Compute the ensemble mean and standard deviation, Electrical Engineering

Write three m ?les to generate M ensemble members of length N, for the following three random processes:

i) function v=rp1(M,N);






ii) function v=rp2(M,N)




iii) function v=rp3(M,N)



v=(rand(M,N)-0.5)*m + a;

Try to understand what kind of signal each process generates and thereby decide which process is ergodic and/or stationary.

- Compute the ensemble mean and standard deviation for each process and plot them as a function of time, using 100 members each of length 100, for each process. Comment on the stationarity of each process.

- Generate 4 members of length 1000 of each process, and measure the mean and standard deviation of each member. Hence comment on the ergodicity of each process.

- Write the mathematical description of each of the three stochastic processes. Calculate the theoretical mean and variance for each case and compare the theoretical results with those obtained by the measurements.

c) Repeat a) but with the randn function which generates a random signal with theoretical ly zero mean and unity standard deviation.

d) The autocorrelation function for a statistically stationary random discrete signal may be calculated from

1922_Compute the ensemble mean and standard deviation.png

More formally, the discrete signal is implicitly being assumed to be autocorrelation ergodic, that is, the nature of the random signal x is such that the discrete samples themselves can be used to calculate the autocorrelation function. In a real application, only a ?nite number of samples, N, of x will be available and, therefore, it is necessary to make an assumption upon unknown values of x. Usually, these are assumed to be zero. An unbiased estimate of the autocorrelation function can be calculated from

137_Compute the ensemble mean and standard deviation1.png

Notice that from a length N vector x,a(2 - 1) length estimated autocorrelation function is obtained.

- Employ the xcorr(x,'unbiased') function within MATLAB to calculate the unbiased estimate of the autocorrelation function for a length 1000 random signal generated with the randn function. Display and explain the result, i.e. is it symmetric and, if so, about which point? Use k = -999:999 for the x axis.

Note: To understand the symmetry in the autocorrelation function, draw a simple ?nite random continuous wave (wave ); below that draw the same wave with a time shift (wave ); below that draw the same wave with time shift - (wave ). Compare the common non-zero regions between and , and the common non-zero regions between and . It is seen that the multiple of the two waves in both non-zero regions is the same.

- Explain what is happening at large | T |

Hint: What happens to the number of non-zero terms on the rhs of the equation? Use the axis command to concentrate upon the region | T | 50. Notice the autocorrelation function is essentially zero for non-zero shifts. This is a fundamental property of such a random signal, that is, the autocorrelation function reveals that there is no correlation between shifted versions of x. In practice, this means that for such a random signal, knowledge of one signal sample has no bearing on any of its past or future values.

The samples are said to be uncorrelated.

In theory, a purely random signal will have an autocorrelation function which is a discrete delta function. This shows that there is no correlation (i.e. similarity) between the random signal and a shifted version of it.

Posted Date: 2/27/2013 5:51:48 AM | Location : United States

Related Discussions:- Compute the ensemble mean and standard deviation, Assignment Help, Ask Question on Compute the ensemble mean and standard deviation, Get Answer, Expert's Help, Compute the ensemble mean and standard deviation Discussions

Write discussion on Compute the ensemble mean and standard deviation
Your posts are moderated
Related Questions
Discuss some features of Pentium series of microprocessors. The Pentium is a CISC microprocessor, 32-bit superscalar.  The term superscalar is utilized for the processor that

1. Determine the capacitance length of a PCB embedded stripline, assuming no fringing of the electrostatic field. 2. Determine the capacitance/unit length of the same embedded stri

Design a low noise amplifier using an Infineon RF transistor BFP640. The amplifier is to be used to amplify the L2 GPS signal and so the centre frequency is 1227MHz and bandwidth 4

Q. A magnetic force exists between two adjacent, parallel current-carryingwires. Let I1 and I2 be the currents carried by the wires, and r the separation between them.

Q. Illustrate simple telephone communication system with circuit and equation of current flow in microphone? Ans: Simple  Telephone  Communication: In the simplest form of

1- Use 4-to-16 decoder and some residue gates to recognize the following functions F1(A,B,C)= S(1,2,4,5,7) F2(A,B,C,D)= S(1,2,4,5,7,10,12,14,15) F3(A,B,C,D,E)= S(1,2,4,5,7,10,12,1

Explain DAA instruction. DAA: The DAA instruction follows the instruction ADC or ADD to adjust the result in a BCD result. The DAA instruction performs only with the AL registe

Q. How to convert Decimal to Binary number? To convert the decimal to binary is slightly more difficult. There are two procedures (Methods) that may be used to convert from dec