EX NO : Room Acoustics and Convolution

DATE :

AIM :
To write and simulate a MATLAB program to compute the how to do the effect of a
room’s impulse response on an audio signal to demonstrate convolution.

SYSTEM SPECIFICATION:

System with MATLAB 17.0.

Processor: Intel(R) Core(TM)2 Duo CPU E7500 @ 2.93GHz 2.94 GHz
System type:32-bit Operating System
ALGORITHM:

1. Create a new M file.

2. Save the file as filename.m

3. The signal is room’s impulse response on an audio signal to demonstrate convolution.

THEORY :
Convolution is a mathematical operation used to determine the output of a linear
time-invariant (LTI) system when an input signal is applied. A real-life example is modeling
how a room’s acoustics (impulse response) affect a transmitted sound signal.
PROGRAM :
% MATLAB Example: Convolution to Model Room Acoustics
Clc;
Clear;
Close all;
Fs = 1000;
T = 0:1/fs:1;
Input_signal = sin(2*pi*5*t);
Room_impulse_response = [1, 0.5, 0.50, 0.100];
Output_signal = conv(input_signal, room_impulse_response, ‘same’);
T_out = linspace(0, length(output_signal)/fs, length(output_signal));
Figure;
Subplot(3,1,1);
Plot(t, input_signal, ‘b’, ‘LineWidth’, 1.5);
Title(‘Input Signal’);
Xlabel(‘Time (s)’);
Ylabel(‘Amplitude’);
Grid on;
Subplot(3,1,2);
Stem(0:length(room_impulse_response)-1, room_impulse_response, ‘r’, ‘LineWidth’,
1.5);
Title(‘Impulse Response of the Room’);
Xlabel(‘Samples’);
Ylabel(‘Amplitude’);
Grid on;
Subplot(3,1,3);
Plot(t_out, output_signal, ‘k’, ‘LineWidth’, 1.5);
Title(‘Output Signal (After Convolution)’);
Xlabel(‘Time (s)’);
Ylabel(‘Amplitude’);
Grid on;
Disp(‘Convolution complete: Room acoustics applied to the input signal.’);

Output :
RESULT :
 EX NO : FIR Filter for Noise Reduction
DATE :

AIM :
To write and simulate a MATLAB program to compute FIR filter to remove high-
frequency noise from a noisy sinusoidal signal.

SYSTEM SPECIFICATION:

System with MATLAB 17.0.

Processor: Intel(R) Core(TM)2 Duo CPU E7500 @ 2.93GHz 2.94 GHz
System type: 32-bit Operating System
ALGORITHM:

1.Create a new M file.

2.Save the file as filename.m

3. noisy signal with added high-frequency noise.

PROGRAM :

% MATLAB Example: ECG Signal Processing with Low-Pass FIR Filter

Clc;
Clear;
Close all;
Fs = 360;
T = 0:1/fs:5;
Ecg_signal = 1.5 * sin(2*pi*1*t) + 0.5 * sin(2*pi*0.5*t);
Noise = 0.2 * randn(size(t));
Noisy_ecg = ecg_signal + noise;
Filter_order = 50;
Cutoff_freq = 40;
Normalized_cutoff = cutoff_freq / (fs/2);
Fir_coeffs = fir1(filter_order, normalized_cutoff);
Filtered_ecg = filter(fir_coeffs, 1, noisy_ecg);
Figure;
Subplot(3,1,1);
Plot(t, ecg_signal, ‘g’, ‘LineWidth’, 1.5);
Title(‘Original Clean ECG Signal’);
Xlabel(‘Time (s)’);
Ylabel(‘Amplitude’);
Grid on;
Subplot(3,1,2);
Plot(t, noisy_ecg, ‘r’, ‘LineWidth’, 1.5);
Title(‘Noisy ECG Signal’);
Xlabel(‘Time (s)’);
Ylabel(‘Amplitude’);
Grid on;
Subplot(3,1,3);
Plot(t, filtered_ecg, ‘b’, ‘LineWidth’, 1.5);
Title(‘Filtered ECG Signal (After Low-Pass FIR Filter)’);
Xlabel(‘Time (s)’);
Ylabel(‘Amplitude’);
Grid on;
Disp(‘FIR Filter Coefficients:’);
Disp(fir_coeffs);

OUTPUT:
FIR Filter Coefficients:
Columns 1 through 7
-0.0010 -0.0010 -0.0004 0.0006 0.0018 0.0026 0.0022
Columns 8 through 14
-0.0000 -0.0035 -0.0068 -0.0073 -0.0035 0.0043 0.0131
Columns 15 through 21
0.0179 0.0140 -0.0000 -0.0201 -0.0374 -0.0403 -0.0199
Columns 22 through 28
0.0257 0.0890 0.1547 0.2041 0.2225 0.2041 0.1547
Columns 29 through 35
0.0890 0.0257 -0.0199 -0.0403 -0.0374 -0.0201 -0.0000
Columns 36 through 42
0.0140 0.0179 0.0131 0.0043 -0.0035 -0.0073 -0.0068
Columns 43 through 49
-0.0035 -0.0000 0.0022 0.0026 0.0018 0.0006 -0.0004
Columns 50 through 51
-0.0010 -0.0010
RESULT :
 EX NO :
Analysis of Clean and Noisy Signal
DATE :

AIM :
To write and simulate a MATLAB program to compute the Spectral Analysis of
Clean and Noisy Signals.

SYSTEM SPECIFICATION:

System with MATLAB 17.0.

Processor: Intel(R) Core(TM)2 Duo CPU E7500 @ 2.93GHz 2.94 GHz
System type:32-bit Operating System

ALGORITHM:

1. Create a new M file.

2. Save the file as filename.m

3. Generate the Spectral Analysis of Clean and Noisy Signals.

4. Plot the graph.

PROGRAM :
Clc;
Clear;
Close all;
Fs = 1000;
T = 0:1/fs:1-1/fs;
F_signal = 50;
% Generate the clean signal (sine wave)
Clean_signal = sin(2*pi*f_signal*t);
Noise = 0.5 * randn(size(t));
Noisy_signal = clean_signal + noise;
% Perform FFT on both signals
N = length(clean_signal);
Freq = fs * (0N/2)) / N;
% FFT of the clean signal
Clean_signal_fft = fft(clean_signal);
Clean_signal_magnitude = abs(clean_signal_fft / N);
Clean_signal_magnitude = clean_signal_magnitude(1:N/2+1);
% FFT of the noisy signal
Noisy_signal_fft = fft(noisy_signal);
Noisy_signal_magnitude = abs(noisy_signal_fft / N);
Noisy_signal_magnitude = noisy_signal_magnitude(1:N/2+1);
% Plot the time-domain signals
Figure;
Subplot(2,1,1);
Plot(t, clean_signal, ‘b’, ‘LineWidth’, 1.5);
Hold on;
Plot(t, noisy_signal, ‘r’, ‘LineWidth’, 1.2);
Title(‘Time-Domain Signals’);
Xlabel(‘Time (s)’);
Ylabel(‘Amplitude’);
Legend(‘Clean Signal’, ‘Noisy Signal’);
Grid on;
% Plot the frequency-domain spectra
Subplot(2,1,2);
Plot(freq, clean_signal_magnitude, ‘b’, ‘LineWidth’, 1.5);
Hold on;
Plot(freq, noisy_signal_magnitude, ‘r’, ‘LineWidth’, 1.2);
Title(‘Frequency-Domain Spectral Analysis’);
Xlabel(‘Frequency (Hz)’);
Ylabel(‘Magnitude’);
Legend(‘Clean Signal Spectrum’, ‘Noisy Signal Spectrum’);
Grid on;
% Display dominant frequencies
[~, clean_peak_idx] = max(clean_signal_magnitude);
[~, noisy_peak_idx] = max(noisy_signal_magnitude);
Fprintf(‘Dominant frequency of clean signal: %.2f Hz\n’, freq(clean_peak_idx));
Fprintf(‘Dominant frequency of noisy signal: %.2f Hz\n’, freq(noisy_peak_idx));
OUTPUT :

Dominant frequency of clean signal: 50.00 Hz

Dominant frequency of noisy signal: 50.00 Hz
RESULT :
 EX NO : Filtering High-Frequency Noise from Sensor Data Using DFT

DATE :

AIM :
To write and simulate a MATLAB program to compute the Filtering High-
Frequency Noise from Sensor Data Using DFT

SYSTEM SPECIFICATION:

System with MATLAB 17.0.

Processor: Intel(R) Core(TM)2 Duo CPU E7500 @ 2.93GHz 2.94 GHz
System type: 32-bit Operating System

ALGORITHM:

1. Create a new M file.

2. Save the file as filename.m

3. Generate the Filtering High-Frequency Noise from Sensor Data Using DFT

4. Plot the graph.

PROGRAM :
% Define the sampling parameters
Fs = 1000;
T = 1;
T = 0:1/fs:T-1/fs;
F_signal = 10;
Sensor_signal = sin(2*pi*f_signal*t);
F_noise = 150;
Noise = 0.5 * sin(2*pi*f_noise*t);
Noisy_signal = sensor_signal + noise;
Noisy_signal_fft = fft(noisy_signal);
N = length(t);
F = (0:n-1)*(fs/n);
% Low-pass filter: Remove frequencies above 50 Hz
Cutoff_freq = 50;
Filter = (f <= cutoff_freq);
% Apply the filter to the DFT of the noisy signal
Filtered_fft = noisy_signal_fft .* filter;
Filtered_signal = real(ifft(filtered_fft));
Figure;
% Plot the original noisy signal
Subplot(2,2,1);
Plot(t, noisy_signal);
Title(‘Noisy Sensor Signal (10 Hz + Noise)’);
Xlabel(‘Time (seconds)’);
Ylabel(‘Amplitude’);
% Plot DFT of the noisy signal (Before filtering)
Subplot(2,2,2);
Plot(f(1:floor(n/2)), abs(noisy_signal_fft(1:floor(n/2))));
Title(‘DFT of Noisy Sensor Signal (Before Filtering)’);
Xlabel(‘Frequency (Hz)’);
Ylabel(‘Magnitude’);
Xlim([0 200]);
% Plot the filtered signal (after applying low-pass filter)
Subplot(2,2,3);
Plot(t, filtered_signal);
Title(‘Filtered Sensor Signal (Low-pass Filtered)’);
Xlabel(‘Time (seconds)’);
Ylabel(‘Amplitude’);
% Plot DFT of the filtered signal (After filtering)
Subplot(2,2,4);
Plot(f(1:floor(n/2)), abs(filtered_fft(1:floor(n/2))));
Title(‘DFT of Filtered Sensor Signal (After Filtering)’);
Xlabel(‘Frequency (Hz)’);
Ylabel(‘Magnitude’);
Xlim([0 200]);

OUTPUT :
RESULT :
 EX NO : Echo Detection in an Audio Signal in correlation

DATE :

AIM :
To write and simulate a MATLAB program to compute the Echo Detection in an
Audio Signal in correlation.

SYSTEM SPECIFICATION:

System with MATLAB 17.0.

Processor: Intel(R) Core(TM)2 Duo CPU E7500 @ 2.93GHz 2.94 GHz
System type: 32-bit Operating System

ALGORITHM:

1. Create a new M file.

2. Save the file as filename.m

3. Generate the Align the Signals Usinf Cross- Correlation of a given sequence
using command.

4. Plot the graph.

PROGRAM :
% Example: Echo detection using correlation
Fs = 1000;
T = 0:1/fs:1;
F = 5;
Original_signal = sin(2 * pi * f * t);
Delay = 0.2;
Delay_samples = round(delay * fs);
Echo_signal = [zeros(1, delay_samples), original_signal];
Echo_signal = echo_signal(1:length(original_signal));
Noisy_signal = echo_signal + 0.1 * randn(size(echo_signal));
[corr_values, lag] = xcorr(noisy_signal, original_signal);
[~, max_index] = max(corr_values);
Detected_delay = lag(max_index) / fs;
Figure;
Subplot(3, 1, 1);
Plot(t, original_signal);
Title(‘Original Signal’);
Xlabel(‘Time (s)’);
Ylabel(‘Amplitude’);
Subplot(3, 1, 2);
Plot(t, noisy_signal);
Title(‘Noisy Echo Signal’);
Xlabel(‘Time (s)’);
Ylabel(‘Amplitude’);
Subplot(3, 1, 3);
Plot(lag / fs, corr_values);
Title(‘Cross-Correlation’);
Xlabel(‘Lag (s)’);
Ylabel(‘Correlation’);
Grid on;
Fprintf(‘Detected delay: %.2f seconds\n’, detected_delay);
OUTPUT :
Correlation
Detected delay: 0.00 seconds
RESULT :