Instantaneous Frequency Measurement Algorithm Based on DFT

In this article, we explore a DFT-based instantaneous frequency measurement algorithm that incorporates interpolation techniques to achieve more accurate and reliable frequency detection results. This algorithm not only enhances our understanding of signal frequency characteristics but also plays a vital role in signal processing applications. We begin by introducing the Discrete Fourier Transform (DFT) and its fundamental role in signal analysis. The core implementation involves calculating the DFT using efficient algorithms like FFT (Fast Fourier Transform), where the frequency resolution is determined by the sampling rate and window length. Next, we delve into the basic principles of instantaneous frequency measurement, explaining how phase differences between consecutive signal frames can be computed using atan2 functions for precise frequency estimation. The interpolation algorithm section details practical implementation methods, including quadratic or Gaussian interpolation applied to DFT bins to refine frequency estimates beyond the inherent DFT resolution limitations. Finally, we visualize the frequency measurement results through graphical representations using plotting libraries like matplotlib, demonstrating how to apply this algorithm to real-world signal processing tasks through comprehensive code examples that handle windowing, zero-padding, and frequency bin interpolation.