Para Mis Estudiantes de PDS

8/12/2019 Para Mis Estudiantes de PDS

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Para mis estudiantes de PDS.

Vamos a probar algunos ejercicios en MATLAB del libro PROCESAMIENTO DE

SEALES DIGITALES de Mitra MCGrawHill.

1) Son dos ejemplos que presentan la graficacin de seales exponenciales.

% Program 2_2

% Generation of complex exponential sequence

% Probar este ejemplo con a=-0.08, b=0.52, K=2, y N=40.

a = input('Type in real exponent = ');

b = input('Type in imaginary exponent = ');

c = a + b*i;

K = input('Type in the gain constant = ');

N = input ('Type in length of sequence = ');

n = 1:N;

x = K*exp(c*n);%Generate the sequence

stem(n,real(x));%Plot the real part

xlabel('Time index n');ylabel('Amplitude');

title('Real part');

disp('PRESS RETURN for imaginary part');

pause

stem(n,imag(x));%Plot the imaginary part


title('Imaginary part');


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% Program 2_3

% Generation of real exponential sequence

%

a = input('Type in argument = ');

K = input('Type in the gain constant = ');

N = input ('Type in length of sequence = ');

n = 0:N;

x = K*a.^n;

stem(n,x);


title(['\alpha = ',num2str(a)]);

2) Relativos a la Convolucin y correlacin

% Program 2_6

% Illustration of Convolution

%

a = input('Type in the first sequence = ');

b = input('Type in the second sequence = ');

c = conv(a, b);

M = length(c)-1;

n = 0:1:M;


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disp('output sequence =');disp(c)

stem(n,c)

xlabel('Time index n'); ylabel('Amplitude');

% Program 2_7

% Computation of Cross-correlation Sequence

% Sea x=[ 1 3 -2 1 2 -1 4 4 2]

% Sea y=[2 -1 4 1 -2 3]

x = input('Type in the reference sequence = ');

y = input('Type in the second sequence = ');

% Compute the correlation sequence

n1 = length(y)-1; n2 = length(x)-1;

r = conv(x,fliplr(y));

k = (-n1):n2';

stem(k,r);

xlabel('Lag index'); ylabel('Amplitude');

v = axis;

axis([-n1 n2 v(3:end)]);

3) De las series de Fourier FFT

% Program 5_1

% Illustration of DFT Computation

% Probar con N=8 y M=16


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% Read in the length N of sequence and the desired

% length M of the DFT

N = input('Type in the length of the sequence = ');

M = input('Type in the length of the DFT = ');

% Generate the length-N time-domain sequence

u = [ones(1,N)];

% Compute its M-point DFT

U = fft(u,M);

% Plot the time-domain sequence and its DFT

t = 0:1:N-1;

stem(t,u)

title('Original time-domain sequence')

xlabel('Time index n'); ylabel('Amplitude')

pause

subplot(2,1,1)

k = 0:1:M-1;

stem(k,abs(U))

title('Magnitude of the DFT samples')

xlabel('Frequency index k'); ylabel('Magnitude')

subplot(2,1,2)

stem(k,angle(U))

title('Phase of the DFT samples')

xlabel('Frequency index k'); ylabel('Phase')


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% Program 5_2

% Illustration of IDFT Computation

%

% Read in the length K of the DFT and the desired

% length N of the IDFT

K = input('Type in the length of the DFT = ');

N = input('Type in the length of the IDFT = ');

% Generate the length-K DFT sequence

k = 0:K-1;

V = k/K;

% Compute its N-point IDFT

v = ifft(V,N);

% Plot the DFT and its IDFT

stem(k,V)

xlabel('Frequency index k'); ylabel('Amplitude')

title('Original DFT samples')

pause

subplot(2,1,1)

n = 0:N-1;

stem(n,real(v))

title('Real part of the time-domain samples')


subplot(2,1,2)

stem(n,imag(v))

title('Imaginary part of the time-domain samples')


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Escriba el siguiente cdigo en un archivo con extensin .m para obtener la serie de Fourier, el

espectro de Amplitud y el espectro de Potencia.

clear

T0= 2;

ep=1;

t0=0;

A=1;

w0=2*pi/T0;

nterm=100;

X0=A*ep/T0;

for kk=1:nterm

X(kk) = X0*(exp(-j*kk-w0*t0))*sin(kk*ep/T0);

end

Am=2*abs(X);

qm=angle(X);

t=linspace(-2*T0+ep/2,2*T0-ep/2,400);

x=X0*ones(size(t));

for jj=1:nterm

x =x + Am(jj)*cos(jj*w0*t+qm(jj));

end

Xt=abs(X);

Amp = [fliplr(Xt),X0,Xt]


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Pt=abs(X).^2;

Pwr=[fliplr(Pt),X0^2,Pt]

w=[-nterm:nterm]*w0;

subplot(221)

plot(t,x)

title('serie de Fourier')

xlabel('Tiempo')

subplot(222)

plot(w,Amp)

title('Espectro bilateral de amplitud')

xlabel('frecuencia,rad/s')

subplot(223)

plot(w,Pwr)

title('Espectro de potencia')

xlabel('frecuencia,rad/s')

Escriba el siguiente cdigo en un archivo con extensin .m y compruebe la FFT.

x=[1 1 0 0];

X=fft(x)

Escriba el siguiente cdigo en un archivo con extensin .m y compruebe la FFT.

nn=0:15;

xx=exp(j*nn/3);


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XX=fft(xx);

kk=nn;

subplot(221)

stem(kk, real(xx))

title('Real part of x[n]'), xlabel('index (n)')

subplot(223)

stem(kk, imag(xx))

title('Imag part of x[n]'), xlabel('index(k)')

subplot(222)

stem(kk, real(XX))

title('Real part of DFT'), xlabel('index(k)')

subplot(224)

stem(kk,imag(XX))

title('IMAG PART OF DFT'), xlabel('INDEX (k)')

% Program 5_4

% Linear Convolution Via the DFT

%

% Read in the two sequences

x = input('Type in the first sequence = ');

h = input('Type in the second sequence = ');

% Determine the length of the result of convolution

L = length(x)+length(h)-1;

% Compute the DFTs by zero-padding


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XE = fft(x,L); HE = fft(h,L);

% Determine the IDFT of the product

y1 = ifft(XE.*HE);

% Plot the sequence generated by DFT-based convolution and

% the error from direct linear convolution

n = 0:L-1;

subplot(2,1,1)

stem(n,y1)


title('Result of DFT-based linear convolution')

y2 = conv(x,h);

error = y1-y2;

subplot(2,1,2)

stem(n,error)

xlabel('Time index n');ylabel('Amplitude')

title('Error sequence')

Para Mis Estudiantes de PDS

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