In The Digital Signal Processing Applications, Spectral Analysis Is One Of The Key Domains To Study The Characteristics Of The Signals, Where Popular Algorithms Such As Fast Fourier Transform (FFT), Fast Hartley Transform (FHT), Etc. Are Implemented For Real Time Applications. In These Domains, Some Of The Special Functions Or Transforms Such As Windowing Functions, Running Fourier Transform And Mellin Transform Have Not Been Well Studied For Suitable VLSI Implementation To Meet Today's And Futuristic Real Time Speci_Cations. Often Digital Signal Processing Architectures Employ Multiply-Accumulate (MAC) As The Elementary Operation. As An Alternative Arithmetic Unit To MAC, CO-Ordinate Rotation Digital Computer (CORDIC) Has Gained Momentum Due To Its Versatility And Hardware Economy. In This Dissertation, A New CORDIC Based Uni_Ed VLSI Architecture For Implementing Popular Windowing Functions Such As Hanning, Hamming And Blackman Has Been Proposed, Which Is Having The Advantage Of High Throughput And _Exibility. Kaiser-Bessel Windowing Is Also A Choice Among The Popular Windowing Function Due To Its Better Spectral Characteristics And Most Of The Implementations Are Based On Look Up Table (ROM). So It Is Essential To Design A Real Time Architecture For Computing Kaiser-Bessel Windowing. In This Dissertation, A New CORDIC Based VLSI Architecture For Implementing Kaiser-Bessel Windowing Suitable For Real Time Applications Has Been Proposed. Next A New CORDIC Based Running Discrete Fourier Transform Architecture Incorporating Refreshing Mechanism Has Been Proposed. This Architecture Is Compared With The Existing Architectures In Terms Of The Hardware Complexity And Con_Nement Of Error Within Certain Limit. Mellin Transform Has Been Used In Many Signal And Image Processing Applications Due To Its Scale Invariant Property. But To Our Knowledge, No One Has Addressed The Real Time Hardware Implementation Of Mellin Transform. In This Dissertation, A New CORDIC Based VLSI Architecture For Computing Mellin Transform Has Been Proposed For Real Time Applications. The New Ef_Cient Architectures Mentioned Above Are Designed Using Veriloghdl And Synthesized Using Commercially Available 0.18 M CMOS Technology And Their Performance In Terms Of Speed, Area And Power Are Reported. Keywords: Uni_Ed Windowing Function, Running DFT, Discrete Mellin Transform, CORDIC, VLSI Architecture, Real Time, Spectral Analysis, Digital Signal Processing.