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Time-frequency analysis

Characteristics:

KLIPPEL R&D System

Time windowed impulse response

TRF

Step response

TRF

Energy time curve

TRF

Group delay response

TRF, MAT

The impulse response in the time domain and the amplitude and phase response in the frequency domain are two alternative descriptions of a linear system which are directly coupled by the Fourier or Laplace transform. However, transforming only a windowed part of the impulse response into the frequency domain and repeating the transformation for shifted position of the window reveals the spectral properties of the impulse response versus time. The width and shape of the window determines the spectral and temporal resolution of the analysis. High spectral resolution (required for low frequency components) requires a long window while high temporal resolution (required for high frequency components) requires a short window length. The Wavelet transform (see figure below) for example uses an effective time window which becomes smaller at higher frequencies. The time-frequency analysis is important to identify resonances with a high quality factor (for example room modes) which cause a long ringing in the time domain but which are not visible in the total impulse response or in the steady-state frequency response.

Spectral and temporal resolution of a dirac impulse and three sinusoidals in the frequency-time domain by using short-term Fourier transform (SFT) and continuous wavelet-transform (CWT).
Spectral and temporal resolution of a dirac impulse and three sinusoidals in the frequency-time domain by using short-term Fourier transform (SHT) and continuous wavelet-transform (CWT).

KLIPPEL R&D SYSTEM (development)

Module

Comment

Transfer Function Module (TRF)

The post-processing capabilities of the TRF provide various methods of frequency-time analysis (cumulative decay, Wigner distribution and sonograph).
The figure above shows the cumulative decay spectrum of a loudspeaker measured at 0.5 m in a normal living room by using the Transfer Function Module (TRF). The curve at time t=0 shows the steady state amplitude response which is dominated by the direct sound generating a smooth and flat response between 100 – 2000 Hz. The waterfall display shows after switching off the excitation signal at t=0 the decaying energy of each sinusoidal component versus time. The direct sound decreases much faster than the energy of the room modes at discrete frequencies which are fading much slower due to the low damping in the room.
The figure above shows the cumulative decay spectrum of a loudspeaker measured at 0.5 m in a normal living room by using the Transfer Function Module (TRF). The curve at time t=0 shows the steady state amplitude response which is dominated by the direct s

Templates of KLIPPEL products

Name of the Template

Application

TRF cumulative decay

Cumulative spectral decay

TRF SPL + waterfall

Sound pressure level and cumulative decay spectrum

TRF sensitivity (Mic 2)

Calibration of the microphone at IN2 using a pistonphone

TRF true acoustical phase

Total phase without time delay

TRF SPL + harmonics

Standard measurement for fundamental component (SPL) and harmonic distortion

Diagnost. MIDRANGE Sp1

Comprehensive testing of midrange drivers with a resonance 30 Hz < fs < 200 Hz using standard current sensor 1

Diagnost. RUB&BUZZ Sp1

Batch of Rub & Buzz tests with increased voltage (applied to high power devices)

Diagnostics MICROSPEAKER Sp2

Comprehensive testing of microspeakers with a resonance 100 Hz < fs < 2 kHz using sensitive current sensor 2

Diagnostics TWEETER (Sp2)

Comprehensive testing of tweeters with a resonance 100 Hz < fs < 2 kHz using sensitive current sensor 2

Diagnostics VENTED BOX SP1

Comprehensive testing of vented box systems using standard current sensor 1

Diagnostics WOOFER (Sp1)

Comprehensive testing of subwoofers with a resonance 30 Hz < fs < 200 Hz using standard current sensor 1

Diagnostics WOOFER Sp1,2

Comprehensive testing of subwoofers with a resonance 30 Hz < fs < 200 Hz using current sensor 1 and 2

IEC 20.6 Mean SPL

Mean sound pressure level in a stated frequency band according IEC 60268-5 chapter 20.6

IEC 21.2 Frequency Range

Effective frequency range according IEC 60268-5 chapter 21.2

IEC 22.4 Mean Efficiency

Mean efficiency in a frequency band according IEC 60268-5 chapter 22.4

Standards:

  • IEC Standard IEC 60268-5 Sound System Equipment, Part 5: Loudspeakers
  • AES2-1984 AES Recommended practice Specification of Loudspeaker Components Used in Professional Audio and Sound Reinforcement


Papers and Preprints:

D. Keele, “Time-Frequency Display of Electroacoustic Data Using Cycle-Octave Wavelet Transforms,” presented at the 99th Convention of Audio Eng. Soc. (October 1995), Paper No. 4136.

D. Newland, “Harmonic Wavelets in Vibration and Acoustics,” Phil. Trans. R. Soc. Lond. A (1999) 357, 2607 –2625.

C. Janse, A. Kaizer, “Time-Frequency Distributions of Loudspeakers: The Application of the Wigner Distribution,” J. of Audio Eng. Soc., Volume 31, Issue 4, pp. 198-223, April 1983.

M. Poletti, “Linearly Swept Frequency Measurements, Time-Delay Spectrometry, and the Wigner Distribution,” J. of Audio Eng. Soc., Volume 36, Issue 6, pp. 457-468, June 1988.

M. Berman, L. Fincham, “The Application of Digital Techniques to the Measurement of Loudspeakers,” J. of Audio Eng. Soc., Volume 25, Issue 6, pp. 370-384, June 1977.