From a theoretical perspective, there are many problems in signal processing (filter design) and machine learning (SVMs) that can be formulated as convex optimization problems. More generally, optimization plays a large role in both fields--in many cases, the optimization problem is to minimize some function of noise/uncertainty subject to constraints that can be tuned, depending on the application. To a certain extent, you can loosely think of the problem of determining weights which maximize the likelihood function in a logistic regression problem as as analogous to determining the FIR filter taps that may minimize ripple over some frequency band of interest.
From a practical perspective, it is often necessary to combine techniques from both signal processing and machine learning to improve prediction accuracy. For example, I work with signals from sensors on wearable devices that contain data that corresponds to human movement--the data can be quite noisy, and it is necessary to perform classical signal processing techniques such as sample rate conversion and filtering to preprocess the data, which is then used for feature extraction. As a result, the training data that is collected is dependent on the filtering parameters that were used to preprocess data--and it is important to consider these parameters while evaluating the efficacy of a predictive model that uses such training data.
