DSP using MATLAB example Example3.7

On the code:

X1 = rand (1,11); x2 = rand (1,11); n = 0:10;alpha = 2; beta = 3;  K = 0:500;              W = (pi/500) *k; % [0,PI] axis divided into 501 points.      X1 = x1 * (exp (-j*pi/500)). ^ (n ' *k);      % DTFT of x1x2 = x2 * (exp (-j*pi/500)). ^ (n ' *k);                % DTFT of x2x = Alpha * x1 + beta * x2;        % Linear combination of X1 & x2x = x * (exp (-j*pi/500)). ^ (n ' *k); % DTFT of xmagX1 = ABS (X1); angX1 = Angle (X1); RealX1 = Real (X1); imagX1 = Imag (X1); magX2 = ABS (X2); angX2 = Angle (X2); RealX2 = Real (X2);  imagX2 = Imag (X2); MAGX = ABS (X);  Angx = Angle (X);  Realx = Real (X);             IMAGX = Imag (X);%verificationx_check = alpha*x1 + beta*x2;              % Linear combination of X1 & x2error = MAX (ABS (X-x_check)); % difference%%--------------------------------------------------------------percent START X1 ' s mag ang real imag%%--- -----------------------------------------------------------figure (' Numbertitle ', ' off ', ' Name ', ' X1 its Magnitude and Angle, Real and imaginary Part '); set (GCF, ' Color ', ' white '); Subplot (2,2,1); Plot (W/PI,MAGX1);  Grid on; % axis ([ -2,2,0,15]); Title (' Magnitude part '), Xlabel (' Frequency in \pi units '); Ylabel (' Magnitude | X1| '); Subplot (2,2,3); Plot (W/pi, angx1/pi);  Grid on; % axis ([ -2,2,-1,1]); title (' Angle part '), Xlabel (' Frequency in \pi units '); Ylabel (' Radians/\pi '); subplot (' 2,2,2 '); Plot (W/pi, realX1); Grid On;title (' Real part '), Xlabel (' Frequency in \pi units '); Ylabel (' Real '); subplot (' 2,2,4 '); Plot (W/pi, imagX1); Grid On;title (' Imaginary part '), Xlabel (' Frequency in \pi units '); Ylabel (' imaginary '); percent--------------------------------------------------------------percent END X1 ' mag ang real imag %% --------------------------------------------------------------%% --------------------------------------------- -----------------percent START X2 ' s mag ang real imag%%--------------------------------------------------------------F Igure (' Numbertitle ', ' off ', ' Name ', ' X2 its Magnitude and Angle, Real and Imaginary part '); Set (GCF, ' Color ', ' white '); Subplot (2,2,1); Plot (W/PI,MAGX2);  Grid on; % axis ([ -2,2,0,15]); Title (' Magnitude part '), Xlabel (' Frequency in \pi units '); Ylabel (' Magnitude | X2| '); Subplot (2,2,3); Plot (W/pi, angx2/pi);  Grid on; % axis ([ -2,2,-1,1]); title (' Angle part '), Xlabel (' Frequency in \pi units '); Ylabel (' Radians/\pi '); subplot (' 2,2,2 '); Plot (W/pi, realX2); Grid On;title (' Real part '), Xlabel (' Frequency in \pi units '); Ylabel (' Real '); subplot (' 2,2,4 '); Plot (W/pi, imagX2); Grid On;title (' Imaginary part '), Xlabel (' Frequency in \pi units '); Ylabel (' imaginary '); percent--------------------------------------------------------------percent END X2 ' mag ang real imag %% --------------------------------------------------------------%% --------------------------------------------- -----------------percent START X ' s mag ang real imag%%--------------------------------------------------------------fi Gure (' Numbertitle ', ' off ', ' Name ', ' X its Magnitude and Angle, Real and Imaginary part '); set (GCF, ' Color ', ' White‘); Subplot (2,2,1); Plot (W/PI,MAGX);  Grid on; % axis ([ -2,2,0,15]); Title (' Magnitude part '), Xlabel (' Frequency in \pi units '); Ylabel (' Magnitude | X| '); Subplot (2,2,3); Plot (W/pi, angx/pi);  Grid on; % axis ([ -2,2,-1,1]); title (' Angle part '), Xlabel (' Frequency in \pi units '); Ylabel (' Radians/\pi '); subplot (' 2,2,2 '); Plot (W/pi, realx); Grid On;title (' Real part '), Xlabel (' Frequency in \pi units '); Ylabel (' Real '); subplot (' 2,2,4 '); Plot (W/pi, IMAGX); Grid On;title (' Imaginary part '), Xlabel (' Frequency in \pi units '); Ylabel (' imaginary '); percent--------------------------------------------------------------percent END X ' s mag ang real imag% % --------------------------------------------------------------

Results:

　　

DSP using MATLAB example Example3.7