Time-Frequency Analysis of the Original and Resampled Square Wave Using Continuous Wavelet Transform and comparison with FFT using MATLAB

Abstract: Square waves play a crucial role in signal processing, digital electronics, control systems, and communication protocols. However, resampling these signals to meet different hardware specifications can introduce spectral distortions and aliasing effects. This study uses the Continuous Wavelet Transform (CWT) to examine the impact of resampling on square wave characteristics, offering superior time-frequency resolution compared to traditional Fourier-based methods. A square wave is generated using harmonic summation and initially sampled at 100 Hz before being resampled to 200 Hz for hardware compatibility. The resampled signal is then analysed using CWT scalograms, Power Spectral Density (PSD) analysis, and waveform comparisons to assess spectral distortions. Results show that CWT provides a detailed understanding of the transient and frequency variations caused by resampling, ensuring optimal signal fidelity. This research highlights the importance of advanced time-frequency analysis techniques in maintaining signal integrity across different sampling rates, with applications in real-time signal processing and embedded system design.

Keywords: MATLAB, Fourier Series, Scalogram, Odd Harmonics, Continuous Wavelet Transform (CWT), FFT