<< Chapter < Page
  Digital signal processing - dsp     Page 12 / 14
Chapter >> Page >

As before, the lengths of the individual time series will be 80, 160, 240, 320, and 400 samples respectively.

Spectral analysis using fourier transform

I will perform a Fourier transform on each of the time series in an attempt to show that the spectrum of each time series consists of two peaks, (two spectral lines) , with one peak corresponding to each of the sinusoids added together to create the time series. The five spectra are shown in Figure 12 .

Figure 12. Spectra of five different time series of different lengths.
missing image

Discuss the longest time series first

Once again, let's begin with the plot at the bottom of Figure 12 . As you can see, this spectrum shows two very distinct spectral peaks. Thus, for this amountof frequency separation and a length of 400 samples, the Fourier transform did a good job of separating the two peaks.

Resolution for shorter averaging windows

Moving upward in Figure 12 , we see that the Fourier transform on the time series with a length of 320 samples (the fourth plot from the top) also did a good job of separating the two peaks.

However, with respect to separation the process began to deteriorate for lengths of 240 samples and 160 samples.

No peak separation for 80-sample average

For a length of 80 samples, the two peaks merged completely.

A horizontally-expanded view of the spectra

Figure 13 shows a horizontally-expanded view of the same spectral data to give you a better idea of the structure of the peaks. The plots in Figure 13 show only the first fifty frequency values.

Figure 13. Spectra of five different time series of different lengths
missing image

You may find it interesting to make a side-by-side comparison of Figures 13 and 11 in separate browser windows.

Zero-valued points in the spectra

Before leaving this topic, there are a few more things that I want to show you. If you go back and look at the bottom plot in Figure 11 , you will note an interesting characteristic of that plot. In particular, starting at the peak andmoving outward in both directions, every second plotted value is zero. I'm going to explain the reason for and the significance of this characteristic.

(As I mentioned earlier, there are also zero-valued points in the spectra of the time series with the shorter averaging windows. Once youunderstand the reason for the zero-valued points, you can correlate the positions of those points to the length of the averaging window.)

400 spectral values were computed

To begin with, the Fourier transform program that was used to compute this spectrum computed 400 values at equally spaced points between zero and thefolding frequency (only the first 50 values are shown in Figure 11 ). Thus, each of the side-by-side rectangles in Figure 11 represents the spectral value computed at one of the 400 frequency points.

Sampling frequency was one sample per second

The sinusoid that was used as the target for this spectral analysis had 32 samples per cycle. Since this sinusoid was generated mathematically instead ofbeing the result of sampling an analog signal, we can consider the sampling frequency to be anything that we want.

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Digital signal processing - dsp' conversation and receive update notifications?