# 4.4 Java1485-spectrum analysis using java, forward and inverse  (Page 3/14)

 Page 3 / 14

This program can be run with either Graph03 or Graph06 in order to plot the results. Enter the following at the command-line prompt to run the program with Graph03 after everything is compiled:

`java Graph03 Dsp035`

The program was tested using JDK 1.8 under Windows 7.

## The order of the plotted results

When the data is plotted (see Figure 1 ) using the programs Graph03 or Graph06 , the plots appear in the following order from top to bottom:

• The input time series
• The real spectrum of the input time series
• The imaginary spectrum of the input time series
• The amplitude spectrum of the input time series
• The output time series produced by the inverse Fourier transform

## The format of the plots

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

## The forward Fourier transform

A static method named transform belonging to the class named ForwardRealToComplex01 was used to perform the forward Fourier transform.

(I explained this class and the transform method in the earlier module titled Spectrum Analysis using Java, Sampling Frequency, Folding Frequency, and the FFT Algorithm .)

The method named transform does not implement an FFT algorithm. Rather, it implements a DFT algorithm, which is more general than, but much slower than anFFT algorithm.

(See the program named Dsp036 later in the module for the use of an FFT algorithm.)

## The inverse Fourier transform

A static method named inverseTransform belonging to the class named InverseComplexToReal01 was used to perform the inverse Fourier transform. I will explain this method later in this module.

## Results

Before getting into the technical details of the program, let's take a look at the results shown in Figure 1 .

The top plot in Figure 1 shows the input time series used in this experiment.

Figure 1. Forward and inverse transform of a time series using DFT algorithm.

## Length is a power of two

The time series is 256 samples long. Although the DFT algorithm can accommodate time series of arbitrary lengths, I set the length of this timeseries to a power of two so that I can compare the results with results produced by an FFT algorithm later in the module.

(Recall that most FFT algorithms are restricted to input data lengths that are a power of two.)

## The input time series

As you can see, the input time series consists of three concatenated pulses separated by blank spaces. The pulse on the leftmost end consists simply of somevalues that I entered into the time series to create a pulse with an interesting shape.

The middle pulse is a truncated sinusoid.

The rightmost pulse is a truncated square wave.

## The objective

The objective of the experiment is to confirm that it is possible to transform this time series into the frequency domain using a forward Fouriertransform, and then to recreate the time series by using an inverse Fourier transform to transform the complex spectrum back into the time domain.

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
how do they get the third part x = (32)5/4
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
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
how do you translate this in Algebraic Expressions
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?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
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
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
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
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
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.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!