Deep Learning, a subfield of artificial intelligence (AI), has significantly transformed many industries due to its capability to extract intricate structures of large-scale data. Signal processing, a different discipline that focuses on analyzing, modifying, and synthesizing signals such as sound, images, and scientific measurements, can greatly benefit from Deep Learning techniques. The integration of Deep Learning into Signal Processing is an advanced development that seeks to effectively interpret raw data signals, which caters to a broad range of applications from healthcare monitoring to predictive analytics and beyond.

• Broad Applicability: Deep Learning methods can manage all varieties of signal processing data; from time-series data, images, sound signals - it aims to provide highly precise predictive and classification models.
• Complex Feature Extraction: Deep Learning algorithms are designed and trained to extract high-level complex features from raw signals, which differ significantly from traditional signal processing techniques.
• Capacity for Learning: Unlike the conventional signal processing methods requiring manual feature engineering and specification, the adoption of deep learning techniques encourages machine-learning, a process that automatically learns and improves from experience without the need for explicit programming.
• Predictive and Descriptive Analytics: Deep Learning for Signal Processing is utilized not only for predictive purposes but also for descriptive analytics, providing more profound insights into the intricacies of the dataset.
• Cost-Effectiveness: Deep Learning algorithms are often open-source and available for free, reducing the requirement for extensive investment in expensive software toolboxes.

Adoption of Deep Learning in signal processing is on the rise across numerous business sectors – due in large part to its adaptability, cost-savings, and the high accuracy of predictive outcomes obtained in varied signal processing tasks.

• Economic Efficiency: Deep Learning software generally requires less financial investment as they are mostly open-source. Adoption of Deep Learning techniques can massively reduce costs incurred in purchasing commercial software tools.
• Time-Saving: Deep Learning techniques substantially reduce the time invested in manual feature extractions and building algorithms from scratch. These systems are designed to automatically learn from data, making the modeling process more straightforward and faster.
• Enhanced Precision: Deep Learning methods bring high degrees of accuracy into signal processing tasks, especially in complex environments, due to their ability to learn intricate signal features and structures.
• Ongoing Support: Many Deep Learning algorithms are backed by extensive communities of developers, ensuring constant updates, bug-fixing, and improvements.
• Ease of Integration: Deep Learning modules can be effortlessly incorporated into existing processing systems to enhance the functionality and predictive power.
• Scalability: Deep Learning models have proven to be highly scalable, catering to various signal processing tasks' growing needs.

Despite its numerous advantages, potential pitfalls associated with Deep Learning techniques in Signal Processing must be considered.

• Data Requirement: Deep Learning models require a massive amount of data for accurate functionality, which may pose a challenge for applications with limited-data.
• Lack of Interpretability: Deep Learning models, often regarded as 'black boxes,' might cause lack of transparency and interpretability - a problem viewed as critical by many industries.
• Training Time: Training Deep Learning models can be time-consuming and require substantial computational resources, which might be a concern for real-time applications.
• Data Privacy: Deploying Deep Learning in signal processing might bring about data privacy concerns, particularly in sensitive sectors such as healthcare.

In the implementation phase, a comprehensive analysis of data requirement, computational resources, and suitability of various deep learning techniques for a specific application is paramount. The balance between maximized utility of deep learning and managing potential challenges such as interpretability and privacy issues must be vigilantly maintained. The success of Deep Learning in Signal Processing significantly relies on careful strategizing, sound execution, and ongoing monitoring.