Paso 4 procesamiento digital de señales.docx

PASO 4 - EJECUTAR ACTIVIDADES APLICANDO LAS HERRAMIENTAS DEL ̃ PROCESAMIENTO DIGITAL DE SE N ALES

Tutor MAURICIO ALBERTO GARCIA.

PROCESAMIENTO DIGITAL DE SEÑALES ESCUELA DE CIENCIAS BASICAS, TECNOLOIA E INGENIERIA. UNIVERSIDAD NACIONAL ABIERTA Y A DISTANCIA UNAD. BOGOTA NOVIEMBRE DE 2018

INTRODUCCION

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Cada estudiante escogerá un (1) tipo de filtro que desee diseñar, y reportará en el foro su decisión, esto con el fin de que cada estudiante diseñe un ecualizador (banco de filtros) diferente. A continuación, se muestra la lista de filtros:

Tipos de filtro Pasa Banda (Bandpass)

        







 

IIR Butterworth IIR Chebyshev tipo I IIR Chebyshev tipo II IIR Elliptic FIR Window Hamming FIR Window Gaussian FIR Window Hann FIR Window Rectangular FIR Window Kaiser

Cada estudiante investigará las características del filtro escogido, si el filtro escogido es IIR , para realizar un informe con los siguientes parámetros: Concepto básico de filtro IIR y un diagrama de bloque y ecuación que ecuación que lo describa. Definición específica del filtro escogido (Por ejemplo, Butterworth, chebyshev, etc). Ecuación de respuesta en frecuencia y función de transferencia. Definición de variables de las ecuaciones anteriores.

El filtro IIR (Infinite Impulse Response o respuesta infinita al impulso) es un tipo de filtro digital que se comporta de manera que si su entrada es un impulso, la salida será un número ilimitado de términos no nulos, es decir, que nunca volverá a un estado de reposo. Para obtener la salida, se emplean valores tanto de la entrada actual como anteriores, además de algunos valores de salida almacenados en la memoria los cuales son realimentados a la entrada

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



=0

=

[]  ∑  [ − ] − ∑ [ − ] El orden del filtro esta dado por el máximo entre P y Q y una de las posibles estructuras del filtro IIR puede ser

Grafica 1

Específicamente, el filtro elíptico o filtro Cauer es un filtro de procesamiento de señal con comportamiento de ondulación igualado tanto en la banda de paso como en la banda de atenuación o parada. La ondulación se comporta de tres formas: 

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A medida que la ondulación en la banda de parada se acerca a cero, el filtro se convierte en un filtro Chevyshev. Cuando la ondulación en la banda de paso se acerca a cero, el filtro se

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Ecuación de la ganancia del filtro elíptico:

() 

1 √ 1 + 2 + 2(,/0)

Donde

      0                   

Cada estudiante diseñará cinco (5) filtros en la herramienta Simulink de Matlab, específicamente utilizará el bloque FDA TOOL para diseñar los filtros. Todos los filtros deben ser del mismo tipo, por ejemplo, si se escogió IIR Butterworth, entonces los cinco (5) Filtros diseñados deben ser IIR Butterworth. Cada uno de los filtros tendrá los siguientes rangos de frecuencia:

Filtro Rango (Hz) Tipo

1 2 3 20 Hz – 200 Hz – 500 Hz – 200 Hz 500 Hz 2Khz Hz Pasa Pasa Pasa Banda Banda Banda He aquí las graficas de los 5 respectivos filtros 1. Filtro pasa banda entre 20 y 200 Hz

4 2 KHz – 8 KHz Pasa Banda

5 8 KHz – 20 KHz Pasa Banda

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2. Filtro pasa banda entre 200 y 500 Hz en el cual se evidencia la banda de paso entre los valores de 200 y 500 Hz

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4. Filtro pasa banda entre 2KHz 2 KHz y 8 KHz.

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Se exportarán los coeficientes de cada uno de los cinco filtros, los cuales equivalen a la respuesta el impulso en el filtro FIR, y a los coeficientes de la función de transferencia en los filtros IIR (matriz SOS). Para ello deben dirigirse al menú archivo –  exportar command window – coeficientes. Cuyos coeficientes deben graficarse mediante la función plot de Matlab. Para los estudiantes que hayan escogido un filtro IIR, exportarán el matriz SOS y de ella podrán obtener los coeficientes de la función de

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Grafica del plot de coeficientes del filtro 1

Grafica del plot de coeficientes del filtro 2

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Grafica del plot de coeficientes del filtro 4

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Una vez diseñados los filtros, cada uno de los estudiantes procederá a ensamblar un ecualizador de sonido, para ello debe agregar el bloque  “From Multimedia Multimedia File” el cual servirá servirá como fuente de entrada (audio) al ecualizador, este audio debe tener como mínimo una frecuencia de muestreo de 44.1 Khz, Khz, y los filtros deben estar configurados a esta misma frecuencia de muestreo. También se debe agregar el bloque  “Slider Gain” Gain” a la salida de cada uno de los filtros, con el fin de controlar el nivel de salida en cada uno de los filtros. Finalmente se sumarán todas las señales con el bloque “add”.

El código para ingresar a matlab es el siguiente

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xlabel('Tiempo xlabel('Tiempo (s)') (s)') % Etiqueta del eje X ylabel('Amplitud ylabel('Amplitud (V)') (V)') % Etiqueta del eje Y xlim([0 10/1000]) % Límite de la señal %% Grabar y reproducir la señal de audio %wavwrite(y,fs,'audio') % wavplay(y,fs) %% FFT de la señal subplot(412) % Llamado a la función que calcula la FFT fft_signal(y,fs);title('ESPECTRO fft_signal(y,fs);title( 'ESPECTRO DE LA SEÑAL ORIGINAL') ORIGINAL') xlim([0 2500]) %% Filtrado de la señal % Frecuencia normalizada fNorm = 1500 / (fs/2); % Cálculo de los coeficientes del filtro (filtro pasa bajas) [b,a] = butter(10, fNorm, 'low' 'low'); ); % Filtrado de la señal y_Low = filtfilt(b, a, y); % Graficación de la señal en el tiempo subplot(413) plot((0:L-1)/fs,y_Low) title('SEÑAL title('SEÑAL FILTRADA') FILTRADA') xlabel('Tiempo xlabel('Tiempo (s)') (s)') ylabel('Amplitud ylabel('Amplitud (V)') (V)') xlim([0 10/1000]) % Graficación de la señal en frecuencia subplot(414)

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%Ploteo de los polos y ceros z= roots(b); % Ceros p = roots(a); % Polos subplot(224) zplane(z,p) title('Polos title('Polos y ceros') ceros') legend('Ceros' legend('Ceros', ,'Polos' 'Polos') ) %% Reproducción de audio de entrada y salida pause(2) disp('Audio disp('Audio de entrada') entrada') wavplay(0.5*y,fs) disp('Audio disp('Audio de salida (señal filtrada)') filtrada)') wavplay(0.5*y_Low,fs)

ingresándolo a Matlab

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2. Las respuestas en magnitud y fase del filtro pasa altos, así como la respuesta al impulso, sus polos y ceros.

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controlar los “Slider Gain” mientras el modelo está corriendo. Se recomienda usar un tiempo de simulación largo, por ejemplo 200.

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BIBLIOGRAFIA. Ambardar, Ambardar, A. (2002). Filtros Digitales Descritos con Ecuaciones de Diferencias. In Procesamiento Procesamiento de señales analógicas y digitales (2nd ed., pp. 103-110). Mexico City: Cengage Learning. Recuperado de http://bibliotecavirtual.unad.edu.c http://bibliotecavir tual.unad.edu.co:2619/apps o:2619/apps/doc/CX40603000 /doc/CX4060300050/GVRL 50/GVRL ?u=unad&sid=GVRL&xid=ee09b0a1 Ambardar, A. (2002). Transformada z. In Procesamiento de señales analógicas y digitales (2nd ed., p. 592). Mexico City: Cengage Learning. Recuperado de http://bibliotecavirtual.unad.edu.c http://bibliotecavir tual.unad.edu.co:2619/apps/d o:2619/apps/doc/CX4060300180 oc/CX4060300180/GVRL /GVRL ?u=unad&sid=GVRL&xid=d11fa7cc Ambardar, A. (2002). Aplicaciones de la Transformada z. In Procesamiento de señales analógicas y digitales (2nd ed., p. 637). Mexico City: Cengage Learning. Recuperado de

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