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IoT uses wireless sensor networks (WSN) to deploy many sensors to track environmental and physical parameters. The WSN measurements are frequently contaminated and altered by noise. The noise in the signal increases the sensor node’s computation and energy utilization, resulting in less longevity of the sensor node. The Finite Impulse Response (FIR) filter is commonly employed in WSN to pre-process sensed signals to remove noise from the sensed signals using delay elements, multipliers, and adders. Traditional multiplier-based FIR filter designs result in hardware-intensive multipliers that consume a lot of energy, and area and have low computation speed. These drawbacks make them unsuitable for IoT-based WSN systems with stringent power efficiency necessities. Approximate computing enhances the energy efficiency of an FIR filter. Arithmetic circuits utilizing approximate computing improve the hardware performance, with some loss of accuracy to save energy utilization and boost speed. A novel approximate multiplier architecture employing a fast and straightforward approximation adder is proposed in this study. Approximate multiplier M1 using OR gate and approximate multiplier M2 using proposed approximate adders are compared. The proposed approximate adder is suited for building an adder tree to accumulate partial product (PP) because it is less complicated than traditional adders. Compared to a one-bit-full adder, the critical path delay (CPD) is reduced significantly in the proposed methods. The accuracy comparison of M1. M2 and Wallace tree using the normalized mean error distance (NMED), the mean relative error distance (MRED), the maximum error (ME), and the error rate (ER) with the number of bits utilized for reducing error. For the area (delay) optimized circuit, when the bit used is 4, the delay is 0.4 ns for M1, 0.43 ns for M2, and 1.08 ns for the Wallace tree multiplier. For the delay (area) optimized circuit, when the bit used is 4, the delay is 0.16 ns for M1, 0.16 ns for M2, and 0.40 ns for the Wallace tree multiplier. To more accurately evaluate performance at the circuit level, the PDP and ADP are computed. The NMED, MRED, ME, and ER versus PDP and ADP are computed. The proposed multipliers M1 and M2 are compared with existing approximate multipliers. When an equivalent MRED, NMED, or ER is taken into account, M1 has the smallest ADP and PDP among other multipliers. The very low likelihood of a significant ED occurring is indicated by the small values of NMED and MRED in M1 and M2. The proposed solutions effectively reduce delay, area, and power while maintaining increased accuracy and performance.