In this article, we explore how radar systems perform one of the most challenging tasks in signal processing: detecting extremely weak echoes buried deep in noise. What appears as sophisticated engineering is actually an elegant implementation of dot products (or more formally an inner product). If you are new to

Vectors aren’t just arrows, they’re a universal language defined by simple rules of addition and scaling. Once you strip away the visual baggage of direction and length, you realize that polynomials, matrices, functions, operators, sequences, even quantum states, are all vectors too. Size and angle? Optional add-ons you

In this article, we connect the abstract math of signal vectors and inner products to the real-world magic of tuning into your favorite station. What seems like simple circuitry is actually a precise implementation of decomposition, projecting signals onto carrier frequencies and filtering out everything else. We’ll break down

Most people learn the Fourier series as a formula, but miss its true identity: an orthogonal decomposition. And that changes everything. Once you see signals as sums of orthogonal components, the Fourier series isn’t just elegant, it becomes the gateway to a whole universe of decompositions. In this post,

Let’s be honest — people love name-dropping “Hilbert space” in everything from signal processing to quantum mechanics. It’s the go-to phrase when someone wants to sound deep. But what does it actually mean? And why is it so central to everything from Fourier analysis to wavefunctions? In this post,

Most people hear “Hilbert space” and nod along without really knowing what it means. But this is where the real math behind DSP starts — not in geometry, but in structure. In this post, we dig into what actually makes a “length” a length and a “dot product” a dot product.

“Signals are vectors.” You probably heard that once — maybe in a DSP lecture or floating around a grad lab — like math gossip no one dared question. This idea is way deeper, weirder, and so elegant. Vectors aren’t just arrows in space. They can be images, sounds, waveforms — even entire