  This paper presents a comprehensive exploration of Fast Fourier Transform
(FFT) and linear convolution implementations, integrating both conventional
methods and novel approaches leveraging the Bit Slicing Multiplier (BSM)
technique. The Bit Slicing Multiplier utilizes Look-Up Tables (LUTs) to execute
bitwise operations in parallel, offering efficient arithmetic operations
ideally suited for digital signal processing tasks. We extensively investigate
the integration of BSM into FFT and linear convolution algorithms, emphasizing
its advantages in terms of speed and resource utilization. Additionally, we
introduce our own innovative ideas for FFT and convolution algorithms,
contributing to the broader discourse on efficient signal processing
techniques. Experimental validation of our implementations is conducted using
Vivado, a leading FPGA synthesis and implementation tool. Comparative analysis
demonstrates the superior performance of our BSM-enhanced approaches,
showcasing their potential for real-time signal processing applications. This
study not only advances the understanding of FFT and convolution
implementations but also highlights the effectiveness of novel techniques like
BSM in enhancing computational efficiency in FPGA-based systems.
