Adding noise to a sine wave signal and filtering that noise ?

Hi every one, can you help me please , i need to plot a sine wave signal without noise at first then plot it when adding noise , then filtering that noise

Answer 1

[Ayush]

Hi @Abdelaziz Elgaafary,

To plot a sine wave signal without a noise and then adding a noise, follow these steps:

• Generating a sine wave signal without noise

% Generate a sine wave signal without noise
frequency = 2; % Frequency of the sine wave (in Hz)
amplitude = 1; % Amplitude of the sine wave
sampling_rate = 100; % Number of samples per second
duration = 1; % Duration of the signal (in seconds)

t = linspace(0, duration, sampling_rate * duration);
signal = amplitude * sin(2 * pi * frequency * t);

% Plot the sine wave without noise
figure;
plot(t, signal);
xlabel('Time (s)');
ylabel('Amplitude');
title('Sine Wave without Noise');
grid on;

• Generation of noise and addition of noise

% Generate random noise
noise_amplitude = 0.2; % Amplitude of the noise
noise = noise_amplitude * randn(size(t));

% Add noise to the signal
noisy_signal = signal + noise;

% Plot the sine wave with noise
figure;
plot(t, noisy_signal);
xlabel('Time (s)');
ylabel('Amplitude');
title('Sine Wave with Noise');
grid on;

Now, filtering the noise:

• Defining a low-pass filter for noise removal

% Apply low-pass filter to remove noise
cutoff_frequency = 10; % Cut-off frequency of the low-pass filter
normalized_cutoff = cutoff_frequency / (sampling_rate / 2);
[b, a] = butter(4, normalized_cutoff, 'low');
filtered_signal = filtfilt(b, a, noisy_signal);

• Plotting filtered signal

% Plot the filtered signal
figure;
plot(t, filtered_signal);
xlabel('Time (s)');
ylabel('Amplitude');
title('Filtered Sine Wave');
grid on;

Hope it helps!