- Generate three sinusoids with frequencies of 60 Hz, 70 Hz, and 100 Hz.
- Ensure that each sinusoid has a power of 1 (unity power).
- Add white Gaussian noise with a power of -6 dB relative to the signal power.
- Sample the signal at a rate of 250 Hz.
To calculate the noise power, you need to relate it to the signal power. If the signal has a power of 1 (0 dB), then the noise needs to have a power of 0.5 (since -6 dB is half the power on a linear scale).
fs = 250; % Sampling frequency in Hz
t = (0:49) / fs; % Time vector for 50 samples
frequencies = [60, 70, 100]; % Frequencies of the sinusoids
% Generate the sinusoids
signal = cos(2 * pi * frequencies(1) * t) + ...
cos(2 * pi * frequencies(2) * t) + ...
cos(2 * pi * frequencies(3) * t);
% Normalize the signal to have unity power
signal = signal / sqrt(mean(signal.^2));
% Generate the noise at -6 dB relative to the signal power i.e -6 DB = 1/4 = 0.25
% in linear scale
noise_power_db = -6; % Noise power in dB
noise_power_linear = 10^(noise_power_db / 10); % Convert dB to linear scale
noise = sqrt(noise_power_linear / 2) * randn(1, length(t)); % Generate noise
% Add the noise to the signal
noisy_signal = signal + noise;
% Plot the signal and the noisy signal
figure;
subplot(2, 1, 1);
plot(t, signal);
title('Original Signal');
grid on
subplot(2, 1, 2);
plot(t, noisy_signal);
title('Noisy Signal');
grid on
This code generates the required signal and noise, adds them together, and then plots both the original clean signal and the noisy signal. Please adjust the code if needed to fit the specific requirements of your application or simulation environment.
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- Embedded Systems | Firmware Developement | Simulations
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