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As mentioned earlier, the DFT algorithm is much more flexible while the FFT algorithm is much faster, particularly for large data lengths.

Peaks merge at the folding frequency

In addition to illustrating these fundamental aspects of the DFT algorithm, this example also illustrates how the mirror image peaks on either side of thefolding frequency merge into a single larger peak as the data frequency approaches the folding frequency.

The input parameters

The input parameters are shown in Figure 10 . Note in particular the values for the following parameters:

  • Data length: 200
  • Sample for zero time: 0
  • Lower frequency bound: 0.4
  • Upper frequency bound: 0.6
Figure 10. The input parameters.
Data length: 200 Sample for zero time: 0Lower frequency bound: 0.4 Upper frequency bound: 0.6Number spectra: 5 Frequencies0.492 0.4940.496 0.4980.5 Amplitudes90.0 90.090.0 90.090.0

A different data length

As you can see, the data length for this experiment is different from the data length of 400 used earlier. In addition, neither data length is a power oftwo.

Computational frequency bounds

As you can also see, the lower and upper frequency bounds are not 0.0 and 1.0 as in the earlier cases. In this case, the frequency bounds describe a muchnarrower range centered on the folding frequency.

Frequencies are close to the folding frequency

Finally, the frequencies of each of the five sinusoids specified in Figure 10 is progressively closer to the folding frequency with the frequency of the fifthsinusoid being equal to the folding frequency.

The spectral analysis output

The output from the spectral analysis for each of the five sinusoids is shown in Figure 11 . (Another interesting view of the same results is shown later in Figure 14 .)

Figure 11. Spectral analysis of five sinusoids.
missing image

Peaks are symmetrical about the folding frequency

The spectral peaks shown in Figure 11 are symmetrical about the folding frequency, which in turn is centered horizontally in each of the graphs. As youalready know, the peaks are always symmetrical about the folding frequency due to the frequency folding at that frequency.

The folding frequency is centered horizontally due to the way that I defined the lower and upper frequency bounds, and the way that I adjusted the plottingparameters.

Peaks are well defined and wider than before

The peaks are well defined because I computed the spectral energy at 200 points across the specified frequency range from 0.4 to 0.6. Thus, the frequencybins at which I computed spectral energy were much narrower than before.

The peaks are wider because I displayed a much smaller slice of the entire frequency spectrum in the same physical screen space.

Peaks merge at the folding frequency

As the frequency of each sinusoid approaches the folding frequency, the two mirror-image peaks corresponding to that sinusoid merge into a single peak withtwice the height at the folding frequency. This agrees with what you saw in Figure 9 , but on a much more detailed basis.

It would be difficult to perform this experiment using an FFT algorithm because of the inherent limitations built into the algorithm. The FFT algorithmsacrifices flexibility for speed.

Questions & Answers

how environment affect demand and supply of commodity ?
Amos Reply
Wht at the criteria for market ?
Amos
what is difference between monitory policy and fiscal policy?
Malik Reply
monetary policy is a policy thrust by National Govt(CBN) to influence government spending, purchase &taxes
Frank
necessity of economics
Pamela Reply
I will say want,choice,opportunity cost,scarcity,scale of preference
Alao
what is monopoly market.How price output are determined under monopoly market
bisham
b) Monopoly market is an impecfect market where s single firm having the innovation to produce a particular commodity.Prices are determined through output since there are no other competitive.
Frank
Monopoly market:firm has market power & does not respond to market price
Frank
Explain the process of price determination under perfect competition market with suitable diagram
bisham Reply
Price determination under perfect competition via this process :firms have no market power to influence price rather firms respond to market price.
Frank
price is different from demand- demand is amount of commodity
Effah Reply
demand is amount /quantity of commodity a potential buyer is willing to buy at a given price at market
Frank
demand is a desire of customer on commodity with the ability to pay it and willing to buy it at given price of commodity
Harika
demand is price of what
Faith Reply
show that shortrun average cost
Baby Reply
what is economics
Mbah Reply
what is money
Mbah
what is money
Mbah
Difine macro economics
agaba
money is a medium of exchange between goods and services,maybe inform of currency.
Wesonga
Economics is study of how human beings strive to satisfy numerous wants using limited available resources.
Wesonga
how do you find the maximum number of workers the firms should employ order to produce where there are increasing returns
Jane
what are implications of computing national income?.
agaba
pl
MUDASIRU
what is the formulae for calculating national income
MUDASIRU
it calculated by value added method
Praveen
classify the production units like agriculture, banking, transport etc
Praveen
money is anything that is generally acceptetable for human
Ogbaji
Estimate the net value added(NVA) at fixed cost by each industrial structure
Praveen
definition of unemployment
Adam Reply
what are the causes of unemployment?
Mbubi Reply
The main causes of unemployment are listed below. 1. Frictional unemployment 2. Cyclical unemployment 3. Structural unemployment
assani
We can also categorize the causes on a broader sense as: 1. Political and 2. Social cause As unemployeement root causes are embaded in this two.
Yonathan
would opportunity cost exist if there was no scarcity?
assani
yes just because the opportunity cost arose when there is Alternative to choose among the alternatives.
BADAMASIU
I am thinking that, if our resources were unlimited, then there wouldn't be any need to forgo some wants. Hence the inexistence if opportunity cost
assani
Politics
Job
politics has done what?
assani
consider time assani
Mary
I'm Emmanuel,...I taught the main cause is the change in gov't.
Emmanuel
...Lack of capital to set up a firm respectively
Emmanuel
🙈
Emmanuel
I would like to bring in Educational levels can also be the cause the cause of the problem respectively
Emmanuel
I think the main causes of unemployment is lack of INFRASTRUCTURAL DEVELOPMENT OVER POPULATION OVER DEPENDENT ON GOVERNMENT LACK OF SELF EMPOWERMENT...
ananti
lack of skills among the new generation is the serious issue.
Vishal
Where I come from , I don't see why education or personal aspects seem to do with unimployment, technically the motivation and eigerness in all works of live is there , dispite the cultural influence and physical bearriors;the thing we lacking is Government Support and open market ethics.
Joe
sorry about that-(repation). We have a over powering ethical political system that's displacing the marketing asspects of economy and causing large scale unemployment right across the board...
Joe
can someone Explain Expansionary Monetary Policy and Contractionary Monetary Policy Using one of the instrument of Monetary Policy? Please am kinda lost here?. ta
Emmanuel Reply
using a graph show the case of substitute and compliment goods
Ade Reply
can anyone give me a simple explanation to Five Sector Macroeconomics?
Emmanuel
Can someone please define what economics is
jason Reply
economics simply is a social science subject that study human behavior.
dajan
economics is a social science which studies human behaviour as a relationship between ends and scarce means that has alternative uses
Alao
Can someone please tell me how to calculate GDP
Emmanuel
emmanual kapal to calculate GDP (Gross Domestic Product) has three method in calculating it (1)income approach (2) expenditure approach (3) value added method
Alao
thanks Alae
Emmanuel
u are welcome
Alao
in basic terms economics is revered to as battery system, it date back to when Men sees the need to exchange sapless goods and produce to gain , either wealth , basic necessities or to establish trading ties for personal benefit or social asspects in terms of coexistence and continuity, future .
Joe
what is the law of demand
Berlinda Reply
keep other thing constant, when the price increases demand decrease when the price decreases demand increases of the commodity.
sj
all things being equal,quantity demanded decrease as price increase and increase as price decrease
Seth
there's practial joke to it ..." the higher the demand ; scarcity, increase in production and drop in quality"... quite the controversy - for example China vs Europe, United States and we are all boxed up in between somewhere...
Joe
Other thing remain constant the low price of commodity the high quantity of commodity and vice versa is true
Baraka
Explain Effective demand
Anita Reply
What is effective demand
Anita
like Modi is in demand...best example of effective demand
Pranav
Don't get you
Anita
Anita you mean you don't get me or who?
Onyeking
level of demand that represents a real intention to purchase by people with the means to pay
Pranav
in a comparison of the stages of meiosis to the stage of mitosis, which stages are unique to meiosis and which stages have the same event in botg meiosis and mitosis
Leah 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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