Complex Modulation Zoom Spectrum Analysis Method Based on Complex Analytic Band-Pass Filter

In this paper, I introduce a complex modulation zoom spectrum analysis method based on complex analytic band-pass filters. This approach enables selective frequency band refinement of signals through complex analytic band-pass filtering, followed by spectral analysis of the refined signal components. Implementation typically involves designing a complex filter with specific passband characteristics using functions like scipy.signal.firwin or custom IIR designs, then applying complex demodulation techniques to shift the frequency band of interest to baseband. The method allows for more accurate analysis and understanding of complex modulated signals' spectral characteristics. Notably, complex analytic band-pass filters serve as highly effective filtering tools that perform precise frequency band selection in the spectral domain, thereby enhancing signal processing precision and accuracy. The core algorithm involves frequency shifting through complex multiplication (e.g., using exp(1j*2*pi*fc*t) for carrier removal), followed by low-pass filtering and decimation for resolution improvement. Consequently, this complex modulation zoom spectrum analysis method based on complex analytic band-pass filters demonstrates significant application potential and can be widely utilized across multiple domains including communications, radar signal processing, and vibration analysis.