MATLAB Implementation of Spectral Analysis with ZOOM-FFT Technique

In spectral analysis, the selection of data length N significantly impacts frequency resolution. Given a sampling frequency fs, the frequency resolution in the spectrum can be calculated as df=fs/N. However, when higher resolution is required, ZOOM-FFT (Zoom Fast Fourier Transform) serves as an effective solution. This technique enhances spectral resolution while maintaining the original data length through interpolation and resampling methods. The MATLAB implementation typically involves three key steps: 1. Bandpass filtering to isolate the frequency band of interest 2. Resampling (decimation) to effectively increase the sampling rate relative to the zoomed band 3. Applying standard FFT to the processed signal with adjusted frequency axis scaling This approach allows localized high-resolution analysis without requiring longer data acquisition times. The algorithm essentially "zooms in" on specific frequency regions by shifting the baseband frequency and modifying the effective sampling rate through rational resampling techniques. Key MATLAB functions utilized in this implementation include: - fft for fundamental Fourier analysis - resample for rate conversion - fir1 or butter for anti-aliasing filter design - freqz for frequency response verification The resulting spectrum provides magnified view of selected frequency bands with improved resolution, making it particularly valuable for analyzing closely-spaced spectral components in vibration analysis, communications systems, and audio signal processing applications.