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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

who is a price taker?
sam Reply
A price taker is a person or a company who have no control to dictate a prices of a goods or services
Unique
Someone who sets price
Nureni
In the trading world, a price taker is a trader who does not affect the price of the stock if he or she buys or sells shares.
Nureni
in a common and suitable sense state the law of diminishing returns
Unique Reply
The higher the satisfaction derived from a particular commodity,the lower the demand for it but that law doesn't match in some instances.
Nureni
state the features of an imperfect competitive market
Naomi
@NURENI instance like wat
Unique
imperfect competitive market involves large number of sellers and buyers price makers selling cost product differentiation free entry and exit of a firms
Unique
is economics a science
Alex Reply
yes. a social science.
Carlos
Yes of cause It uses scientific principles in its research. That is to say, analyzing data, making experiment as well as making deductions and drawing conclusions
Aziz
U can understand the scientific nature of economics by learning about the methods used by Abhijit Banerjee(indian) ,the nobel prize laureate 2019.
Harshita
it is considered as a social science
idk
Hence, economics is a science, a social science many can call it, or more appropriately, a young science
Taha
it can be called social science because of behaviour ,which is unpredictable.There r many theroies in economics which make economics a social science But some economic theories makes it science
Harshita
human behaviour*
Harshita
remember science derives from the root words "to know". With that being said most fields of study can be considered as a science or soft science, for they possess key knowledge to attaining understanding of our world.
Alexander
economics is a science cos it deals with human wants, desire or neads in order to satisfy them
Unique
what's the question?
Nureni Reply
Discuss economics system
Henry Reply
discuss institutional system
Henry
Give 3 at most advantages and disadvantages of economics system and institutional syatem
Henry
Give the features characteristics of market or free enterprise
Henry
The structure of an economy is largely determined by the economic system which is a function of the economic ideology of the nation
Nureni
The economic system is grouped into 5 groups: 1: Pure market 2: Developed market 3: Centrally planned or Socialist 4: Mixed market and 5: Market Socialist Economic systems
Nureni
what is inflation
Prince Reply
hello everyone , I'm New here, third degree price discrimination?
Saeed Reply
2nd degree price discrimination?
Saeed
hi
Kini
hi
Mitchel
Hi
MP
price paid by consumers after the sales tax is called?
Pinias Reply
why government impose price floor on certain products?
Pinias
how can black market be occurred when price ceiling is introduced?
Pinias
How can inflation affect goods and services?
Ph
When prices rise for energy, food, commodities, and other goods and services, the entire economy is affected
Joan
If inflation becomes too high the economy can suffer conversely, if inflation is controlled and at reasonable levels, the economy may prosper. With controlled, lower inflation, employment increases.
Joan
Is it necessary to make decision when it fails you
Evelin Reply
Pls when what fails u
MP
I think so
Kini
well i might naught know what you on about but i gotta tell you, it is necessary
Troy
yep
Ibe
Kk
MP
yep
Ibe
how can the demand side approach solve unemployment
Tshepiso Reply
demand solves unemployment when it is addressed with supply you can't just expect demand to work alone without supply the two are interconnected
Nureni
demand side approach to solve unemployment
Tshepiso Reply
no get ur questions
Ibe
differentiate between choice and scale of preference
ALFRED Reply
choice are the various wants of every individual whiles scale of preference is the list of unsatisfied wants arranged in order of important priority
Kini
choice refers to the act of selecting from alternatives or it refers to the act of choosing one thing instead of the other but Scale of preference refers to the listing of wants in order of important by providing the pressing need on top and the less pressing need at the bottom
Ebenezer
four cardinal types of demand
Henry Reply
what are the types of demand
Henry
they are the derived,complementary,substitute and supplementary demands
Kini
What is equilibrium
Khan
hi
Ayesha
hello
Kini
equilibrium is the state of balance where there is no tendency for a change to occur.
Kini
Derived, competitive, complementary and composite demands
Aziz
Hi
MP
why is economics said to be a dismal science?
Kini
hi friends
Ibe
hello
Owusu
fyn
Ibe
fyn what is meaning of monopoly
Ibe
monopoly is when a particular good is produced without competing with any other good.
Ebenezer
good evening
Tweneboah
draw the market demand curve from the individual demand curve?
Shilpa
With the aid of diagrams,compare the short run equilibrium positions of a perfect competitor and an imperfect competitors
Monlay Reply
What is the term consultation in economics?
Nthabiseng Reply
Could you please shed some light on this so called CONSULTATION?
Nureni
what is tourism
forgive Reply
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
Beverly 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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