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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

  • 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