Additive synthesis is a sound synthesis technique that creates timbre by adding sine waves together.
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor.
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing signals, such as sound, images, potential fields, seismic signals, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, improve subjective video quality, and to detect or pinpoint components of interest in a measured signal.
Time stretching is the process of changing the speed or duration of an audio signal without affecting its pitch. Pitch scaling is the opposite: the process of changing the pitch without affecting the speed. Pitch shift is pitch scaling implemented in an effects unit and intended for live performance. Pitch control is a simpler process which affects pitch and speed simultaneously by slowing down or speeding up a recording.
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing.
In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of systems, such as audio and control systems, where they simplify mathematical analysis by converting governing differential equations into algebraic equations. In an audio system, it may be used to minimize audible distortion by designing components so that the overall response is as flat (uniform) as possible across the system's bandwidth. In control systems, such as a vehicle's cruise control, it may be used to assess system stability, often through the use of Bode plots. Systems with a specific frequency response can be designed using analog and digital filters.
A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals. The input signal that most common spectrum analyzers measure is electrical; however, spectral compositions of other signals, such as acoustic pressure waves and optical light waves, can be considered through the use of an appropriate transducer. Spectrum analyzers for other types of signals also exist, such as optical spectrum analyzers which use direct optical techniques such as a monochromator to make measurements.
In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time, as in time series. Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how the signal is distributed within different frequency bands over a range of frequencies. A complex valued frequency-domain representation consists of both the magnitude and the phase of a set of sinusoids at the frequency components of the signal. Although it is common to refer to the magnitude portion as the frequency response of a signal, the phase portion is required to uniquely define the signal.
The short-time Fourier transform (STFT) is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practice, the procedure for computing STFTs is to divide a longer time signal into shorter segments of equal length and then compute the Fourier transform separately on each shorter segment. This reveals the Fourier spectrum on each shorter segment. One then usually plots the changing spectra as a function of time, known as a spectrogram or waterfall plot, such as commonly used in software defined radio (SDR) based spectrum displays. Full bandwidth displays covering the whole range of an SDR commonly use fast Fourier transforms (FFTs) with 2^24 points on desktop computers.
Audio analysis refers to the extraction of information and meaning from audio signals for analysis, classification, storage, retrieval, synthesis, etc. The observation mediums and interpretation methods vary, as audio analysis can refer to the human ear and how people interpret the audible sound source, or it could refer to using technology such as an audio analyzer to evaluate other qualities of a sound source such as amplitude, distortion, frequency response. Once an audio source's information has been observed, the information revealed can then be processed for the logical, emotional, descriptive, or otherwise relevant interpretation by the user.
Stransform as a time–frequency distribution was developed in 1994 for analyzing geophysics data. In this way, the S transform is a generalization of the short-time Fourier transform (STFT), extending the continuous wavelet transform and overcoming some of its disadvantages. For one, modulation sinusoids are fixed with respect to the time axis; this localizes the scalable Gaussian window dilations and translations in S transform. Moreover, the S transform doesn't have a cross-term problem and yields a better signal clarity than Gabor transform. However, the S transform has its own disadvantages: the clarity is worse than Wigner distribution function and Cohen's class distribution function.
A phase vocoder is a type of vocoder-purposed algorithm which can interpolate information present in the frequency and time domains of audio signals by using phase information extracted from a frequency transform. The computer algorithm allows frequency-domain modifications to a digital sound file.
In mathematics, a wavelet series is a representation of a square-integrable function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform.
The method of reassignment is a technique for sharpening a time-frequency representation by mapping the data to time-frequency coordinates that are nearer to the true region of support of the analyzed signal. The method has been independently introduced by several parties under various names, including method of reassignment, remapping, time-frequency reassignment, and modified moving-window method. The method of reassignment sharpens blurry time-frequency data by relocating the data according to local estimates of instantaneous frequency and group delay. This mapping to reassigned time-frequency coordinates is very precise for signals that are separable in time and frequency with respect to the analysis window.
The Hilbert–Huang transform (HHT) is a way to decompose a signal into so-called intrinsic mode functions (IMF) along with a trend, and obtain instantaneous frequency data. It is designed to work well for data that is nonstationary and nonlinear. In contrast to other common transforms like the Fourier transform, the HHT is an algorithm that can be applied to a data set, rather than a theoretical tool.
Automatic target recognition (ATR) is the ability for an algorithm or device to recognize targets or other objects based on data obtained from sensors.
Fault detection, isolation, and recovery (FDIR) is a subfield of control engineering which concerns itself with monitoring a system, identifying when a fault has occurred, and pinpointing the type of fault and its location. Two approaches can be distinguished: A direct pattern recognition of sensor readings that indicate a fault and an analysis of the discrepancy between the sensor readings and expected values, derived from some model. In the latter case, it is typical that a fault is said to be detected if the discrepancy or residual goes above a certain threshold. It is then the task of fault isolation to categorize the type of fault and its location in the machinery. Fault detection and isolation (FDI) techniques can be broadly classified into two categories. These include model-based FDI and signal processing based FDI.
Time–frequency analysis for music signals is one of the applications of time–frequency analysis. Musical sound can be more complicated than human vocal sound, occupying a wider band of frequency. Music signals are time-varying signals; while the classic Fourier transform is not sufficient to analyze them, time–frequency analysis is an efficient tool for such use. Time–frequency analysis is extended from the classic Fourier approach. Short-time Fourier transform (STFT), Gabor transform (GT) and Wigner distribution function (WDF) are famous time–frequency methods, useful for analyzing music signals such as notes played on a piano, a flute or a guitar.
Audio forensics is the field of forensic science relating to the acquisition, analysis, and evaluation of sound recordings that may ultimately be presented as admissible evidence in a court of law or some other official venue.
Perceptual-based 3D sound localization is the application of knowledge of the human auditory system to develop 3D sound localization technology.