Adding White Noise to a Sine Wave in MATLAB: Examples and Techniques

In the world of signal processing and communication systems, adding white noise to a sine wave is a common task that engineers and researchers need to tackle. White noise is a random signal that has equal intensity at different frequencies, giving it a constant power spectral density. MATLAB, an essential tool for engineers and scientists, provides various functionalities for generating, processing, and visualizing signals, making it easy to add white noise to a sine wave. In this article, we will discuss some examples for adding white noise to a sine wave in MATLAB and illustrate the process step by step.

Example 1: Adding White Noise to a Basic Sine Wave

Let's start with a basic sine wave equation:

x(t) = A _ sin(2 _ pi _ f _ t)

Where A is the amplitude, f is the frequency in Hz, and t is the time in seconds.

To generate this sine wave in MATLAB, we first need to create an array of time samples. We'll use the following parameters as an example:

A = 1;
f = 10; % frequency of 10 Hz
t = 0:1/1000:1; % time vector from 0 to 1 with a step of 1/1000

Now, we can create the sine wave using the sin function:

sine_wave = A _ sin(2 _ pi _ f _ t);

Next, we need to generate the white noise signal. MATLAB has a built-in function called 'randn' that generates normally distributed random numbers. We can use this function to create a white noise signal with a specific standard deviation (noise power). Let's use a standard deviation of 0.5:

noise_power = 0.5;
whitenoise = noisepower * randn(size(t));

To add the white noise to the sine wave, we simply perform element-wise addition:

noisysinewave = sinewave + whitenoise;

Finally, we can visualize the original sine wave, the white noise, and the noisy sine wave using the 'plot' function:

figure
hold on
plot(t, sine_wave, 'b');
plot(t, white_noise, 'r');
plot(t, noisysinewave, 'g');
legend('Sine Wave', 'White Noise', 'Noisy Sine Wave')
xlabel('Time (s)');
ylabel('Amplitude');
title('Adding White Noise to a Sine Wave in MATLAB');
hold off

Example 2: Adjusting the Noise Power

We can explore the effect of different noise powers on the noisy sine wave by changing the value of the noisepower variable. For instance, setting noisepower to a higher value (e.g., 1) will result in more noise being added to the sine wave, making it less distinguishable. Lowering the noise_power value (e.g., 0.1) will result in a cleaner sine wave with less added noise.

These examples demonstrate the ease of adding white noise to a sine wave in MATLAB. By understanding the basic principles and using built-in MATLAB functions, engineers and researchers can easily simulate and analyze such signals in various applications.