Answer Happy

Modify the Matlab code to do the following: 1. Make x1 a four second cosine pure tone with analog frequency 1 kHz and play it through the sound card. 2. Make x2 a four second cosine pure tone with analog frequency 3 kHz and play it through the sound card. 3. Make x3 = x1 + x2 and play x3 through the sound card. 4. Apply a lowpass digital Butterworth filter to x3 to keep the 1 kHz pure tone but filter out the 3 kHz pure tone. You can use 1 dB for the maximum passband ripple Rp and 60 dB for the minimum stopband attenuation Rs. You will need to set the passband edge frequency 1 kHz. Note that this is 2 x 1000/Fs in radian digital frequency. Divide that by to get the minimum value for the normalized digital passband edge frequency Wp. You will need to set the stopband edge frequency 3 kHz. This is 27 x 3000/Fs in radian digital frequency. Divide that by π to get the maximum value for the normalized digital passband edge frequency Ws. 5. Play the lowpass filtered signal through the sound card.
clear, close all Fs = 44100; % sampling frequency in Hz N = Fs* 4; % length of the 4 sec signal n = 0:N-1; % discrete time variable f_analog = 250; % pure tone analog frequency w_dig = 2*pi*f_analog/Fs; radian digital frequency x1 = cos (w_dig * n); % the pure tone sound (x1, Fs, 16); % play it through sound card pause (5); % wait for sound card to clear f_start_analog = 1000; w_start_dig = 2*pi*f_start_analog/Fs; f_stop_analog = 3000; w_stop_dig M 2*pi*f_stop_analog/Fs; phi M (w_stop_dig-w_start_dig)/(2* (N-1))*(n.*n) + w_start_dig*n; x2 = cos(phi); sound (x2, Fs, 16); % play it through sound card pause (5); % wait for sound card to clear x3 = x1 + x2; x3 = x3 / max (abs(x3)); % normalize the range to [-1,1] sound (x3,Fs,16); % play it through sound card pause (5); % wait for sound card to clear Wp = w_dig/pi; % normalized passband edge freq Ws = w_start_dig/pi; % normalized stopband edge freq Rp = 1; % max passband ripple Rs = 60; % min stopband attenuation [Nf, Wn] [num, den] buttord (Wp, Ws, Rp, Rs); % design filter order butter (Nf, Wn); % design the filter h-fvtool (num, den); % show frequency response figure (2); freqz (num, den, 1024); % plot frequency response title('Lowpass Frequency Response'); y1 = filter (num, den, x3); % apply the filter y1 = y1 / max (abs(y1)); % normalize filtered signal sound (y1,Fs,16); % play it through sound card pause (5); % wait for sound card to clear Ws = w_dig/pi; % normalized stopband edge freq
Wp H Ws = w_dig/pi; % normalized stopband edge freq w_start_dig/pi; % normalized passband edge freq 1; % max passband ripple Rp = Rs = 60; % min stopband attenuation E [Nf, Wn] = buttord (Wp, Ws, Rp, Rs); % design filter order [num2, den2] butter (Nf, wn, 'high'); % design the filter dfilt.df1(num2, den2); % make filter object addfilter (h, Hd); % add filter 2 to fvtool figure (3); Hd E freqz (num2, den2, 1024); % plot frequency response title(' Highpass Frequency Response'); y2 = filter (num2, den2, x3); % apply the filter y2 = y2 / max (abs(y2)); % normalize filtered signal sound (y2, Fs,16); % play it through sound card