EXPERIMENT 4 FREQUENCY MODULATION USING SCILAB 1.0 OBJECTIVES: 1.1 To perform he frequency modulation simulation using Scilab. 1.2 To analyze the frequency-modulated signal in time domain and frequency domain representation. 1.3 To plot the frequency spectrum of frequency-modulation signal using Scilab. 2.0 Equipment / Apparatus 1.0 SCILAB Software 3.0 INTRODUCTION Before an information signal is transmitted through a communication channel, some type of modulation process is typically utilized to produce a signal that can easily be accommodated by the channel. There are three properties of an analog signal that can be varied (modulated) by the information signal. Those properties are amplitude, frequency and phase. In previous lab, we have deal with amplitude modulation. Phase modulation (PM) and frequency modulation (FM) are both forms of angle modulation. The main difference between angle modulation and amplitude modulation is that in angle modulation, the information is contained in the angle of the carrier whereas in amplitude modulation, the information is in the amplitude of the carrier. We will be dealing only with FM in this lab. The theories and concepts are similar for PM. FREQUENCY MODULATION: In FM, the phase angle of a carrier signal Ac cos(2πfct) is varied proportionally to the integral of the message signal x(t), the frequency modulated signal xc(t) is: (1) where kf is a constant. The instantaneous frequency of the FM signal is given by: (2) In the special case of tone-modulated FM, the message signal is a sinusoid EKT231 – COMMUNICATION SYSTEM the instantaneous phase deviation of the modulated signal is (3) and the modulated signal is given by: (4) where the parameter β is called the modulation index defined as (5) (6) and represents the maximum phase deviation produced by the message signal. The parameter ∆f represents the peak frequency deviation of the modulated signal. The modulation index is defined only for tone modulation. The calculation of the spectrum of an FM signal is difficult since frequency modulation is a nonlinear process. However, for the special case of tone-modulation an equivalent expression for Eq.(4) is (7) This equation describes the modulated signal as a series of sinusoids whose coefficients Jn(β) are given by the Bessel function of the first kind and nth order. The bandwidth of the tone-modulated FM signal can be estimated by the Carlson’s rule, and it depends on the modulation index and the frequency of the modulating tone: (8) From this equation it can be noticed that a small value of β << 1 will result in a bandwidth of about 2fx. Modulated signals with this condition are referred to as narrowband FM signals. Large values of the modulation index will produce signals with relatively large bandwidth, or wideband FM signals. The examples below show how to use Scilab Software to produce frequency modulation signals in time domain and frequency domain. Study the source code given and simulate to see the plotting signal. EKT231 – COMMUNICATION SYSTEM I) Plotting frequency modulation signal in time domain This source-code is to plot frequency modulation signal in time domain representation. Example 1: t= 0:1/1000:1; // declare time interval Ac = 9; // amplitude of carrier signal Am = 4; // amplitude of modulating signal fc = 100; // carrier frequency fm = 50; // modulating frequency //Carrier signal Vc = Ac *cos (((2*%pi)*fc)*t); //Modulating signal Vm = Am * sin (((2*%pi)*fm)*t); //Frequency modulation signal m = 2; //modulation index Vfm = Ac*cos(((( 2*%pi)*fc)*t)+m*sin(((2*%pi)*fm)*t)); // plot signal subplot (311); plot (t, Vm) title (‘Modulating signal’) subplot (312); plot (t,Vc); title (‘Carrier signal’) subplot (313); plot (t,Vfm) title (‘Frequency modulating signal’) EKT231 – COMMUNICATION SYSTEM II) Plotting frequency modulation signal in both time and frequency domain. We now consider the calculation of the spectrum of an FM (or PM) signal using the FFT algorithm. As can be seen from the Scilab soure-code, a modulation index of 3 is assumed. Example 2: N = 1024; // Number of points fs = 4096; // Sampling frequency t = (0:N-1)/fs; // Time vector fm = 50; // Message Freq 1 Em = 3; // Amplitude of modulating signal m = 3; // Modulation Index fc = 300; // Carrier frequency Vm = Em*cos(2*%pi*fm*t); // Modulating signal // Frequency Modulation (FM) Vfm = cos(2*%pi*fc*t+Vm); Vf = (2/N)*abs(mtlb_fft(Vfm,2048))1024; //Frequency modulation in time domain f = (fs*(0:N/2))/N; subplot(2,1,1); //Time domain plot plot(t(1:N/2),Vfm(1:N/2),t(1:N/2),Vm(1:N/2),"r"); title(‘Time Domain Representation’); xlabel(‘Time’); ylabel(‘Modulated signal’); subplot(2,1,2); //Frequency Domain Plot plot(f(1:256),Vf(1:256)); title(‘Frequency Domain Representation’); xlabel(‘Frequency (Hz)’); ylabel(‘Spectral Magnitude’); EKT231 – COMMUNICATION SYSTEM III) Plotting FM frequency Spectrum In this example, we consider a Scilab program to computing the amplitude spectrum of an FM (or PM) signal having a message signal consisting of a pair of sinusoids. The single-sided amplitude spectrum is calculated. The single-sided spectrum is determined by using only the positive portion of the spectrum represented by the first N/2 points generated by the FFT program. In the following Scilab code, N is represented by the variable number of points. Example 3: fs = 1000; // sampling frequency delt = 1/fs; //sampling increment t = 0:delt:1-delt; //time vector N=1024 // number of points fn = (0:N/2)*(fs/N); // frequency vector for plot m1 = 2*cos(((2*%pi)*50)*t); // modulation signal 1 m2 = 2*cos(((2*%pi)*50)*t) + 1*cos(((2*%pi)*5)*t); //modulation signal 2 xc1 = sin((((2*%pi)*250)*t)+m1); // modulated carrier 1 xc2 = sin((((2*%pi)*250)*t)+m2); // modulated carrier 2 asxc1 = (2/N)*abs(fft(xc1)); // amplitude spectrum 1 asxc2 = (2/N)*abs(fft(xc2)); //amplitude spectrum 2 ampspec1 = asxc1(1:((N/2)+1)); // positive frequency portion 1 ampspec2 = asxc2(1:((N/2)+1)); // positive frequency portion 2 subplot(211) plot2d(fn,ampspec1) xlabel('Frequency - Hz'); ylabel('Amplitude'); subplot(212) plot(fn, ampspec2, 'k'); xlabel('Frequency - Hz'); ylabel('Amplitude'); EKT231 – COMMUNICATION SYSTEM 4.0 QUESTIONS: 1. Why we are using FFT algorithm in the Scilab program? 2. What is the carrier frequency used in Example 2 and 3? 3. Perform the following instructions: i) Create a vector time 't' that varies from zero to one cycle with an interval 1/1000 or 1/5000 ii) Create a message and carrier signal with a single sine frequency. Use the following values: - Amplitude of carrier signal = 5V - Amplitude of carrier signal = 7V - Carrier frequency = 100 Hz - Modulating frequency = 20 Hz iii) Create the modulated signal using FM equation. The value of modulation index is equals to 5. iv) Plot and label the FM signal in time and frequency domain. 4. Given the message signal in a form of sinusoidal signal as below: x ( t ) cos 2 ( 25 ) t cos 2 ( 15 ) t The modulation is given by m ( t ) 2 sin 2 ( 25 ) t 4 sin 2 ( 15 ) t The modulated carrier signal becomes x ( t ) cos[ 2 ( 300 ) t 2 sin 2 ( 25 ) t 4 sin 2 ( 15 ) t ] c Use Scilab to illustrate the single-sided amplitude spectrum of the above. EKT231 – COMMUNICATION SYSTEM

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# Experiment 4 - Frequency Modulation using Scilab