Introduction to Signal Denoising in Python

Key Takeaways

Welcome to this section on signal denoising. In this section, we will study three important filters that are commonly used to remove noise from signals. These filters are called signal deninoisers because their purpose is to remove noise or in other words to recover the original signal from a noisy one. The three filters we will cover are the moving average filter, the Gaussian mean filter, and the median filter. Let's begin with the first one. The moving average filter, also known as the mean filter. As the name suggests, it is a moving filter, which means it slides over the noisy signal and takes the average of the samples it covers in order to smooth out or remove noise. For example, if the order of the moving average filter is 10, it means that each time the filter moves along the noisy signal, it takes the average of 10 samples of that signal to produce a denoised output. This filter moves over the signal in the same way that a kernel moves over a signal during convolution. The second filter is the Gaussian mean filter. This filter is designed according to the Gaussian equation. You may already know that the Gaussian function represents a well known bell shape distribution in statistics. Similarly, the Gaussian mean filter is a popular smoothing filter in signal processing that follows the same Gaussian principle. It calculates the weighted mean of the noisy signal based on the Gaussian function as it moves along the data. The Gaussian mean filter gives more weight to the central samples and less weight to the outer samples which helps it preserve the overall shape of the signal while removing noise effectively. The third filter is the median filter. Unlike the first two, the median filter is a nonlinear filter. While the moving average and Gaussian mean filters are linear, the median filter operates nonlinearly because of its nonlinear nature. It has a wider range of applications compared to the other two. The median filter is especially effective in removing spike like noise also known as impulse or salt and pepper noise without blurring the edges of the signal. In this section, we will use the median filter not only for general signal denoising but also to recover a signal that has been corrupted by spiky noise. We will explore two important applications of the median filter to understand how it performs under different types of noise conditions. So let's begin this section and learn how these three filters, the moving average filter, the Gaussian mean filter, and the median filter help us recover clean signals from noisy data.