Amplitude Modulation and Demodulation - Lab #4 | EEE 304, Lab Reports of Signals and Systems

Download Amplitude Modulation and Demodulation - Lab #4 | EEE 304 and more Lab Reports Signals and Systems in PDF only on Docsity! EEE 304 - Lab 4 Amplitude Modulation and Demodulation Introduction This lab introduces one of the basic modulation schemes known as the Amplitude Modulation (AM), through a simple and intuitive example in LabVIEW. AM is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave In addition to the graphical approach followed to perform a certain task in the previous labs, this exercise introduces the MathScript functionality in LabVIEW. MathScript adds math-oriented, textual programming to LabVIEW that utilizes .m file script syntax, the syntax widely used by alternative technical computing software such as MATLAB. It is possible to combine the intuitive LabVIEW graphical programming with MathScript. This lab contains two parts. The first part introduces Amplitude Modulation using a single tone (Sine Wave) as a message signal, which makes the understanding of the modulation technique very straight forward. The second part introduces the MathScript functionality and performs modulation of a speech signal. This will be helpful to understand the effects of modulation-demodulation on the quality of the reconstructed speech. 1. Basic Concepts 1.1. Modulation Modulation is a process that causes a shift in the range of frequencies of a signal. There are many applications in which shifting the spectrum is necessary. Audio signal frequencies are so low that impracticably large antennas are required for effective power radiation. In this case, shifting the spectrum to higher frequencies by modulation would be a simpler solution. Another application where modulation-demodulation is necessary is Frequency Division Multiplexing (FDM), where several signals are transmitted simultaneously over a channel by sharing its frequency bands. Communication that uses modulation to shift the frequency spectrum of a signal is known as carrier communication. In this mode, one of the basic parameters (amplitude, frequency, or phase) of a sinusoidal carrier of high frequency ωc is varied in proportion to baseband signal m(t). 1.2. Amplitude Modulation Amplitude modulation is characterized by the fact that the amplitude Ac of the carrier Accos(ωct +θc) is varied in proportion to the baseband (message) signal m(t), the modulating signal. The frequency and the phase of the carrier are fixed. Here for simplicity, we can assume that θc = 0. If the carrier amplitude Ac is made directly proportional to the modulating signal m(t), we obtain the signal m(t)cos(ωct). The carrier R(ω) = 1 1 ( ) [ ( 2 ) ( 2 )] ( ) [ ( 2 ) ( 2 )]. 2 2 2 4 c c c c c c A A M M M π δ ω δ ω ω δ ω ω ω ω ω ω ω+ + + − + + + + − It is evident from the equation above that the one part of the demodulated signal spectrum is centered at zero frequency and the other part is centered at 2ωc. In order to retrieve the original message signal M(ω), and to remove the high frequency components, r(t) is passed through a low pass filter with a cutoff frequency greater than B Hz. 1.4 Modulation Index Modulation index (µ) is defined as the ratio between the peak value of the message signal and the amplitude of the carrier signal. This indicates by how much the modulated signal varies around its original level. The value of µ < 1 results in under- modulation and µ > 1 results in over-modulation. Over modulation results in erroneous signal reconstruction if non-coherent demodulation (envelope detection) is used, but in case of coherent demodulation, any value of µ provides perfect reconstruction. 2. Exercise – Amplitude Modulation and Demodulation 2.1. Using a sine wave as the message signal. Now, as we have enough background of modulation theory, it is very straight forward to implement in LabVIEW. Figure 2 illustrates the basic block diagram for this modulation exercise. Figure 2. Basic block diagram for Amplitude Modulation 2.1.1 Generating message and carrier signals In this exercise, a sine wave is used as the message signal and the carrier is also a sine wave. The first step in this exercise is to generate the waveforms with desired input frequencies and a specific sampling rate. Place two Sine waveform generator functions in your block diagram. The sampling info to both the sine waveform generators use the following parameters. - Sampling frequency: 20 kHz. - # of Samples: 10000. # SAMPLES SAMPLING FREQUENCY BUNDLE SAMPLING INFO Figure 3. Building sampling info. Now, in order to study the effect of modulation index, generate controls for the amplitudes of message and carrier signal. Calculate the modulation index from these two amplitudes, as mentioned previously and display it in the front panel. To examine the effect of carrier frequency with respect to message frequency, generate controls corresponding to these two parameters. Notice that, these parameters are inputs to the sine wave generators. The range of the message signal frequency is set to be from 10Hz to 40Hz and the range of carrier frequency is set from 10Hz to 500Hz. The initial parameters to be chosen for the message signal are - Frequency: 10 Hz - Amplitude: 1 The initial parameters to be chosen for the carrier signal are - Frequency: 200 Hz - Amplitude: 1 Notice here, that the carrier frequency is much higher compared to the frequency of the message signal. 2.1.2 Get Waveform Components In order to use the signal outputs from the sine wave generators, it may be required to convert the output signal into an array of double values. This is accomplished by the function Get Waveform Components. This function can found in the functions palette (Programming >> Waveform >> Get Wfm Components). 2.1.3 Modulation The modulation process is accomplished in two steps - multiply the message signal to the carrier signal - Add the carrier signal to the result. In Figure 2, the modulated signal is provided to the Build Array function as one of the inputs, and the second input to this block is the message signal. This facilitates to view the input signal and modulated signal simultaneously. Now switch to the front panel and place a Waveform graph. Switch to the block diagram and connect the output of Build array block to the waveform graph. Also compute the FFT of the two time domain signals and view their frequency responses on another Waveform graph in the front panel. 2.1.4 Demodulation The task of the demodulation is left as an exercise for the students. As can be seen from the block diagram, only the inputs and the outputs of the demodulator are shown in the block diagram, as the underlying functionality has been grouped into a subvi. Hint: From the block diagram, it can be seen that the inputs to the demodulator are the carrier and the modulated signals. As described earlier, the demodulation is identical to the modulation process and it involves two steps. Figure 5. Illustration of MathScript Node. You can type the MathScript commands inside the blue structure or import an .m file directly. By right-clicking on the boundary, you can find options to create input and output nodes to the Mathscript node, which can in turn be used to communicate with other LabVIEW functions. In Figure 5, one input variable x and one output variable y have been created. Create a new VI and place a Mathscript node in it. Add one input variable x and one output variable y as shown in Figure 6. Type the following code inside the MathScript node. % Comments are preceded by % % Input Vector A A = [0 1 2 3 0]; % Square element of x to get y y = A.^x; % Notice that there is a dot after A % Plot x and y stem(x); hold on; stem(y,'r'); Pass a constant value to the input variable x (=2) and display the output variable y. Save and execute the VI. What do you observe? 2.3. Using an input speech file In this exercise you will design a modulator-demodulator for the input speech file provided (y.wav). You can reuse most part of the block diagram from Exercise 2.1 except for the following changes. Figure 6. shows the block diagram for this exercise. 2.3.1 Message and Carrier Signals The message signal is not a sinusoid but the input speech. You will make use of Mathscript nodes to read the .wav file and also playback the reconstructed speech. But you will use the same carrier signal of different frequency Exercise 2 (60 pts) 2(a) Write a mathscript “Mathscript node 1” with following parameters Input - Filename (String): Get the path of the input file and convert it into a string. Outputs - y (Dbl Array): Contains the contents of the speech file. - fs (Dbl): Sampling Frequency. - Am (Dbl): Peak value of y (use the command max(abs(y))). - len (Dbl): Number of samples in y (use the command length(y)); [You can read a .wav file in MathScript using the command [y,fs,nb] = wavread(Filename). nb is the number of bits, but we do not use that in this exercise.] 2(b) Write a mathscript “Mathscript node 2” with following parameters to playback the reconstructed speech. Input - y (Dbl Array): Output from the demodulator. - fs (Dbl): Sampling frequency. In general, to playback speech you can use the command sound(y,fs). In this exercise, use the command sound(4*(y-0.5),fs). Here, 4 is an amplification factor and 0.5 is an offset. 2(c) Why is there the amplification factor and the offset? (Give reasons with equations if possible) 2(d) Provide the snapshot of the block diagram and the front panel with the above mathscripts for the following parameters. Carrier signal - Frequency: 2000 Hz - Amplitude: 2 - low cutoff freq: 2500 [The sampling info to this sine waveform generator is obtained from the outputs of the Mathscript node 1.] What is the value of the modulation index obtained? 2.3.2 Design of the low-pass filter Try varying the # taps and the cut-off frequency, so that the reconstructed speech sounds like the original. If you hear a lot of distortion, you need to tune these two parameters. Fix the sampling frequency of this filter also to be fs. 2(e) Vary the low cut off frequency. At what low cut-off frequency do you observe distorted filtered signal ?