Digital Signal Processing (DSP) is critical in the development and optimization of modern telecommunication and wireless systems. The advent of complex standards like 5G and AI-native networks has increased the need to revisit classical and new DSP algorithms. This paper presents a systematic review of DSP techniques that include time-domain, frequency-domain, and advanced signal processing methods, as well as new AI-based approaches, such as Deep Reinforcement Learning (DRL), Neural Architecture Search (NAS), Graph Neural Networks (GNN), and Bayesian Optimization (BO). The survey explores basic DSP principles, historical developments, and key performance metrics like latency, throughput, and computational complexity. It compares classical and new algorithms, analysing their merits, limitations, and suitability for real-world applications, such as modulation schemes (QAM, OFDM), channel estimation, noise suppression, MIMO, and beamforming. Additionally, the paper addresses the integration with Software-Defined Radio (SDR), edge computing, and the Internet of Things (IoT), highlighting challenges related to real-time implementation and hardware acceleration using FPGA and ASIC platforms. Key research challenges and future directions are identified, such as the need for scalable, adaptive DSP in dynamic environments, power-efficient hardware implementation of AI models, and the growing importance of optimization in future wireless systems. This review is a comprehensive resource for researchers at the intersection of signal processing, wireless communication, and intelligent systems.