The Z-transform is a powerful mathematical tool that extends the Fourier Transform to analyze discrete-time signals and systems. This article covers its fundamental concepts, including stability analysis, poles and zeros, and its role in solving difference equations.
Discover how linear transformations are represented in different bases and why similar matrices preserve essential properties. Understand the mathematics behind change-of-basis operations.
Explains the principles and characteristics of L1 and L2 regularization, their connection to Maximum a Posteriori (MAP) estimation, and how to apply regularization to prevent overfitting in deep learning models.
A statistical method used to evaluate whether differences between two sample means are significant or due to chance.
A detailed exploration of Cross-Entropy and KL Divergence, deriving their formulas step-by-step from the principles of probability and information theory.
The Z-transform is a powerful mathematical tool that extends the Fourier Transform to analyze discrete-time signals and systems. This article covers its fundamental concepts, including stability analysis, poles and zeros, and its role in solving difference equations.
This post introduces the Discrete Fourier Transform (DFT) for frequency analysis and the Fast Fourier Transform (FFT), which optimizes computation using a divide-and-conquer approach.
This article explores the process of converting continuous analog signals into digital form, detailing each step—from pre-processing and A/D conversion to D/A reconstruction using methods like ideal, zero-order, and first-order holds. It also discusses key challenges such as aliasing and practical limitations in achieving perfect signal recovery.
This article introduces the key concepts of LTI systems using impulse response, convolution, and difference equations. It explains how these concepts reveal the system's behavior and how to mathematically solve for its response.
This article explores the basics of discrete-time signals, including periodic signals and key types like impulse, step, and exponential signals. It also explains LTI systems and how to analyze their stability.
