The short-time Fourier transform (STFT) is essential for non-stationary signal analysis in areas such as audio processing, communication systems, and real-time spectrum analysis (RTSA). However, in practical RTSA instruments, conventional hardware implementations of the STFT are typically restricted to fixed window functions and fixed hop sizes, and they consume excessive logic cells and multiplier resources to meet high-throughput, low-latency streaming requirements, making them difficult to deploy on resource-constrained or portable platforms. This paper proposes a novel parallel windowed short-time Fourier transform (PW-STFT) architecture that leverages FFT-based processing techniques. By integrating parallel window multipliers and runtime parameterizable multipliers based on canonical signed digital (CSD) encoding, the design flexibly supports arbitrary window and hop sizes while minimizing hardware overhead. Experiments on a 32-point STFT with a hop size of 8 show that the proposed PW-STFT architecture significantly reduces resource usage (658 slices and 24 DSPs) compared to previous approaches while still maintaining an acceptable signal-to-noise and distortion ratio (SINAD) of 40.31 dB. This balance between hardware savings and output fidelity makes the design well suited for real-time STFT applications across a wide range of window types and signal conditions. Therefore, the PW-STFT architecture provides a flexible and resource-efficient solution for real-time spectrum analysis, enabling high-throughput and precise time-frequency analysis of non-stationary signals.