Dear Tarek Mohamed Salem, Power spectral density function is a very useful tool if you want to identify oscillatory signals in your time series data and want to know their amplitude. Power spectral density tells us at which frequency ranges variations are strong and that might be quite useful for further analysis.

using PSD can i know the frequencies carrier range for oscillatory signals.

and why used bandpass filter after compute PSD

As Afaq Ahmad well said above, if you compute power spectral density of your signal you have estimated its frequency content and that is rather useful. For instance, in the analysis of atrial fibrillation (AF) it is important to know what are the dominant frequencies and where are they as they relate to atrial activation and it is useful to know the path of the abnormal atrial activation to be able to ablate the sites responsible for triggering or maintaining AF. Still in cardiology one very famous QRS detector developed by Pan and Tompkins uses as a pre-emphasis filter a bandpass to increase the SNR of the QRS complexes while attenuating other waveforms and noise. The bandpass is around 17 Hz or 19 Hz. How do we know that? We estimated the power spectrum associated to a large population of QRS complexes. The examples are many. As you work more in Biomedical Engineering you will collect your own. Best wishes!

Another example of where PSD analysis can be very useful is in determining the frequency content of Images. Determining the frequency content of images is one of the initial and important steps to many image processing techniques like compression,edge detection and analysis, contour detection etc.

PSD is only useful for stationary signals. If the signal to analysis is non-stationary, you 'd better try wavelet spectrum or Hilbert-Huang spectrum.

@Xu what do you mean by stationary signa

The statistical parameters of stationary signals remains constant over time. (http://en.wikipedia.org/wiki/Stationary_process) Deterministic signals and some random signals such as white noise belong to this category. As PSD calculates the FFT over the whole signal, so the resulting spectrum you get is the overall situation. You will never know the happening time of a specific frequency. So, PSD can be used for stationary signals, because such signal's statistical parameters don't change over time.

However, there still exist non-stationary signals, such as speech signals and bio-physical signals. (http://iitg.vlab.co.in/?sub=59&brch=164&sim=371&cnt=1104) Their parameters such as the mean and variance changes over time, so PSD is not suitable for these signals anymore. Although Short TimeFourier Transformation can be used for this, wavelet analysis and Hilbert-Huang spectrum are better tools for non-stationary signals.

http://www.hpl.hp.com/hpjournal/94dec/dec94a6a.pdf

http://paos.colorado.edu/research/wavelets/

https://www.google.com.hk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&ved=0CD4QFjAC&url=http%3a%2f%2fwww%2eifremer%2efr%2fweb-com%2fmolagnon%2fbv%2fschlurmann%2epdf&ei=qeF6UuDmI6iSiAeTrICIAw&usg=AFQjCNHT96KRVoQL4evRX3Nvyxjgh_u6Pw

Please i want to know what is cyclic prefix for signal properties

PSD gives you the strength of a signal over a period of time. it is nothing but different ways of computing the sum of FFT of a signal.

What is the reason of smoothing out the short time power spectrum of noisy speech signal?

Dear Sam Wesley

The reason for smoothing out the power spectrum is that the spectrum is like a histogram. Say you generate a histogram of the ages of the students in a school. If your class size is too small (say a couple of days) then the histogram becomes noisy. As you increase the class size then the histogram becomes smoother (but you lose resolution). If the number of individuals is high then you can have a smaller class size (higher resolution) and still obtain a reasonably smooth histogram. I hope this is clear and helpful :-)

No not clear.

@ Sam Wesley

Draw histogram of the ages of your classmates using different class sizes. I suggest you use a range of short class sizes say histogram 1 uses class size of 2 months, histogram 2 uses class size of 6 months, histogram of 1 year and histogram 4 of 2 years. Then put them side by side and think.