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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 Sd

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 Hx(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 Hx(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 fs Mechanical quality factor Qms Electrical quality factor Qes DC resistance Re Force factor Bl(x=0) Mechanical resistance Rms(v=0) Stiffness Kms(x=0) and compliance Cms(x=0) Additional Thiele-Small parameters (e.g. Vas) 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 Cms(x) versus displacement x Mechanical stiffness Kms(x) versus displacement x Incremental stiffness Kinc(x) versus displacement x Inductance L(x,i) versus displacement x and current i Mechanical resistance Rms(v) versus velocity v Force-deflection curve F(x)

Single-valued nonlinear parameters

  • Voice coil offset Xoffset Suspension asymmetry Ak Maximal peak displacement Xmax Force factor limited peak displacement Xbi Suspension limited peak displacement Xc Inductance limited peak displacement XL Stiffness Kms(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 xsym in force factor curve

Electrical impedance

  • Amplitude and phase response Nominal electrical impedance Zn Impedance measured by using a large signal model

Parameters of the enclosure

  • Port resonance fb Quality factor Qlb 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 Kmx(x) Distortion generated by inductance Le(x) Distortion generated by inductance Le(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 Qms Port resonance frequency fp Quality factor representing box leakage


  • Distortion generated by force factor Bl(x) Distortion generated by stiffness Kmx(x) Distortion generated by inductance Le(x) Distortion generated by inductance Le(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 δTv Increase of magnet temperature δTm Bypass factor Power Pcoil transferred to coil Power Pcon transferred by convection cooling Power Peg 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 Preal Power P­Re dissipated on Re Pn nominal impedance Zn Short term maximum input power Long term maximum power