MATLAB Implementation of Fast Fourier Transform and Linear Chirp Z-Transform Algorithms

By utilizing Fast Fourier Transform (FFT) and Linear Chirp Z-Transform (LFM-Z/CZT), we can implement efficient algorithms in signal processing. The FFT algorithm provides a computational approach for converting signals from time domain to frequency domain using butterfly operations and recursive decomposition, typically implemented via MATLAB's fft() function with O(N log N) complexity. The Linear Chirp Z-Transform serves as a specialized method for radar and communication systems, enabling pulse compression and distance measurement through spiral sampling in the Z-plane, which can be coded using chirp z-transform algorithms with adjustable frequency resolution. These algorithms find broad applications in spectral analysis, filter design, and signal characterization. Understanding their implementation - including FFT's radix-2 implementation with bit reversal and CZT's Bluestein algorithm using convolution - is crucial for signal processing professionals. MATLAB implementations typically involve: 1. FFT: Using built-in fft() with zero-padding for frequency resolution control 2. CZT: Custom implementation defining spiral contour parameters for targeted frequency analysis Mastering these algorithms enables better interpretation of signal features and optimization of digital signal processing systems.