School of Applied Medical Sciences
Biomedical Engineering Department
Medical Signal Processing Fall 2014/2015
Experiment Title: Amplitude Modulation Post Lab Report
Student: Deema Abuzaid ID: 2009302030
MATLAB Codes Implemented & Results: Part 1: t=(1:1/2000:2); % x=sawtooth(2*pi*5*t); c=cos(2*pi*250*t); AM=x.*c; figure subplot(3,1,1) plot(t,x) title ('Signal x(t)') xlabel ('time (s)') ylabel ('Amplitude') subplot(3,1,2) plot(t, c) title ('Signal c (t)') xlabel ('time (s)') ylabel ('Amplitude') subplot(3,1,3) plot(t, AM) title ('Signal AM (t)') xlabel ('time (s)') ylabel ('Amplitude')
Resulting Graphs
Figure 1: Original sawtooth signal vs. carrier signal vs. amplitude modulated sawtooth signal resulting from the multiplication of both signals
Part 2: n=length(x); Freq= (-2000/2:2000/n:(2000/2)-(2000/n)); X=fft(x); C=fft(c); MagX=abs(X); PhaseX=angle(X); MagC=abs(C); PhaseC=angle(C); PSDX=abs(X.^2); PSDC=abs(C.^2); figure subplot(5,1,1) plot(t,x); title 'Original Signal x(t)' xlabel 'time (s)' ylabel 'Amplitude' subplot(5,1,2) plot(Freq, MagX); title 'Magnitude of X' xlabel 'Frequency Hz' ylabel 'Magnitude' subplot(5,1,3) plot(Freq, PhaseX); title 'Phase of X' xlabel 'Frequency Hz' ylabel 'Angle' subplot(5,1,4) plot(Freq, X); title 'Density Distribution of X' xlabel 'Frequency Hz' ylabel 'FFT of X' subplot(5,1,5) plot(Freq, PSDX); title 'PSD of X' xlabel 'Frequency Hz' ylabel 'PSD of X' figure subplot(5,1,1) plot(t,y); title 'Original Signal c(t)' xlabel 'time (s)' ylabel 'Amplitude' subplot(5,1,2) plot(Freq, MagC); title 'Magnitude of C' xlabel 'Frequency Hz' ylabel 'Magnitude' subplot(5,1,3) plot(Freq, PhaseC); title 'Phase of C' xlabel 'Frequency Hz' ylabel 'Angle' subplot(5,1,4) plot(Freq, C);
title 'Density Distribution of C' xlabel 'Frequency Hz' ylabel 'FFT of C' subplot(5,1,5) plot(Freq, PSDC); title 'PSD of C' xlabel 'Frequency Hz' ylabel 'PSD of C'
Resulting Graphs
Figure 2: Original sawtooth signal plotted vs. the magnitude, phase, and PSD after FFT
Figure 3:The carrier signal plotted vs. the magnitude, phase, and PSD after FFT
Part 3: AM2=4*[1+(0.5*x)].*c; figure subplot(3,1,1) plot(t,x) title ('Signal x(t)') xlabel ('time (s)') ylabel ('Amplitude') subplot(3,1,2) plot(t, c) title ('Signal c (t)') xlabel ('time (s)') ylabel ('Amplitude') subplot(3,1,3) plot(t, AM2) title ('Signal AM2 (t)') xlabel ('time (s)') ylabel ('Amplitude')
Resulting Graphs
Figure 4: Original, carrier and amplitude modulated signal after loweing the modulation index to half
Part 4: fs=2000; x2=ppgorginal; x2=x2'; t2=(1:length(x2))/fs; c2=cos(2*pi*750*t2); %carrier signal AM3=x2.*c2; %amp. modulated signal figure subplot(3,1,1) plot(t2,x2) title ('Signal x2(t)') xlabel ('time (s)') ylabel ('Amplitude') subplot(3,1,2) plot(t2, c2) title ('Signal c2 (t)') xlabel ('time (s)') ylabel ('Amplitude') subplot(3,1,3) plot(t2, AM3) title ('Signal AM3 (t)') xlabel ('time (s)') ylabel ('Amplitude')
Resulting Graphs
Figure 5: PPG signal vs. carrier signal vs. amplitude modulated PPG
Discussion
In part one, a ‘sawtooth’ signal is generated in MATLAB and another sinusoidal signal is generated and set to be the carrier signal in order to do amplitude modulation on the sawtooth signal. In figure 1, the original signal, carrier signal, and the modulated signal generated by multiplying both signals are plotted. As seen in the g raph, the carrier signal carried the original sawtooth signal from one frequency band to another. The frequency of the carrier signal is set to be much higher than the highest frequency in the original signal in order to make it easier to separate the two signals after demodulation. In part two, the FFT is applied to the sawtooth signal and the carrier signal (each separated) and the magnitude, phase and PSD of each signal after FFT are plotted. As seen in the graphs, the important information on each signal’s frequency can be extracted. In part three, the effect of the modulation index is tested by cutting it to half and observing how it affects the amplitude modulated sawtooth signal. As seen in figure 4, the AM signal looks like
half of the original signal, which indicates that the modulation index defines the range of the original signal to be modulated. In part four, a prerecorded PPG signal (which is the measurement of the changes in the blood flow or volume in a specific organ) recorded using a PPG sensor on the finger is used and processed using amplitude modulation. After choosing the appropriate frequency of the carrier signal, the PPG signal is multiplied by the carrier signal and the result is plotted in figure 5. After applying AM the signal that is now carried to a different frequency band can be demodulated and useful information can be extracted from it now th at it is moved to a frequency range away from any noise effects. Conclusion
A PPG is a way to measure the changes in the blood flow or volume in a specific organ. It is usually used on the tip of the finger. It can be useful in approximating the amount of oxygen reaching the cells. Amplitude modulation is a sign al processing technique that can be used for de-noising signals. During amplitude modulation the original signal is multiplied by a carrier signal which must have a much larger frequency than the highest frequency in th e original signal (f c > 2f max). This results in carrying the original signal to a different frequenc y band which is defined by the carrier signal. The modulation index controls the range of which the original signal is to be carried. There are many applications for amplitude modulation in medical signal processing. One application is the detection of blood loss which is done using the AM of the PPG signal. [1]
References
[1] http://www.ncbi.nlm.nih.gov/pubmed/22255583
