of Figure 3 , I attempted to come up with a set of sample values that would produce a net area of zero. In other words, the area above thehorizontal axis was intended to perfectly balance the area below the horizontal axis.)
Figure 3. Plot of values in a time series.
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A periodic example

A periodic time series is one in which a set of sample values repeats over time, provided that you record enough samples to include one or more periods. Figure 4 shows a plot of a periodic time series. You can see that the same set of values repeats as you move from left to right on the curve plotted in Figure 4 .

Figure 4. Area under a periodic curve.
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The sum of two curves

Periodic curves can often be viewed as the sum of two curves. One of the curves is the periodic component having a zero net area under the curve whenmeasured across an even number of cycles. The other component is a constant bias offset that is added to every value of the periodic curve.

Each of the solid dark blobs in Figure 4 is a sample value. The horizontal line represents a sample value of zero. (The empty circle is the sample value half way through the sampling interval. The only reason it is different isto mark the mid point.)

The net area under the curve

What is the net area under the curve in Figure 4 ? Can you examine the curve and come up with a good estimate. As it turns out, the net area under the curvein Figure 4 is very close to zero (at least it is as close to zero as I was able to draw it) .

Now take a look at Figure 5 . What is the net area under the curve in Figure 5 ?

Figure 5. Area under a periodic curve with an offset.
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Compare Figure 5 To Figure 4

Each of these curves describes the same periodic shape (although Figure 4 has a larger peak-to-peak amplitude, meaning simply that every value in Figure 4 has been multiplied by the same scale factor) .

However, the curve in Figure 5 is riding up on a positive bias, while the curve in Figure 4 is centered about the horizontal axis. While the net area under the curve in Figure 4 is near zero, the net area under the curve in Figure 5 is a non-zero positive value.

The curve in Figure 5 can be considered to consist of the sum of two parts. One part is a straight horizontal line on the positive side of the horizontalaxis. The other part is the periodic curve from Figure 4 , added to that positive bias.

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
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
I'm not sure why it wrote it the other way
I got X =-6
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
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
I'm not good at math so would you help me
what is the problem that i will help you to self with?
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
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
anybody can imagine what will be happen after 100 years from now in nano tech world
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
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
can nanotechnology change the direction of the face of the world
Prasenjit Reply
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.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
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