Recent advancements in sensing, measurement, and computing technologies have significantly expanded the potential for signal-based applications, leveraging the synergy between signal processing and Machine Learning (ML) to improve both performance and reliability. This fusion represents a critical point in the evolution of signal-based systems, highlighting the need to bridge the existing knowledge gap between these two interdisciplinary fields. Despite many attempts in the existing literature to bridge this gap, most are limited to specific applications and focus mainly on feature extraction, often assuming extensive prior knowledge in signal processing. This assumption creates a significant obstacle for a wide range of readers. To address these challenges, this paper takes an integrated article approach. It begins with a detailed tutorial on the fundamentals of signal processing, providing the reader with the necessary background knowledge. Following this, it explores the key stages of a standard signal processing-based ML pipeline, offering an in-depth review of feature extraction techniques, their inherent challenges, and solutions. Differing from existing literature, this work offers an application-independent review and introduces a novel classification taxonomy for feature extraction techniques. Furthermore, it aims at linking theoretical concepts with practical applications, and demonstrates this through two specific use cases: a spectral-based method for condition monitoring of rolling bearings and a wavelet energy analysis for epilepsy detection using EEG signals. In addition to theoretical contributions, this work promotes a collaborative research culture by providing a public repository of relevant Python and MATLAB signal processing codes. This effort is intended to support collaborative research efforts and ensure the reproducibility of the results presented.