Digital biquad filterIn signal processing, a digital biquad filter is a second order recursive linear filter, containing two poles and two zeros. "Biquad" is an abbreviation of "biquadratic", which refers to the fact that in the Z domain, its transfer function is the ratio of two quadratic functions: The coefficients are often normalized such that a0 = 1: High-order infinite impulse response filters can be highly sensitive to quantization of their coefficients, and can easily become unstable.
Digital filterIn signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is typically an electronic circuit operating on continuous-time analog signals. A digital filter system usually consists of an analog-to-digital converter (ADC) to sample the input signal, followed by a microprocessor and some peripheral components such as memory to store data and filter coefficients etc.
Floating-point arithmeticIn computing, floating-point arithmetic (FP) is arithmetic that represents subsets of real numbers using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. Numbers of this form are called floating-point numbers. For example, 12.345 is a floating-point number in base ten with five digits of precision: However, unlike 12.345, 12.3456 is not a floating-point number in base ten with five digits of precision—it needs six digits of precision; the nearest floating-point number with only five digits is 12.
High-pass filterA high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency depends on the filter design. A high-pass filter is usually modeled as a linear time-invariant system. It is sometimes called a low-cut filter or bass-cut filter in the context of audio engineering. High-pass filters have many uses, such as blocking DC from circuitry sensitive to non-zero average voltages or radio frequency devices.
Filter designFilter design is the process of designing a signal processing filter that satisfies a set of requirements, some of which may be conflicting. The purpose is to find a realization of the filter that meets each of the requirements to a sufficient degree to make it useful. The filter design process can be described as an optimization problem where each requirement contributes to an error function that should be minimized. Certain parts of the design process can be automated, but normally an experienced electrical engineer is needed to get a good result.
Filter (signal processing)In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of many other targets for filtering exist.
Single-precision floating-point formatSingle-precision floating-point format (sometimes called FP32 or float32) is a computer number format, usually occupying 32 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 231 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2−23) × 2127 ≈ 3.
Linear filterLinear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant (or shift invariant) in which case they can be analyzed exactly using LTI ("linear time-invariant") system theory revealing their transfer functions in the frequency domain and their impulse responses in the time domain. Real-time implementations of such linear signal processing filters in the time domain are inevitably causal, an additional constraint on their transfer functions.
Memory cell (computing)The memory cell is the fundamental building block of computer memory. The memory cell is an electronic circuit that stores one bit of binary information and it must be set to store a logic 1 (high voltage level) and reset to store a logic 0 (low voltage level). Its value is maintained/stored until it is changed by the set/reset process. The value in the memory cell can be accessed by reading it. Over the history of computing, different memory cell architectures have been used, including core memory and bubble memory.
Interval arithmetic[[File:Set of curves Outer approximation.png|345px|thumb|right|Tolerance function (turquoise) and interval-valued approximation (red)]] Interval arithmetic (also known as interval mathematics; interval analysis or interval computation) is a mathematical technique used to mitigate rounding and measurement errors in mathematical computation by computing function bounds. Numerical methods involving interval arithmetic can guarantee relatively reliable and mathematically correct results.
Electronic filterElectronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped electronic components, as opposed to distributed-element filters. That is, using components and interconnections that, in analysis, can be considered to exist at a single point. These components can be in discrete packages or part of an integrated circuit. Electronic filters remove unwanted frequency components from the applied signal, enhance wanted ones, or both.
IEEE 754The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and portably. Many hardware floating-point units use the IEEE 754 standard.
ArithmeticArithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th century, Italian mathematician Giuseppe Peano formalized arithmetic with his Peano axioms, which are highly important to the field of mathematical logic today.
Half-precision floating-point formatIn computing, half precision (sometimes called FP16 or float16) is a binary floating-point computer number format that occupies 16 bits (two bytes in modern computers) in computer memory. It is intended for storage of floating-point values in applications where higher precision is not essential, in particular and neural networks. Almost all modern uses follow the IEEE 754-2008 standard, where the 16-bit base-2 format is referred to as binary16, and the exponent uses 5 bits.
Computer memoryComputer memory stores information, such as data and programs for immediate use in the computer. The term memory is often synonymous with the term primary storage or main memory. An archaic synonym for memory is store. Computer memory operates at a high speed compared to storage which is slower but less expensive and higher in capacity. Besides storing opened programs, computer memory serves as disk cache and write buffer to improve both reading and writing performance.
Flash memoryFlash memory is an electronic non-volatile computer memory storage medium that can be electrically erased and reprogrammed. The two main types of flash memory, NOR flash and NAND flash, are named for the NOR and NAND logic gates. Both use the same cell design, consisting of floating gate MOSFETs. They differ at the circuit level depending on whether the state of the bit line or word lines is pulled high or low: in NAND flash, the relationship between the bit line and the word lines resembles a NAND gate; in NOR flash, it resembles a NOR gate.
Semiconductor memorySemiconductor memory is a digital electronic semiconductor device used for digital data storage, such as computer memory. It typically refers to devices in which data is stored within metal–oxide–semiconductor (MOS) memory cells on a silicon integrated circuit memory chip. There are numerous different types using different semiconductor technologies. The two main types of random-access memory (RAM) are static RAM (SRAM), which uses several transistors per memory cell, and dynamic RAM (DRAM), which uses a transistor and a MOS capacitor per cell.
DiagramA diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word graph is sometimes used as a synonym for diagram.
Round-off errorIn computing, a roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. Rounding errors are due to inexactness in the representation of real numbers and the arithmetic operations done with them. This is a form of quantization error.
Random-access memoryRandom-access memory (RAM; ræm) is a form of computer memory that can be read and changed in any order, typically used to store working data and machine code. A random-access memory device allows data items to be read or written in almost the same amount of time irrespective of the physical location of data inside the memory, in contrast with other direct-access data storage media (such as hard disks, CD-RWs, DVD-RWs and the older magnetic tapes and drum memory), where the time required to read and write data items varies significantly depending on their physical locations on the recording medium, due to mechanical limitations such as media rotation speeds and arm movement.
