Biomedical signals are the space–time representation of physiological activities of organisms. The various sources of biomedical signals are heart rhythm, blood glucose level, blood pressure, nerve conduction, brain activities, and so on. The electrical activity of the heart, brain, and muscles are measured as bioelectric signals namely electrocardiogram, electroencephalogram, and electromyogram. These signals are a measure of the bio-potentials between the electrodes placed on the skin surface and are often corrupted with power-line noise, baseline wander, muscle artifacts, and other high-frequency noise components. Biomedical signal processing focuses on extracting the useful information and removing noise from the real-time biomedical signals for effective diagnosis and clinical analysis. Digital filters are employed to remove noise from the recorded real-time biomedical signals. The method proposed in this work is to design a finite impulse response filter using simulated annealing and genetic algorithm optimization techniques for effective signal de-noising. The performance indices are calculated to evaluate the accuracy and consistency of the proposed design. It is found that the simulated annealing optimized filter meets the objective efficiently and minimizes the error to 0.00641.