The Fourier analysis of signals includes the Fourier transform of continuous signals and the Fourier transform of discrete signals. Fourier Transform of Continuous Signals Definition Let x(t) be a continuous-time signal. If x(t) is absolutely integrable, that is, then the Fourier transform of x(t) exists and is defined as Its inverse transform is In the … Read more
Recently, during interviews, I found that many hardware test engineers are completely unaware of the concept of oscilloscope bandwidth, and some with over three years of experience do not understand the concept of bandwidth. Some candidates can roughly state the conclusion: the recommended bandwidth for an oscilloscope should be 3-5 times the signal frequency. However, … Read more
Learn about the time domain and frequency domain of signals, Fast Fourier Transform (FFT), windowing, and how these operations deepen your understanding of signals. Understanding Time Domain, Frequency Domain, FFT The Fourier Transform helps to understand common signals and how to identify errors within them. Although the Fourier Transform is a complex mathematical function, understanding … Read more
1. Calling Methods X=FFT(x); X=FFT(x, N); x=IFFT(X); x=IFFT(X, N) When performing spectral analysis with MATLAB, note: (1) The data structure of the return value from the FFT function is symmetric. Example: N=8; n=0:N-1; xn=[4 3 2 6 7 8 9 0]; Xk=fft(xn) →Xk =39.0000 -10.7782 + 6.2929i 0 – 5.0000i 4.7782 – 7.7071i 5.0000 4.7782 … Read more
Last year, the ban on Matlab at Harbin Institute of Technology and Harbin Engineering University sparked heated discussions among engineering students (Breaking: Harbin Institute of Technology and Harbin Engineering University banned Matlab software). So what exactly is this amazing software Matlab? How does it benefit us, the materials science professionals? MATLAB is an engineering application … Read more
MATLAB – Simple Implementation of Numerical PDE Solving Introduction Traditional numerical methods for solving PDEs include characteristic line methods, finite element methods, boundary element methods, multigrid methods, spectral methods, Fourier transform methods, etc. Due to limitations in knowledge, this article will only utilize Finite Difference, FT, and Characteristic Line Methods to implement numerical solutions for … Read more
This article introducesThe Hong Kong University of Science and Technology (Guangzhou)a paper on efficient fine-tuning of large models (LLM PEFT Fine-tuning) titled “Parameter-Efficient Fine-Tuning with Discrete Fourier Transform”, which has been accepted by ICML 2024, and the code has been open-sourced. Paper link: https://arxiv.org/abs/2405.03003 Project link: https://github.com/Chaos96/fourierft Background Large foundation models have achieved remarkable successes … Read more
Here, we introduce the concepts of time domain and frequency domain. The time domain shows how the amplitude of a signal varies over time. In the time domain example, we create an unusual waveform by adding two sine waves. One is a sine wave with a peak voltage of 1V and a frequency of 1kHz, … Read more
Hello everyone! Today I want to share with you a powerful C library – FFTW (Fastest Fourier Transform in the West). It is one of the fastest open-source libraries for Fourier Transform and is widely used in fields such as signal processing and image processing. Don’t worry if you don’t know what Fourier Transform is; … Read more