Fourier analysisIn mathematics, Fourier analysis (ˈfʊrieɪ,_-iər) is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics.
Noise (electronics)In electronics, noise is an unwanted disturbance in an electrical signal. Noise generated by electronic devices varies greatly as it is produced by several different effects. In particular, noise is inherent in physics and central to thermodynamics. Any conductor with electrical resistance will generate thermal noise inherently. The final elimination of thermal noise in electronics can only be achieved cryogenically, and even then quantum noise would remain inherent. Electronic noise is a common component of noise in signal processing.
Signal-to-noise ratioSignal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to noise power, often expressed in decibels. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise. SNR is an important parameter that affects the performance and quality of systems that process or transmit signals, such as communication systems, audio systems, radar systems, imaging systems, and data acquisition systems.
Fourier transformIn physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.
Fourier seriesA Fourier series (ˈfʊrieɪ,_-iər) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series, but not all trigonometric series are Fourier series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation.
Carrier-to-noise ratioIn telecommunications, the carrier-to-noise ratio, often written CNR or C/N, is the signal-to-noise ratio (SNR) of a modulated signal. The term is used to distinguish the CNR of the radio frequency passband signal from the SNR of an analog base band message signal after demodulation. For example, with FM radio, the strength of the 100 MHz carrier with modulations would be considered for CNR, whereas the audio frequency analogue message signal would be for SNR; in each case, compared to the apparent noise.
Sampling biasIn statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of a population (or non-human factors) in which all individuals, or instances, were not equally likely to have been selected. If this is not accounted for, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling.
Noise (signal processing)In signal processing, noise is a general term for unwanted (and, in general, unknown) modifications that a signal may suffer during capture, storage, transmission, processing, or conversion. Sometimes the word is also used to mean signals that are random (unpredictable) and carry no useful information; even if they are not interfering with other signals or may have been introduced intentionally, as in comfort noise. Noise reduction, the recovery of the original signal from the noise-corrupted one, is a very common goal in the design of signal processing systems, especially filters.
Tomographic reconstructionTomographic reconstruction is a type of multidimensional inverse problem where the challenge is to yield an estimate of a specific system from a finite number of projections. The mathematical basis for tomographic imaging was laid down by Johann Radon. A notable example of applications is the reconstruction of computed tomography (CT) where cross-sectional images of patients are obtained in non-invasive manner.
Shot noiseShot noise or Poisson noise is a type of noise which can be modeled by a Poisson process. In electronics shot noise originates from the discrete nature of electric charge. Shot noise also occurs in photon counting in optical devices, where shot noise is associated with the particle nature of light. In a statistical experiment such as tossing a fair coin and counting the occurrences of heads and tails, the numbers of heads and tails after many throws will differ by only a tiny percentage, while after only a few throws outcomes with a significant excess of heads over tails or vice versa are common; if an experiment with a few throws is repeated over and over, the outcomes will fluctuate a lot.
Joseph FourierJean-Baptiste Joseph Fourier (ˈfʊrieɪ,_-iər; fuʁje; 21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations. The Fourier transform and Fourier's law of conduction are also named in his honour. Fourier is also generally credited with the discovery of the greenhouse effect.
Noise figureNoise figure (NF) and noise factor (F) are figures of merit that indicate degradation of the signal-to-noise ratio (SNR) that is caused by components in a signal chain. These figures of merit are used to evaluate the performance of an amplifier or a radio receiver, with lower values indicating better performance. The noise factor is defined as the ratio of the output noise power of a device to the portion thereof attributable to thermal noise in the input termination at standard noise temperature T0 (usually 290 K).
Noise reductionNoise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree. Noise rejection is the ability of a circuit to isolate an undesired signal component from the desired signal component, as with common-mode rejection ratio. All signal processing devices, both analog and digital, have traits that make them susceptible to noise.
Survivorship biasSurvivorship bias or survival bias is the logical error of concentrating on entities that passed a selection process while overlooking those that did not. This can lead to incorrect conclusions because of incomplete data. Survivorship bias is a form of selection bias that can lead to overly optimistic beliefs because multiple failures are overlooked, such as when companies that no longer exist are excluded from analyses of financial performance.
Image noiseImage noise is random variation of brightness or color information in s, and is usually an aspect of electronic noise. It can be produced by the and circuitry of a or digital camera. Image noise can also originate in film grain and in the unavoidable shot noise of an ideal photon detector. Image noise is an undesirable by-product of image capture that obscures the desired information. Typically the term “image noise” is used to refer to noise in 2D images, not 3D images.
Bias (statistics)Statistical bias, in the mathematical field of statistics, is a systematic tendency in which the methods used to gather data and generate statistics present an inaccurate, skewed or biased depiction of reality. Statistical bias exists in numerous stages of the data collection and analysis process, including: the source of the data, the methods used to collect the data, the estimator chosen, and the methods used to analyze the data. Data analysts can take various measures at each stage of the process to reduce the impact of statistical bias in their work.
BiasBias is a disproportionate weight in favor of or against an idea or thing, usually in a way that is closed-minded, prejudicial, or unfair. Biases can be innate or learned. People may develop biases for or against an individual, a group, or a belief. In science and engineering, a bias is a systematic error. Statistical bias results from an unfair sampling of a population, or from an estimation process that does not give accurate results on average. The word appears to derive from Old Provençal into Old French biais, "sideways, askance, against the grain".
Selection biasSelection bias is the bias introduced by the selection of individuals, groups, or data for analysis in such a way that proper randomization is not achieved, thereby failing to ensure that the sample obtained is representative of the population intended to be analyzed. It is sometimes referred to as the selection effect. The phrase "selection bias" most often refers to the distortion of a statistical analysis, resulting from the method of collecting samples. If the selection bias is not taken into account, then some conclusions of the study may be false.
Non-uniform discrete Fourier transformIn applied mathematics, the nonuniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier transform, but in which the input signal is not sampled at equally spaced points or frequencies (or both). It is a generalization of the shifted DFT. It has important applications in signal processing, magnetic resonance imaging, and the numerical solution of partial differential equations.
Media biasMedia bias is the bias of journalists and news producers within the mass media in the selection of many events and stories that are reported and how they are covered. The term "media bias" implies a pervasive or widespread bias contravening of the standards of journalism, rather than the perspective of an individual journalist or article. The direction and degree of media bias in various countries is widely disputed.
