communication system porject

ECE401: Communication Systems

MATLAB Project 1- Due March 13@8:00AM

Single Side Band – Large Carrier Modulation and Coherent Demodulation The goal of this project is to explore transmission of a Single Side Band- Large Carrier (SSB- LC) signal and recovery of the message signal via Coherent Demodulation. You have been provided the MATLAB script file ‘ECE401_project1_student.m’ as a starting point. The provided code will generate a sampled 5000Hz carrier signal and plot a portion of the carrier signal in the time domain (vs. time) and its corresponding spectrum/PSD in the frequency domain. Examine the code and the resultant plots. In particular, closely examine how a portion (indices used) of the carrier signal is plotted and how the spectrum/PSD of the carrier signal is computed and plotted (since you will be using the same indices to plot portions of different signals, but more importantly since you will be applying the same technique/function (periodogram.m) to compute the spectrum of various filter’ impulse responses and signals. Note that the key of such technique/function is one of its input arguments, namely, the sampling frequency. Do help on periodogram.m for more information) You are to add your own code between each commented lines to perform the following four tasks:

1. Your first task is to generate a band limited message signal (limited to 500Hz). We shall denote such a band limited message signal as the original message (that will eventually be transmitted). To generate the original message signal:

a. Generate a [1 x n] array comprised of random values using the built-in function randn.m (i.e., signal without any band limitation) with the same number of samples, n, as the carrier signal. Note that you may use the ‘seed’ option to reproduce the same random values if desired (optional). Do help on randn.m for more information about the function in question. Plot a portion of the obtained result (signal without any band limitation) in the time domain (vs. time). Utilize the same indices used to display a portion of the carrier signal (i.e., 1000:3000) for plotting purposes only.

b. Next, you will design a Low Pass Filter (LPF) with a cut-off frequency in the order of 500Hz using the Filter Design and Analysis toolbox (type fdatool at the MATLAB command prompt). Refer to the appropriate commented lines for the technical specifications of the LPF. Export the impulse response of the LPF as the variable, ‘lpf’, in your workspace and ensure to save it. You will find the export command under ‘File’ of the fdatool window. Provide a plot of the impulse response vs. the sample indices, n. Provide a plot of the spectrum (effective frequency response) of the LPF filter using periodogram.m. You may want to increase the number of samples by a factor of two and use the axis command in order to obtain a decent plot when using periodogram.m.

c. Implement the LPF filter. In other words, process/filter the signal without any

band limitation by convolving the array generated in part (a) with the impulse response of the LPF to get the band limited message signal (Hint: use conv2.m with the ‘same’ option). Plot a portion (again using the same indices: 1000:3000) of the band limited message signal (the original message) vs. time and compare it to that of the portion signal without any band limitation in the time domain. Note that the resultant plot of the original message should look like what you saw in the lab (lab2 and lab3) when talking into the microphone and observing the amplified message signal on the scope. Moreover, provide a plot of the spectrum of the original message.

2. Your second task is to transmit the original message using Single Side Band-Large

Carrier (SSB-LC) Amplitude Modulation. To perform SSB-LC:

a. Perform amplitude modulation to obtain a Double Side Band – Suppressed Carrier (DSB-SC) modulated signal. Provide a plot of a portion (using the same indices as always) of the DSB-SC modulated carrier and the corresponding portion of the original message superimposed on the same plot vs. time in the time domain. Provide a plot of the spectrum of the DSB-SC modulated carrier signal.

b. Next, design a Band Pass Filter (BPF) using fdatool centered at 5500Hz with a bandwidth in the order of approximately 1000Hz. Refer to the appropriate commented lines for the technical specifications of the BPF. Export and save its impulse response. Provide a plot of the BPF impulse response vs. sample indices. Provide a plot of the spectrum (effective frequency response) of the BPF filter.

c. As discussed in class, filter the DSB-SC modulated carrier signal using the BPF to

obtain a Single Side Band – Suppressed Carrier (SSB-SC) modulated carrier signal. Plot a portion of the SSB-SC signal and the corresponding portion of the message signal superimposed on the same plot vs. time in the time domain. Provide a plot of the spectrum of the SSB-SC signal and compare it to that of the spectrum of the DSB-SC signal.

d. Generate a Single Side Band – Large Carrier (SSB-LC) modulated carrier signal

by simply adding the carrier signal to the SSB-SC modulated carrier signal. Plot a portion (using the same indices as always) of the SSB-LC signal and the corresponding portion of the original message superimposed on the same plot vs. time (note that you will need to add a DC offset to the original message (+1) for comparison purposes). Note that the SSB-LC is the transmitted signal. By transforming the DSB-SC to a SSB-LC, we have reduced transmission bandwidth and it will make it easier for coherent demodulation.

3. Your third task is to perform what is known as Coherent Demodulation with the assumption of receiving the transmitted SSB-LC signal.

Perform demodulation (by simply multiplying the received SSB-LC modulated carrier signal with the carrier signal). Process/filter the obtained signal using a LPF (the one that you previously designed in Task 1) to obtain the demodulated signal. Provide a plot of a portion of the demodulated signal with the appropriate scaling factor (i.e., multiplied by 4) and the corresponding portion of the original message signal superimposed on the same plot vs. time (Note that you will need to add a DC offset to the original message (+2) for comparison purposes).

4. Your last task is to investigate the loss of information of the communication system. In other words, to examine the error (absolute difference) between the demodulated signal (with the appropriate scaling factor) and the original message (with the appropriate DC offset).

a. Compute the error function.

[Hint: error_function = abs ( 4 *demodulated_signal – (original_message + 2 ) ) Provide a plot of a portion of the error function (using the same indices as usual/always) vs. time in the time domain.

b. Find the average of the portion of the error function in question (plotted in part (a)) and its standard deviation using MATLAB’s built-in functions: mean.m and std.m. What aspects of the communication system do you think contributed to such loss of information (error)? Moreover explain the reasoning behind scaling the demodulated signal (i.e., multiplying by 4) and offsetting the original message signal (i.e., adding 2).

Preparation and Submission of Project Prepare a formal report. Include all of your results. Figures should have a figure number and caption. Be sure figures are fully labeled and include legends as appropriate. In the body of the write-up explain all your figures and/or other results. All superimposed plots and comparisons should be accompanied with a clear and concise discussion about the similarities or discrepancies observed. (you can use the publish command in MATLAB for this purpose.) Please submit a hard copy of your formal report and copy of your MATLAB code, as well as a an electronic copy of the formal report and MATLAB script file to isidore (you can Zip all the files together). The electronic copy is to allow the teaching assistant to run your code to verify the results you submitted. You will be evaluated on your formal report and your code.. Note: You have to work alone on this project. Copying/sharing code from your friends is strictly prohibited. Violators (the one who copies and the one you copy from will both get a zero in the project.) Good Luck!