Muestreo de señales en matlab
July 25, 2019 | Author: vadv1989 | Category: N/A
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Universidad Tecnológica de Panamá Centro Regional de Chiriquí Facultad de Ingeniería Eléctrica
Materia Control 2
Práctica N° 1 Muestreo y reconstrucción de señales Cuantización Cuantización y error de cuantización
II semestre
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U.T.P.
F.I.E.
Í ndice ndice
1.
Objetivos
2. Introducción
3. Contenido y Resultados
4. Conclusiones
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U.T.P.
F.I.E.
Objetivos
-Familiarizar
al alumno con la generación y adquisición de señales atendiendo a
aspectos tales como el muestreo y aliasing .
-Introducir
al alumno con la generación y adquisición de señales atendiendo a aspectos
tales como el muestreo, cuantización, y error de cuantización.
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F.I.E.
Introducción
El muestreo de una señal es importante para la reconstrucción de ondas y también para conocer los errores que pueda tener una señal muestreada, para ello, se harán experiencias para aprender a muestrear bien una onda y conocer el muestreo incorrecto. Se utilizará MATLAB para e jecutar cada simulación y luego tam bién se utilizará SIMULINK para observar el mismo efecto.
La cuantificación es la conversión de una señal analógica a digital . En la conversión de señales se utilizan niveles de cuantización para codificar o descodificar las señales y de esa manera pasar de un estado a otro. El error de cuantización se crea al establecer los niveles de cuantización, esto ocurre porque la señal analógica tiene infinitos niveles y la señal digital tiene niveles finitos . Utilizando la aplicación de MATLAB, SIMULINK, se creará un modelo para observar que es la cuantización y el error de cuantización, además se observara la función de modificar los niveles de cuantización y su relación con el error de cuantización.
Procedimiento
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U.T.P.
F.I.E.
I parte. Muestreo y reconstrucción de señales a) Generación de señales. Generar en MATLAB un seno de frecuencia de 2kHz y amplitud de 0.5 muestreado a distintas frecuencias de muestre . Dicha señal se observará tanto en el ordenador como en el osciloscopio, siendo posi ble, así mismo, escucharla. %% Generación de señales f=2000 fso=1e6 No= fso*1e-3 to=(0:No-1)/fso xo=0.5*sin(2*pi*f*to) for fs=[44100 22050 11025 8000 5000] N=fs*1 t=(0:N-1)/fs x=0.5*sin(2*pi*f*t) sound(x,fs) plot (to*1e3,xo,'k' (to*1e3,xo,'k',t*1e3,x, ,t*1e3,x,'b-o' 'b-o') ) axis([0, 1, -1, 1]) legend ('Señal ('Señal original', original','Señal muesteada') muesteada') xlabel('milisegundos' xlabel('milisegundos') ) pause end Figura
Cuatro
1.
gráficas en donde se observa
la
original muestreada 1
2
señal y
la a
distintas frecuencia. Cabe destacar que a menor frecuencia de muestreo,
menor
será la cantidad de muestras.
3
4
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1.
F.I.E.
Añada otras frecuencias frecuencias de muestreo mayor o menor que la frecuencia de la señal. Comente lo observado.
Figura2.
En la primera gráfica se observa la señal muestreada a 10000Hz y la segunda a
1500Hz
Cuando se muestreo la señal original a 10KHz, se escucho un sonido bastante agudo aunque no tanto como las frecuencias que esta ban en el procedimiento anterior, y en la segunda gráfica se observa la señal muestreada a 1,5kHz la cual emitió un sonido grave . Al muestrear una señal, por encima de la frecuencia original se observa que tenemos muchas mas muestras que cuando se muestrea por deba jo de la frecuencia original. Al tener mayor cantidad de muestras se hace mas fácil la reconstrucción de la frecuencia original.
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U.T.P.
2.
F.I.E.
El muestreo ideal se realiza utilizando impulsos unitarios al muestrear. La función stem() es la utilizada para realizar gráficas por impulsos. Utilice esta función y grafique la señal muestreada idealmente. Objeción
Se observa en la primera gráfica la función a muestrear, y en la segunda grafica, vemos la reconstrucción ideal de la función anterior por medio de impulsos unitarios . El muestreo por impulsos unitarios es una forma de muestrear muy efectiva con el único objeto que es ideal y en la vida real no funciona
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U.T.P.
b)
F.I.E.
Muestreo incorrecto. Generar en MATLAB un seno de frecuencia 9kHz y
amplitud 0.5 muestreado a distintas frecuencias de muestreo. Dicha señal se observará tanto en el ordenador como en el osciloscopio y se escuchará con los auriculares.
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F.I.E.
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U.T.P.
F.I.E.
¿Cuáles frecuencias no funcionan para la reconstrucción de la señal? ¿Cuale sería la frecuencia mínima de muestreo para la señal de 9kHz? Las frecuencias que no funcionaron para la reconstrucción de la señal original fueron las que no cumplieron con el teorema de muestreo, dichas frecuencias son 11025Hz y 8000Hz.
El teorema no indica que
Observando el teorema se conoce la razón por la que algunas frecuencias de muestreo
no funcionaron. Utilizando este teorema, se puede encontrar una frecuencia mínima de muestreo.
Como se observa en el procedimiento anterior 180001Hz es la frecuencia mínima para que la señal se pueda reconstruir teóricamente con mucha exactitud a partir de la señal muestreada.
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F.I.E.
IIparte. Cuantización y error de cuantización. a) Realice en simulink la siguiente simulación.
b) Coloque un stop time de 0.005 y corra la simulación. Describa lo observado en cada scope. Analice los valores de cuantización, el error máximo de cuantización, etc .
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F.I.E.
Los valores de cuantización son ±1, ±0.5 y 0, los valores de cuantización tam bién puede ser interpretados como los niveles a los que ser muestreo la grafica . Estos valores fueron tomados de la grafica del scope1. Observando la grafica del scope2, el error -3
máximo fue de 0.207x10 .
c) Añada el bloque llamado To workspace, como se muestra en la figura, y
cambie las propiedades (nombre y save format) como lo indicado. En Matlab escriba el siguiente comando: hist(Qe) % el cual muestra el histograma y mean(Qe) %el cual calcula la media de Qe .
Figura
5. Histograma que muestra la
cantidad de veces que un valor fue cuantificado.
>> mean(Qe) %el cual calcula la media de Qe
ans =
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d) En las propiedades del quantizer, disminuya el intervalo de cuantización a .25
y a 0.1. ¿Aumenta o disminuye el error e rror de cuantizacion?¿Por qué?¿Cómo cambia el histograma?
Figura6
Izquierda, scope del error de cuantización Derecha,
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Figura7.
Izquierda, scope del error de cuantización. Derecha,
histograma a 0.1 el intervalo de cuantización.
F.I.E.
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F.I.E.
IIIparte. Muestreo y reconstrucción reconstrucción en simulink a) Realice el siguiente diagrama en simulink:
b) Note que la primera parte (hasta el scope 1) es un muestreo ideal. La
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F.I.E. Scope2. First-order hold
Figura
9.Gráficas de los scopes del diagrama de
simulink Fs=4000 Scope1
Scope2. Zero-order hold
Scope2
First-order
hold
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F.I.E. Scope2. First-order hold
Figura
11.Gráficas de los scopes del diagrama de
simulink Fs=16000 Scope1
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U.T.P.
F.I.E.
e) Modifique la frecuencia de la señal o del Pulse generator para que dé
e jemplos de aliasing.
Se modificó la señal del pulse generator para e jemplificar el aliasing, Fs=500hz.
Scope2. First-order hold
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F.I.E.
Conclusión
-
Si se desea reconstruir una señal, primero se debe muestrear para obtener muestras de su ciclo y luego pasar a la reconstrucción utilizando los hold.
-
Para un buen muestreo es importante saber que la frecuencia de muestreo debe ser por lo mínimo el do ble de la frecuencia de la onda, de otra manera,
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U.T.P.
F.I.E.
Bibliografía
[1] Microsoft ® Encarta ® 2008. © 1993-2007 Microsoft Corporation. Reservados
todos los derechos.
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