Spectral Analysis of Sound

1. Spectral Analysis of Sound Robert Mannell Macquarie University

2. Spectral Analysis of Sound Sub-topics:- • Complex Waves and Line Spectra • Fourier Transforms • Linear Prediction Analysis • Filtering • Spectrograms: Time, Frequency & Intensity

3. Complex Waves and Line Spectra • The addition of more than one pure tone produces complex waveforms. • These waveforms are not readily analysed by eye. • As complex waves increase in complexity it becomes increasingly difficult to determine anything from their waveform except for the fundamental frequency.

4. Complex Waves and Line Spectra • A line spectrum is a spectral representation that displays the frequencies and relative intensities of the component sine waves. • Each sine wave is displayed as a single vertical line placed at the appropriate frequency on the x-axis. • The height of the line represents the amplitude of the component sine wave. • The amplitude is usually displayed as relative sound pressure level in dB. • Phase information is absent in such a display.

5. Complex Waves and Line Spectra In this diagram we can see the waveform and the line spectrum of two 100 Hz pure tones, one with an amplitude of “1” and the second with an amplitude of “2”. On a line spectrum this amplitude could be in Pascals or dB. The associated line spectrum clearly displays this difference, but it could also easily be deduced from the waveforms.

6. Complex Waves and Line Spectra These two waves are complex sounds that have been derived by adding together 2 or 3 pure tones. We can’t easily tell from the waveforms what these tones were, but if we have a line spectrum we can easily see the frequencies and relative amplitudes of these tones.

7. Fourier Transforms and FFT • The addition of pure tones (sine waves) results in a complex sound. • A frequency analysis of such a sound attempts to determine the original pure tones. • The Fourier Transform (Fourier, 1820's) is the main way of doing this. • The Fast Fourier Transform (FFT) is a very fast and commonly used method of computing a Fourier transform on a digital computer.

8. Fourier Transforms and FFT In this FFT spectrum we have intensity (in dB) on the y axis and frequency (in kHz - kiloHertz) on the x axis. Many of the fine detailed peaks are multiples of F0 or harmonics (~105 Hz) superimposed over broader spectral peaks. FFT analysis of the centre of the Australian English vowel /3:/ spoken by an adult male

9. Linear Prediction Analysis (LPC) • A Linear Prediction Analysis is a method that selects the main resonance peaks (or “formants”) of speech sounds. Formant peaks tell us about the position of the tongue, lips, etc. • LPC analysis, if done correctly, provides a smoothed spectrum with easily analysable formants. (We’ll talk more about formants in another topic)

10. Linear Prediction Analysis (LPC) In this LPC spectrum, the four clear peaks are the first four resonance peaks (formants) for this vowel. They tell us that the vowel is a mid central unrounded vowel spoken by an adult male. The pattern of harmonics has been ignored by this analysis. LPC analysis of the centre of the Australian English vowel /3:/ spoken by an adult male

11. FFT/LPC spectra It’s often useful to display both the FFT and LPC together and this kind of plot is used in a number of topics. It’s an easy way of seeing harmonic and formant information together. FFT + LPC analysis of the centre of the Australian English vowel /3:/ spoken by an adult male

12. Acoustic Filtering • It’s sometimes necessary to “filter” sounds so that some frequencies are available for analysis (“passed” by the filter) and other frequencies are removed. • Low pass (LP) filters pass sound below a certain frequency, high pass (HP) filters pass sound above a certain frequency and band pass (BP) filters pass sound between two frequencies. All other frequency components are blocked (“stopped”) .

13. Acoustic Filtering High pass (HP), low pass (LP) and band pass (BP) filters. Note that BP filters pass frequencies between the HP and LP frequencies. Green is passed and white is stopped.

14. Acoustic Filtering • In most practical acoustic filters there is a region around the cut-off frequency where frequencies are partially allowed to pass. • This provides a more gentle transition between the pass-band (the frequencies which are unattenuated) and the stop-band (the frequencies which are attenuated).

15. Spectrograms • FFT and LPC spectra are two dimensional (2D) spectra with the dimensions amplitude (usually y axis) and frequency (usually x axis). They display the spectrum for a short window of time. • Spectrograms are three dimensional spectra showing an additional time dimension.

16. Spectrograms A spectrogram displays three acoustic dimensions. Here, y axis is frequency (kHz), x axis is time (s) and intensity is grey scale (with black being the most intense). A broad band spectrogram has good time resolution (vertical bars show glottal cycles) and poor frequency resolution. Broad band spectrogram of the word “heard” spoken by an adult male speaker of Australian English.

17. Spectrograms Narrow band is the same as broad band, except that it has a poor time resolution (vertical bars don’t show) and good frequency resolution (visible horizontal bars represent harmonics - multiples of F0). Narrow band spectrogram of the word “heard” spoken by an adult male speaker of Australian English.

18. Spectrograms • In the spectrograms on the previous two slides the four parallel horizontal bands represent the first four formants (numbered 1-4 from bottom to top). • If we take a single time slice through the middle of the vowel (the part with the four prominent dark bands) we see the same peaks that we saw in the FFT and LPC plots. (it’s the same vowel and speaker)

19. Readings • For more detail and additional suggested readings go to the topic web site at:- http://www.ling.mq.edu.au/speech/acoustics/frequency/spectral.html