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The vertical common subexpression elimination (CSE) method proposed by Jang et al. does not guarantee hardware reduction over conventional horizontal CSE method in practical linear phase finite impulse response (LPFIR) filter implementations. A method to implement FIR filters with a minimum number of adders by efficiently combining horizontal and vertical common subexpressions is proposed here. Introduction: Multiple constant multiplications (MCM) in digital filters refer to multiplication of one variable with multiple constants [1]. Common subexpression elimination proposed to tackle the MCM problem minimizes the number of additions by extracting the common parts among the constants represented in canonic signed digit (CSD) form [1]-[3]. Methods proposed in [2] and [3] eliminate redundant computations in multiplier blocks by employing the most common horizontal subexpressions among the CSD coefficients. Recently, Jang et al. proposed a vertical CSE technique as a better solution to the MCM problem [4]. However, this method does not guarantee hardware savings over

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