# 4.1 Java1482-spectrum analysis using java, sampling frequency,  (Page 10/24)

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## Size of the peak at the folding frequency

Note that the peak in the bottom graph is approximately twice the height of the peaks in the other graphs. This is because the peak at the folding frequencyhas no mirror-image partner, and all the energy is concentrated in that single peak.

(Another interpretation is that two mirror-image peaks converge at the folding frequency causing the resulting peak to be twice as large aseither mirror-image peak. I will illustrate this effect with another example later.)

## A short fat peak at the top

You may also have noticed that the peaks in the top graph are shorter and wider than the peaks in the other graphs. This may be because the actualfrequency of the sinusoid for the top graph is about half way between the values of the twelfth and thirteenth bins for which spectral energy was computed. Thus,the energy in the sinusoid was spread between the bins on either side of the actual frequency.

This frequency spreading effect can be minimized by increasing the data length to 800 samples. This causes the frequency bins to be only half as wideand the peak in the top graph becomes tall and narrow just like the peaks in the other graphs. You should try this and observe the result when you run theprogram later.

It is also instructive to plot these spectra with a data length of 400 using the program named Graph06 . This will show you how the energy is distributed between the frequency bins. This is most effective when the graph isexpanded as described in the next section.

## Mapping the peaks to pixels

The broadening of the peak in the top graph may also have to do with the requirement to map the peaks in the spectrum to the locations of the actualpixels on the screen. If the location of the peak falls between the positions of two pixels, the plotting program must interpolate the energy in the peak so asto display that energy in actual pixel locations.

This effect can be minimized by plotting the same number of spectral values across a wider area of the screen. When you run this program later, click themaximize button on the Frame to cause the display to occupy the entire screen. That will give you a much better look at the actual shape of eachof the peaks. Do this using both Graph03 and Graph06 to plot the results.

(Note: When switching between the plotting programs, you may need to delete the class files from the old program and compile the new program toavoid having class files with the same names from the two programs becoming intermingled in the same directory.)

## Another DFT example

This next example is designed to illustrate the following features of the DFT algorithm which don't generally apply to an FFT algorithm:

• Ability to do spectral analysis on data of arbitrary lengths. (With many FFT algorithms, the data length must be a power of two.)
• Ability to zero in on an arbitrary range of frequencies and to ignore all other frequencies. (Most FFT algorithms always compute the spectrum at uniform frequency increments from zero to one unit less than the samplingfrequency.)

what is math number
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Need help solving this problem (2/7)^-2
x+2y-z=7
Sidiki
what is the coefficient of -4×
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
An investment account was opened with an initial deposit of \$9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
12, 17, 22.... 25th term
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
hi
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
Augustine
how do they get the third part x = (32)5/4
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
how
Sheref
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?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
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salma
Commplementary angles
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Sherica
im all ears I need to learn
Sherica
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Tamia
hii
Uday
hi
salma
hi
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Hello
opoku
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Ali
greetings from Iran
Ali
salut. from Algeria
Bach
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Nharnhar
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has \$5 and \$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
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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