FFT-Based Interpolated Frequency Estimation Algorithm with MATLAB Implementation

This article presents an FFT-based interpolated frequency estimation algorithm accompanied by practical MATLAB implementation. The algorithm significantly enhances frequency estimation accuracy for signals, playing a crucial role in signal processing and communication systems. Through spectral interpolation techniques applied to FFT results, we achieve sub-bin frequency resolution by fitting curves to FFT magnitude peaks using polynomial interpolation methods. The implementation involves calculating the standard FFT of the input signal, identifying peak magnitudes in the frequency domain, and applying interpolation formulas (such as quadratic or Gaussian interpolation) around detected peaks to refine frequency estimates beyond the standard FFT resolution. Key MATLAB functions include fft() for Fourier transformation, findpeaks() for spectral peak detection, and custom interpolation routines for precise frequency calculation. We provide detailed explanations of the algorithmic workflow including windowing considerations, interpolation coefficient calculations, and frequency correction formulas. Sample code demonstrates practical implementation with synthetic signals, showing how to handle parameters like sampling frequency, signal-to-noise ratio, and window functions. The MATLAB implementation includes configuration options for different interpolation methods and visualization tools for spectrum analysis. This resource aims to assist researchers and engineers working on frequency estimation challenges, offering both theoretical foundations and practical coding examples to enhance understanding and application in real-world scenarios. The algorithm's performance evaluation metrics and comparison with conventional FFT methods are also discussed to highlight its advantages in precision-critical applications.