This paper presents an FPGA implementation of highly modular universal discrete transforms. The implementation relies upon the unified discrete Fourier Hartley transform (UDFHT), based on which essential sinusoidal transforms including discrete Fourier transform (DFT), discrete Hartley transform (DHT), discrete cosine transform (DCT) and discrete sine transform (DST) can be realized. It employs a reconfigurable, scalable and modular architecture that consists of a memory-based FFT processor equipped with pre- and post-processing units. Besides, a pipelining technique is exploited to seamlessly harmonize the operation between each sub-module. Experimental results based on Xilinx Virtex-II Pro are given to examine the performance of the proposed UDFHT implementation. Two practical applications are also shown to demonstrate the flexibility and modularity of the proposed work.