Part 4.2.3: Downsampling Done

downsample_analysis.m

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+clear all
+close all 
+clc
+
+% Modify the desired frequency foir the whole code here
+desired_freq = 4000;
+% Read and Set up coeficient
+[y, fs] = audioread("sound/modulator22.wav");
+decrease_coef = round(fs/desired_freq);
+
+% Modify Signal with downsample
+% Only keeps one sample out of decrease_coef
+down_y = downsample(y,decrease_coef);
+down_fs = fs/decrease_coef;
+audiowrite("sound/down_output.wav", down_y, down_fs);
+% Plot Down Modified 
+plot(0:1/down_fs:(length(down_y)-1)/down_fs,down_y);
+xlabel("Time (s)");
+ylabel("Amplitude");
+title("Downsample Sound Amplitude Over Time");
+
+% Modify Signal with decimate
+% Only keeps one sample out of decrease_coef
+deci_y = decimate(y,decrease_coef);
+deci_fs = fs/decrease_coef;
+audiowrite("sound/deci_output.wav", deci_y, deci_fs);
+% Plot Down Modified 
+figure;
+plot(0:1/deci_fs:(length(deci_y)-1)/deci_fs,deci_y);
+xlabel("Time (s)");
+ylabel("Amplitude");
+title("Decimate Sound Amplitude Over Time");
+
+
+% Filter Signal with FIR filter
+order = 30;
+cutoff_freq = 1000; % in Hz
+fir_b = fir1(order, cutoff_freq/(fs/2));
+% Show Filter
+figure
+freqz(fir_b)
+% Apply filter
+fir_y = filter(fir_b, 1, y);
+audiowrite("sound/fir_output.wav", fir_y, fs);
+% Plot Down Modified 
+figure;
+plot(0:1/fs:(length(fir_y)-1)/fs,fir_y);
+xlabel("Time (s)");
+ylabel("Amplitude");
+title("FIR Filter Sound Amplitude Over Time");
+
+% Filter Signal with Butter filter
+order = 8; 
+cutoff_freq = 1000; % in Hz
+[b, a] = butter(order, cutoff_freq/(fs/2), 'low');
+% Show Filter
+figure
+freqz(b)
+% Apply filter
+butt_y = filter(b, a, y);
+audiowrite("sound/butt_output.wav", butt_y, fs);
+% Plot Down Modified 
+figure;
+plot(0:1/fs:(length(butt_y)-1)/fs,butt_y);
+xlabel("Time (s)");
+ylabel("Amplitude");
+title("Butter Filter Sound Amplitude Over Time");
+
+% Test FIR Filter Stability
+% Find the transfer function
+H = tf(fir_b, 1);
+% Get the poles of the transfer function
+poles = pole(H);
+% Check if all poles are inside the unit circle
+if all(abs(poles) < 1)
+    disp('The FIR filter is stable');
+else
+    disp('The FIR filter is unstable');
+end
+% Test Butter Filter Stability
+% Find the transfer function
+H = tf(b, a);
+% Get the poles of the transfer function
+poles = pole(H);
+% Check if all poles are inside the unit circle
+if all(abs(poles) < 1)
+    disp('The Butter filter is stable');
+else
+    disp('The Butter filter is unstable');
+end
+
+% Modify Signal with downsample
+% Only keeps one sample out of decrease_coef
+down_fir_y = downsample(fir_y,decrease_coef);
+down_fir_fs = fs/decrease_coef;
+audiowrite("sound/down_fir_output.wav", down_fir_y, down_fir_fs);
+% Plot Down Modified 
+figure
+plot(0:1/down_fir_fs:(length(down_fir_y)-1)/down_fir_fs,down_fir_y);
+xlabel("Time (s)");
+ylabel("Amplitude");
+title("Downsample FIR Sound Amplitude Over Time");
+
+% Modify Signal with downsample
+% Only keeps one sample out of decrease_coef
+down_butt_y = downsample(butt_y,decrease_coef);
+down_butt_fs = fs/decrease_coef;
+audiowrite("sound/down_butt_output.wav", down_butt_y, down_butt_fs);
+% Plot Down Modified 
+figure
+plot(0:1/down_butt_fs:(length(down_butt_y)-1)/down_butt_fs,down_butt_y);
+xlabel("Time (s)");
+ylabel("Amplitude");
+title("Downsample Butter Sound Amplitude Over Time");