Amplitude response peak measurement

International Standard Book Number — Click for https://mathworld.wolfram.com/ISBN.html

A sinusoidal model for sound approximates each tonal component of the sound as a sum of slowly varying sinusoids. For tonal sounds such as from vibrating strings or wind instruments (including voiced speech), a sinusoidal model can provide a compact, high-fidelity representation. In addition to providing an intuitive, malleable representation for sound, sinusoidal models are also used in advanced audio compression. — Click for https://ccrma.stanford.edu/~jos/sasp/Sinusoidal_Modeling_Sound.html

Fast Fourier Transforms (FFT) are fast algorithms for computing the Discrete Fourier Transform (DFT) — Click for https://ccrma.stanford.edu/~jos/mdft/Fast_Fourier_Transform_FFT.html

Spectrum analysis of sound is analogous to decomposing white light into its component colors by means of a prism — Click for https://ccrma.stanford.edu/~jos/mdft/Example_Applications_DFT.html

A resonator is a recursive filter that boosts signal amplitude at a particular frequency. The simplest resonator is made using a two-pole filter. The impulse response of the two-pole resonator is an exponentially decaying sinusoidal oscillation, where the zero-crossing rate is (twice) the resonance frequency. — Click for https://ccrma.stanford.edu/~jos/filters/Two_Pole.html

A sinusoid is any function of the form A sin(ω t+φ), where t is the independent variable, and A, ω, φ are fixed parameters of the sinusoid called the amplitude, (radian) frequency, and phase, respectively. Sinusoidal motion is produced by any 'pure' vibration, such as that of an ideal tuning fork or mass-spring system. — Click for https://ccrma.stanford.edu/~jos/mdft/Sinusoids.html

The impulse signal is the shortest pulse signal. For discrete time (digital) systems, the impulse is a 1 followed by zeros. In continuous time, the impulse is a narrow, unit-area pulse (ideally infinitely narrow). The impulse is typically denoted by the Greek delta symbol δ and is often called the 'Dirac delta function', after Paul Dirac who pioneered its use (in addition to being a lead contributor in the development of Quantum Mechanics). — Click for https://ccrma.stanford.edu/~jos/filters/Impulse_Response_Representation.html

In the context of linear time-invariant filter analysis, a zero is a point in the complex s or z plane at which the transfer function goes to zero. A pole is a point in the s or z plane at which the transfer function goes to infinity. The s plane is used to analyze analog filters while the z plane is used for digital filters. — Click for https://ccrma.stanford.edu/~jos/filters/Pole_Zero_Analysis_I.html

A filter in the audio signal processing context is any operation that accepts a signal as an input and produces a signal as an output. Most practical audio filters are linear and time invariant, in which case they can be characterized by their impulse response or their frequency response. — Click for https://ccrma.stanford.edu/~jos/filters/What_Filter.html

The midpoint of the passband. — Click for http://en.wikipedia.org/wiki/Bandpass

The amplitude response of an LTI filter is simply the magnitude of the (complex) frequency response — Click for https://ccrma.stanford.edu/~jos/filters/Amplitude_Response_I_I.html

The impulse response of a system is its output signal in response to the impulse signal. For discrete time (digital) systems, the impulse is a 1 followed by zeros. In continuous time, the impulse is a narrow, unit-area pulse (ideally infinitely narrow). — Click for https://ccrma.stanford.edu/~jos/filters/Impulse_Response_Representation.html

The frequency response is defined for LTI filters as the Fourier transform of the filter output signal divided by the Fourier transform of the filter input signal — Click for https://ccrma.stanford.edu/~jos/filters/Frequency_Response_I.html

The size of the passband, typically expressed in Hz. — Click for http://en.wikipedia.org/wiki/Bandpass

Amplitude response peak measurement

The longest ringing modes are associated with the narrowest bandwidths. When they are important resonances in the frequency response, they also tend to be the tallest peaks in the frequency response magnitude. (If they are not the tallest near the beginning of the impulse response, they will be the tallest near the end.) Therefore, one effective technique for measuring the least-damped resonances is simply to find the precise location and width of the narrowest and tallest spectral peaks in the measured amplitude response of the resonator. The center-frequency and bandwidth of a narrow frequency-response peak determine two poles in the resonator to be factored out. Expressing a filter in terms of its poles and zeros is one type of ``parametric'' filter representation, as opposed to ``nonparametric'' representations such as the impulse response or frequency response. Prony's method [452,299,275] is one well known technique for estimating the frequencies and bandwidths of sums of exponentially decaying sinusoids (two-pole resonator impulse responses).

In the factoring example presented in §8.8.6, the frequency and bandwidth of the main Helmholtz air mode are measured manually using an interactive spectrum analysis tool. However, it is a simple matter to automate peak-finding in FFT magnitude data. (See, for example, the peak finders used in sinusoidal modeling, discussed a bit further in §8.8.1 below.)

Amplitude response peak measurement

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4 Copyright © 2024-06-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University