# Overview

# Signal and System Analysis

## Waveform and spectrum

- Time domain analysis Statistical analysis Spectral analysis Signal to noise ratio SNR

## Magnitude and phase response

- Complex transfer function Total phase (unwrapping, without constant time delay) Minimal-phase, excess-phase response Polarity Nyquist plot

## Impulse response

- Time windowed impulse response Step response Energy time curve Group delay response Excess time delay response Constant time delay detection

## Time-frequency analysis

- Wigner-distribution Cumulative decay spectrum Sonagraph Wavelet transform

# Sound Radiation and Propagation

## Far field sound pressure on-axis

- SPL sensitivity at 1W and 1m on-axis Mean level in frequency band Effective frequency range

## Directional radiation characteristics

- Off-axis far field SPL response Directional response pattern Polar and balloon plots Coverage and radiation angle Directivity index Sound power response

## Near field measurement

- Extrapolated far-field SPL response Low frequency measurements without anechoic condition Splicing near-field/ far-field measurement Merging multiple sound sources Distortion measurements at high SNR

## Area of radiation

- Effective radiation area S
_{d}

## Radiation analysis

- Far field SPL-response generated in a half space Directivity index, sound power response Polar and balloon plot In-phase component (constructive contribution to SPL) Anti-phase component (destructive contribution to SPL) Quadrature component (no contribution to SPL)

# Mechanical Vibration

## Voice coil displacement

- Transfer-function H
_{x}(f)=X(f)/U(f) between voltage and displacement Linear parameters (Thiele-Small) Nonlinear parameters Peak, rms and dc displacement Rub & Buzz analysis

## Scanning mechanical vibration

- Complex transfer function H
_{x}(r, f) at point r on the radiator’s surface Magnitude and phase plot Animated vibration pattern Distributed mechanical parameters

## Vibration analysis

- Accumulated acceleration level AAL Modal analysis (natural frequencies, modal loss factor, mode shape) Radial and circumferential modes Rocking modes

## Scanning geometry

- Geometry of the surface in cylindrical coordinates Export in dxf, stl and other format

## Material parameters of loudspeaker parts

- Young’s E modulus Modal loss factor

# Transducer Parameters

## Small signal lumped parameters

- Resonance frequency f
_{s}Mechanical quality factor Q_{ms}Electrical quality factor Q_{es}DC resistance R_{e}Force factor Bl(x=0) Mechanical resistance R_{ms}(v=0) Stiffness K_{ms}(x=0) and compliance C_{ms}(x=0) Additional Thiele-Small parameters (e.g. V_{as}) Visco-elastic parameter (creep factor λ) Lossy inductance parameters (Wright, Leach, LR2 model)

## Transducer nonlinearities (curve shape)

- Force factor Bl(x) versus displacement x
Mechanical compliance C
_{ms}(x) versus displacement x Mechanical stiffness K_{ms}(x) versus displacement x Incremental stiffness K_{inc}(x) versus displacement x Inductance L(x,i) versus displacement x and current i Mechanical resistance R_{ms}(v) versus velocity v Force-deflection curve F(x)

## Single-valued nonlinear parameters

- Voice coil offset X
_{offset}Suspension asymmetry A_{k}Maximal peak displacement X_{max}Force factor limited peak displacement X_{bi}Suspension limited peak displacement X_{c}Inductance limited peak displacement X_{L}Stiffness K_{ms}(x=0) at the voice rest position Force factor Bl(x=0) at the voice coil rest position Effective stiffness related to effective resonance frequency Symmetry point x_{sym}in force factor curve

## Electrical impedance

- Amplitude and phase response
Nominal electrical impedance Z
_{n}Impedance measured by using a large signal model

## Parameters of the enclosure

- Port resonance f
_{b}Quality factor Q_{lb}of vented enclosure

# Nonlinear Distortion

## Harmonic distortion

- Total harmonic distortion (THD, THD+N) Nth-order component versus frequency and amplitude Hi-2 distortion (weighted low order harmonics) Equivalent input distortion

## Intermodulation distortion

- Nth-order difference-tone and summed-tone intermodulation Total intermodulation distortion (absolute and relative) Amplitude modulation distortion

## Multi-tone distortion

- Relative multi-tone distortion Distortion-noise-ratio

## Separated loudspeaker distortion

- Total distortion in a reproduced audio signal
Distortion generated by force factor Bl(x)
Distortion generated by stiffness K
_{mx}(x) Distortion generated by inductance L_{e}(x) Distortion generated by inductance L_{e}(i)

## Compression of fundamental components

- Output amplitude versus input amplitude Thermal power compression Nonlinear amplitude compression

## DC displacement – dynamic offset the voice coil

- DC displacement versus frequency DC displacement versus amplitude Asymmetrical probability function pdf Peak-bottom value

## Rub & Buzz and impulsive distortion

- Peak value of higher-order harmonics Rms value of higher-order harmonics Crest-factor of higher-order harmonics Crest-factor versus voice coil displacement Peak value of deterministic component Peak value of random component Isolated defect distortion Noise immunity

## Air leakage noise

- Absolute envelope of modulated noise MOD
Relative envelope of modulated noise RMOD
Peak value of random distortion RAND
Peak value of deterministic distortion DET
Crest factor of deterministic distortion CREST
Inter-channel delay time
Incident angle
Mechanical loss factor Q
_{ms}Port resonance frequency f_{p}Quality factor representing box leakage

## Auralization

- Distortion generated by force factor Bl(x)
Distortion generated by stiffness K
_{mx}(x) Distortion generated by inductance L_{e}(x) Distortion generated by inductance L_{e}(i) Voice coil displacement Voice coil temperature Voltage, current and input power

## Maximum SPL

- Tone burst measurement according to ANSI CEA-2010

# Power Handling and Heat Dissipation

## Accelerated life and power testing

- Input power versus time Displacement versus time Voice coil temperature Durability, endurance, reliability Parameter variation over time (aging)

## Voice coil temperature

- Variation of dc resistance Re versus time Increase of voice coil temperature δTv Heating and cooling curves

## Thermal parameter measurements

- Thermal resistances of voice coil and magnet Thermal capacities of voice coil and magnet Air convection cooling coefficient Eddy current heating factor

## Thermal analysis and heat transfer

- Increase of voice coil temperature δT
_{v}Increase of magnet temperature δT_{m}Bypass factor Power P_{coil}transferred to coil Power P_{con}transferred by convection cooling Power P_{eg}transferred by eddy currents

## Voltage and current

- Rated noise voltage Short term maximum voltage Long term maximum voltage Peak and rms value, crest factor Probability density function

## Electrical input power

- Real input power P
_{real}Power P_{Re}dissipated on R_{e}P_{n}nominal impedance Z_{n}Short term maximum input power Long term maximum power