Wavelet Transform Implementation for Weak Signal Detection with BPSK, QAM, and FSK Modulation Analysis

Wavelet transform is a widely used signal processing technique that enables efficient detection of weak signals. Beyond weak signal detection, wavelet transforms find applications in numerous domains, including modulation techniques such as Binary Phase Shift Keying (BPSK), Quadrature Amplitude Modulation (QAM), and Frequency Shift Keying (FSK). By integrating wavelet analysis with these modulation schemes, we can gain deeper insights into signal characteristics through multi-resolution decomposition. The implementation typically involves applying discrete wavelet transform (DWT) functions like wavedec() in MATLAB or pywt.wavedec() in Python's PyWavelets library to decompose signals into approximation and detail coefficients. For modulation analysis, wavelet coefficients at specific scales can reveal temporal patterns of phase shifts (BPSK), amplitude variations (QAM), and frequency transitions (FSK). Key algorithmic advantages include the ability to localize transient features through mother wavelet selection (e.g., Daubechies for oscillatory patterns) and noise reduction via thresholding techniques. Consequently, wavelet transforms hold significant importance in modern signal processing applications ranging from communications to biomedical engineering.