Pulse pressure is a manifestation of arterial palpation of the heartbeat. Wrist pulse signal contains important information about the health status of a person and pulse signal diagnosis has been employed in oriental medicine for a very long time. This paper mainly addresses the problem of removing artifacts from wrist pulse signals. Noise is an irregular function that accompanies a transmitted electrical signal and tends to obscure it. The collected wrist pulse signals contain noise. The type of noise which the signal contains may be random noise, structured noise or physiological interference. In our paper, we have employed signal processing techniques in order to remove noise from the wrist pulse signal. Low Pass Filter (LPF) and Wavelet Transform (WT) techniques are used for this purpose. In our work, we have considered simulation and actual cases. In simulation cases, we have added noise to the signal and tried to remove it. In actual cases, we have considered the results of the simulation and implemented the signal processing techniques on actual noisy wrist pulse signals. Our work has studied the efficacy of LPF and WT techniques in minimizing artifacts in wrist pulse signals in simulation and in actual cases. Calculated mean square error for a simulated signal show that wavelet denoising has lesser mean square error than low pass filtering. Hence we have concluded that wavelet denoising is a better filtering than low pass filter.