# 4.2 Java1483-spectrum analysis using java, frequency resolution  (Page 9/19)

 Page 9 / 19

## What we have learned so far

So far, the main things that we have learned is that shorter pulses require greater bandwidth, and the bandwidth required to faithfully represent atruncated sinusoidal pulse is the reciprocal of the length of the pulse.

## Separating closely spaced frequencies

Now we will look at the issues involved in using spectral analysis to separate and identify the frequencies of two closely-spaced spectral peaks for apulse composed of the sum of two sinusoids. Once again, we will begin by looking at some results and then discuss the code that produced those results.

## Five new pulses

The five pulses that we will be working with in this example are shown in Figure 4 . As you can see, these pulses are a little more ugly than the pulses shown in Figure 1 . As you can also see, as was the case in Figure 1 , each pulse appears to be a shorter or longer version of the other pulses in terms of itswaveform.

Figure 4. Five pulses with two sinusoids each.

## Produced by dsp032a

The plots in Figure 4 were produced by the program named Dsp032a , which I will briefly discuss later. (A complete listing of the program is shown in Listing 11 near the end of the module.) This program creates and displays pulses identical to those processed by the program named Dsp032 , which I will also briefly discuss later. (A complete listing of the program named Dsp32 is presented in Listing 12 .)

## Five time series containing pulses

The program creates and displays five separate time series, each 400 samples in length. Each time series contains a pulse and the pulses are differentlengths. As before, each of the pulses shown in Figure 4 is half the length of the pulse below it.

## The sum of two sinusoids

Each pulse consists of the sum of two sinusoids at closely spaced frequencies. The frequencies of the two sinusoids for all pulses are the same.

All frequency values are specified as type double as a fraction of the sampling frequency. The frequencies of the two sinusoids areequidistant from a center frequency of 0.0625 times the sampling frequency.

(Recall that 0.0625 was the frequency of the only sinusoid contained in the pulses shown in Figure 1 and processed by the program named Dsp031 .)

## The frequencies and pulse lengths

The frequency of one sinusoid is (0.0625 - 2.0/len) times the sampling frequency, where len is the length of the time series containing the pulse. (The value for len is 400 samples in this program.) The frequency of the other sinusoid is (0.0625 + 2.0/len) times the sampling frequency.

The lengths of the five pulses are:

• 25 samples
• 50 samples
• 100 samples
• 200 samples
• 400 samples

(Note that Figure 4 has tick marks every 25 samples.)

## The program named Dsp032a

The only new code in this program is the code in the constructor that creates the pulses and stores them in the data arrays. This code consists of fiveseparate for loops, one for each pulse. The code for the first for loop, which is typical of the five, is shown in Listing 6 .

Listing 6. New code in the the program named Dsp032a.
```public Dsp032a(){//constructor //Create the raw datafor(int x = 0;x<len/16;x++){ data1[x]= amp*Math.cos(2*pi*x*freq1) + amp*Math.cos(2*pi*x*freq2);}//end for loop //... code removed for brevity}//end constructor```

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Got questions? Join the online conversation and get instant answers!