Several Methods for DTFT Calculation

In this article, I will provide a detailed introduction to several methods for calculating the Discrete-Time Fourier Transform (DTFT) in MATLAB. DTFT serves as a fundamental signal processing tool that enables us to analyze frequency domain characteristics of signals. MATLAB offers multiple approaches for DTFT computation, including implementations through M-files. I will systematically present each method with practical examples to help readers gain a deeper understanding of these concepts.

The implementation typically involves defining the frequency vector, creating the complex exponential kernel, and performing matrix multiplication with the input signal. Key MATLAB functions often utilized include exp() for exponential operations, linspace() for frequency range generation, and element-wise multiplication operations. For longer sequences, frequency domain sampling and zero-padding techniques can be employed to improve spectral resolution. Each method will be accompanied by code snippets demonstrating practical implementation details and algorithmic considerations.