Memo: Wavelet filter bank

The discrete wavelet transformation (DWT) on paper is realized in practice in the form of filter banks. A filter bank consists of low-pass and high-pass filters that can be represented as coefficients matrices. These matrices are derived from the impulse response analysis of the base filter functions in z-domain. To be qualified as a DWT filter… Continue reading Memo: Wavelet filter bank

Memo: Wavelets compression basics

Data compression is the representation or re-encoding of information from its complete, readily usable form, to a mere recipe. The recipe can then be transmitted compactly and reconstructed at the end-user using the building blocks at the end system. In the data compression scene, the two most prevalent players are the classic Fourier transformation (and… Continue reading Memo: Wavelets compression basics

Memo: Deadbeat controller

Not all applications will require a PID controller. Some simpler applications such as conveyor belt and bottle filling in the industry sometimes are just about turning on for x amount of time and then turning off the output. They are called deadbeat controllers, the most primitive of all digital controllers, and they work well for… Continue reading Memo: Deadbeat controller

Memo: Digital PID controller

Digital controllers are more expensive to build in simple applications than analog counterparts but they are universally easier to implement at all scales. Digital controllers are limited by their sampling rates while they are capable of reaching steady state in a finite time and have much greater noise tolerance. Continuing from the last memo concerning analog PID,… Continue reading Memo: Digital PID controller

Memo: Design an analog PID controller

A controller transforms a plant (uncontrolled process) into a controlled system. A controller alters the input signal of the plant in order to correct the output error, which is the difference between the momentary output of the entire system and a reference value. The most popular controller in education and industry is the Proportional-Integral-Derivative controller (PID… Continue reading Memo: Design an analog PID controller

Memo: Thermodynamic processes

When investigating thermodynamic systems, especially gaseous systems, scientists often keep one of the three variables (pressure, volume, temperature) at constant and vary the remaining two. The act of fixating one variable and changing the others gives rise to thermodynamic, conjugate variable processes: Isobaric: constant pressure. Isothermal: constant temperature. Isometric / Isochoric / Isovolumetric: constant volume.… Continue reading Memo: Thermodynamic processes

Memo: Chemical bonding models

Beyond the level of individual atoms, atomic theory also concerns itself with the mechanism of molecular bonding and the geometry of molecules. There are three relevant chemical bonding models nowadays: Valence shell electron pair repulsion theory (VSEPR): the simplest, most primitive model based on electron field repulsions and Lewis structure. Valence bond theory (VB): a modern… Continue reading Memo: Chemical bonding models

Memo: Atomic models

Atoms are composed of subatomic particles whose quantity and arrangement affect their properties. The scientific theory correlating subatomic particles' quantity, their arrangement in an atom, and the atom's properties is called "atomic theory". Atomic theory attempts to explain how certain electron configurations affect the reactivity of elements, how certain elements are polarized while others aren't,… Continue reading Memo: Atomic models

Memo: Thermodynamics in Chemistry

All energy transferences are done in two ways: by heat or by work. In any given system and any given process, the total energy transferred is the sum of the heat transferred and the amount of work transferred. This says nothing about the ratio of work and heat in the total energy, or why energy can only… Continue reading Memo: Thermodynamics in Chemistry

Memo: Gas laws

Historically, the proportionalities of temperature, volume, and pressure of an ideal gas are described in pair empirically by Boyle's law (pressure-volume), Charles' law (temperature-volume), and Gay-Lussac's law (pressure-temperature). These early gas laws; along with Avogadro's law, which links the study of gas in Physics to the number of molecules in Chemistry; are combined to form the modern ideal… Continue reading Memo: Gas laws