Power spectral density, Electrical Engineering

Assignment Help:

Power Spectral Density:

  • To introduce the Power Spectral Density (PSD) of a random signal.
  • To study classical methods for PSD estimation.
  • To investigate model-based methods for PSD estimation.

Exercises:

The Power Spectral Density (PSD) of an ergodic (i.e. time average statistics are identical to ensemble average statistics), discrete, random signal is the Fourier transform of its autocorrelation function, as given by

1233_Power Spectral Density.png

where xx( ) is the autocorrelation function for the discrete random signal x and is normalised frequency. This is also known as the Wiener-Khintchine theorem. To calculate this expression exactly requires knowledge of all the autocorrelation function values for the discrete random signal x. Given only a ?nite length data record, as in many practical problems such as speech and array processing, namely [ ] =0 1 -1 it is only possible to estimate this quantity.

One method to estimate the PSD is based on the Fast Fourier Transform (FFT). This method is called the periodogram, as defined by

818_Power Spectral Density1.png

Notice that the PSD is being estimated at N discrete-frequencies, which in terms of normalised frequencies corresponds to =0 1 ( -1) . The sampling interval T is implicity assumed, for convenience, to be unity.


Related Discussions:- Power spectral density

Name 5 different addressing modes, The five addressing modes are given belo...

The five addressing modes are given below: Immediate, Register, Direct, Implied addressing modes           Register indirect,

Determine modulation index, Q. If the output signal fromanAMmodulator is gi...

Q. If the output signal fromanAMmodulator is given by u(t) = 5 cos 1800 πt + 20 cos 2000 πt + 5 cos 2200 πt , determine: (a) The modulating signal m(t) and carrier c(t). (b)

Demodulators for FM, Demodulators for FM Figure  shows a block diagram ...

Demodulators for FM Figure  shows a block diagram of a general FM demodulator, which is implemented by generating an AM signal whose amplitude is proportional to the instantane

Electric automobile system specifications, The automobile shall not rely on...

The automobile shall not rely on fossil fuel for energy. The automobile shall be designed using available and emerging technology. The automobile shall seat at least five

Define sampling frequency, Define Sampling Frequency? Since real analog...

Define Sampling Frequency? Since real analog signals consist of several frequencies, spectrum of the input signals should be limited to make sure that no signal energy exists a

Show capital asset pricing model, Q. Show Capital asset pricing model? ...

Q. Show Capital asset pricing model? This model was developed by the William F Sharpe ( 1990 Nobel prize winner in the economy ) and john linter in 1960. The model attempt to c

Thevenins theorem, advantages and disadvantages of thevenins theorem

advantages and disadvantages of thevenins theorem

Find load resistance and voltage, Q. Find load resistance and voltage? ...

Q. Find load resistance and voltage? Let the amplifier block be connected to a current source at the input terminals, as shown in Figure(a), and to a load resistance R L at it

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd