# 4.4 Java1485-spectrum analysis using java, forward and inverse  (Page 9/14)

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(The real and complex parts of the frequency spectrum were computed at 256 frequencies between zero and the sampling frequency.)

There were 256 values plotted horizontally in each separate plot. Once again, to make it easier to view the plots on the rightmost end, I plotted the valueson a grid that is 270 units wide. This leaves some blank space on the rightmost end to contain the numbers, thus preventing the numbers from being mixed in withthe plotted values. The last actual data value coincides with the rightmost tick mark on each plot.

## Perform an inverse fourier transform

After modifying the complex spectrum as described above, the program performs an inverse Fourier transform on the modified complex spectrum to produce thefiltered impulse.

## The filtered impulse

The filtered impulse is shown as the bottom plot in Figure 4 . As you can see, the pulse is smeared out in time relative to the input pulse in the top plot.This is the typical result of reducing the bandwidth of a pulse.

(This particular modification of the complex spectrum resulted in a filtered pulse that has the waveform of a SIN(X)/X function. A differentmodification of the complex spectrum would have resulted in a filtered pulse with a different waveform.

This example also illustrates one of the miracles of digital signal processing. Energy appears in the output before it occurs in the input.Obviously that is not possible in the real world of analog systems, but many things are possible in the digital world that are not possible in the realworld.)

## Beginning of the class for Dsp037

Listing 8 shows the beginning of the class definition for the program named Dsp037.

Listing 8. Beginning of the class for Dsp037.
```class Dsp037 implements GraphIntfc01{ final double pi = Math.PI;int len = 256; double[]timeDataIn = new double[len];double[] realSpect = new double[len]; double[]imagSpect = new double[len];double[] angle = new double[len];//unused double[]magnitude = new double[len];double[] timeOut = new double[len];```

Listing 8 simply declares and initializes some variables that will be used later.

## Beginning of the constructor

The constructor begins in Listing 9 .

Listing 9. Beginning of the constructor.
```public Dsp037(){//constructor timeDataIn= 90;```

Listing 9 creates the raw pulse data shown in the topmost plot in Figure 4 .

When the array object referred to by timeDataIn is created, the values of all array elements are set to zero by default. Listing 9 modifies one of the elements to have a value of 90. This results in a single impulse atan index of 32.

## Compute the Fourier transform

Continuing with the constructor, the code in Listing 10 uses an FFT algorithm in the method named transform (discussed earlier) to compute the Fourier transform of the impulse.

Listing 10. Compute the Fourier transform.
```//Compute FFT of the time data and save it in // the output arrays.ForwardRealToComplexFFT01.transform( timeDataIn,realSpect, imagSpect,angle, magnitude);```

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
hi vedant can u help me with some assignments
Solomon
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
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Abhi
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Commplementary angles
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Ali
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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?
how did you get the value of 2000N.What calculations are needed to arrive at it
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