INSTRUCTIONS: To obtain the information the Police and the FBI are asking you, you will have to follow the following instructions: 1.- Choose the population groups you want to analyze. You will have to ask for the evidence to different groups, depending of the age and gender, that means, you will have to record a person from the different groups saying the sentence you have to analyze, and you will have to obtain the fundamental frequency for each group. Write down your criterion for choosing the different groups. (You will have to decide the selected groups with a reasoned criterion and include the references, articles, books you have used, in your report in the bibliography). 2.- Create a Matlab routine which permits to the user: a. Using a sampling frequency of 8KHz, record 1 second of the signal that we want to analyze. (This function will help us to collect the data from the population groups we have chosen in the previous point.) You can use the routine "audiorecorder", looking for the help in Matlab. Use only one channel and 8bits/sample. b. Using the routine "espectro.m given in Blackboard, plot the magnitude of the Fourier Transform in dB of each recorded signal. In the routine espectro.m" you will have to identify if the correct units appear in the graphs or if you have to modify the routine to obtain the correct units (dB). The routine espectro.m" given, plots the square of the magnitude of the Fourier Transform versus the frequency in Hz. The input parameters of the routine are the signal we want to analyze and the sampling frequency. Do not forget to upload the new version of the routine if you have made any changes in the routine. c. Analyzing the magnitude of the plots of the Fourier Transform of each recorded signal, determine the value of the fundamental frequency and put them in a table. d. For each recorded signal, add in the report its time and frequency graph, showing the fundamental frequency you have chosen. Do not forget to label all the axes with the corresponding units in all your graphs. In the routine espectro.m" you will have to add the units in dB if they do not appear in the graphs. e. Plot the results in two different graphs (males and females) depending of the age. (Do not forget to label all the axes with the corresponding units because these two graphics are the most important data to be analyzed by the Police Station). f. Repeat the points a) to c) but with higher and lower sampling frequency. What are the differences in the frequency with the highest magnitude or the fundamental frequency? What can you conclude about the sampling frequency? How you can obtain the best sampling frequency? Explain with your own words with a reasoned criterion. g. What can you conclude about the fundamental frequency of the voice between different ages and genders? Explain with your own words with a reasoned criterion. --- M function [M, freq]=espectro(x, fm); % X seal de entrada % fm frecuencia de muestreo % magnitud de la transformada de Fourier % freq eje de frecuencia en Hz Np=8192; % Nomero de puntos de la DET L=length(x); % Longitud de la sebal Tm=(1/fm); % Tiempo de muestreo Mp=ceil(Np/2); % Mitad de puntos de la FFT wd=0:2*pi/Np: 2*pi* (Np-1)/Np; % Vector de Frec. discreta wdo=zeros(1, NP); % Vector de Frec. disc. organizadas Wc=zeros(1, Np); % Vector de Frec. cont. en rad/seg fc=zeros(1, Np); % Vector de Frec. cont. en Hz z=abs(fft(x,Np)); % Magnitud de FFT de la selal zorzeros(1, Np); % Vector para reorganizar la FFT t=0: Tm: Tm* (L-1); % Vector de tiempo % Reorganizacion de frecuencias wdo(Np-Mp+1:end)=wd(1:Mp); wdo(1: Np-Mp)=wd (Mp+1:end)-2*pi; % Frecuencia continua en Hz WC=wdo/Tm; fc=wc/(2*pi); % Reorganizacion de la FFT ZO (Np-Mp+1: end)=2(1:Mp); 20 (1: Np-Mp)=z(Mp+1:end); M=zo; freq=fc; figure; plot(freq,M); title('Magnitud de la transformada de Fourier');