Information Theory and Signal Processing Assignment

Question(1).

a). Consider the following expression, which refers to an M-input N-output communication channel, using  the usual channel notation, which is proposed to give a value of Q shown in the equation (1),

Sketch a diagram that describes the channel referred to by Q, label your sketch with the parameters given in the equation. Use a value of M =4 and N = 4.

List all the parameters and give a brief explanation of each one in relation to the equation for Q.

Assuming equation (1) refers to a channel with a probability of symbol error p given as 0.0001, which is the same for all error transitions, and that p(x0) = 0.5, p(x1) = 0.15, p(x2) = 0.1, p(x3) = 0.25. Use these values to provide a description of the channel based on information theory. Demonstrate the effect of these values on the value of Q when  a log base of four is used.

b).

A discrete memoryless source is described by the following distribution.

P(x0) = 5/10, p(x1) = 4/10 and p(x2) = 1/10.

Encode this alphabet into binary words using the Huffman coding method.  Apply information theory such as entropy, coding average, coding efficiency to fully quantify this method.

Assuming the source generates symbols at 1 million symbols per second sketch a suitable labelled signal diagram that could be used to represent an input word of x0,x1,x2.

Based on the same source specification explain how the efficiency could be increased whilst still incorporating Huffman coding.

Question (2).

A  message signal comprises a sine wave of amplitude 1V frequency 1 Hz, and phase zero added to another sine wave of amplitude 1V, frequency 1 Hz, and unknown phase, the message is to be subsequently converted to digital. The relevant data relating to this process is contained in the spreadsheet assignmentFirstSit, worksheet Q2 that is in the assessment folder on Blackboard.  Plot the data in the columns D and E on the y axis against the data in column A on the x axis.

Provide a description of the plot of column D.

Provide a description of the plot of column E.

Provide a description of the data in columnC.

Provide a description of the data in column B.

Modify plot D so that that the value of each point is repeated ten times and then repeated five times followed by  five zeros, plot and describe the resulting shapes produced for each one as compared to that in column D alone.

Question 2 is to be saved in an Excel file in a worksheet labelled  Q2 with the Excel file name your_name.xls that displays relevant plots, and is to uploaded onto Blackboard by the date and time given in the assignment

Question (3).

A modulated signal is given as  where (t) = [km(t)]2.

Plot a labelled graph in Excel of   and  over a time scale from t = 0 to 1e-3 when m(t) ramps linearly from 1 to 0 and k = /5 over this time scale.

Provide a technical discussion of how this can be used to implement modulation.

Include the plots in your assignment.

Question 3 is to be saved in an Excel file in a worksheet labelled  Q3 with the Excel file name: your_name.xls that displays relevant plots, and is to uploaded onto Blackboard by the date and time given in the assignment.

Assessment criteria applies to individual and part of, questions.

Assessment criteria – see the Excel as

Module learning outcomes to be assessed:

·Describe the techniques and components used to communicate signals over a particular media.

·Characterise and analyse the performance of computer networks and communication systems using appropriate methods.