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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

## Far Field Sound Pressure On-axis

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

• Off-axis far field SPL response
• Directional response pattern
• Polar and balloon plots
• 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

• 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)
• 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

## Auralization

• 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