2/2/17. Amplitude. several ways of looking at it, depending on what we want to capture. Amplitude of pure tones

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1 Amplitude several ways of looking at it, depending on what we want to capture Amplitude of pure tones Peak amplitude: distance from a to a OR from c to c Peak-to-peak amplitude: distance from a to c Source: H. Rogers 1

2 Amplitude of speech ( and many other sounds) Peak amplitude, peak-to-peak amplitude --- not useful Amplitude of speech Often we are interested in the overall or average amplitude of a stretch of speech e.g., vowel, consonant, syllable Need a way of computing an average of a set of points 2

3 Amplitude Amplitude of a signal at any discrete point = quantization number stored in audio file HOW CAN WE CAPTURE OVERALL AMPLITUDE? What if we just took the average of all points? For every positive value ---a corresponding negative value with same absolute magnitude. Sum of all measurements = 0 For a simple periodic sound, the mean is 0, which fails to capture the nature of the sound. 3

4 SOLUTION: RMS Amplitude root-mean-square amplitude [cf. standard deviation in statistics] RMS captures the average distance of all points from the 0 line RMS Amplitude root-mean-square amplitude COMPUTATION 1. Square each measurement of the waveform. 2. Add the squares of all measurements: a a a Divide by the total number of points [an average] 4. Compute the square root of the result [to get back to same-size units] 4

5 RMS Amplitude root-mean-square amplitude RMS Amplitude root-mean-square amplitude RMS of 5, 8, 2, -5, -8, -2? 5 2 = 5 x 5 = = 8 x 8 = = 2 x 2 = = -5 x -5 = = -8 x -8 = = -2 x -2 = 4 SUM = 186 MEAN =!"# # 31 = 5.6 = 31 RMS amplitude = 5.6 units 5

6 RMS Amplitude root-mean-square amplitude for a pure tone, rms amplitude =.707 of peak RMS Amplitude In speech research, we might want to determine the amplitude of a word, vowel, consonant, syllable, or even just a release burst. RMS is easily computable for all of these. 6

7 Another perspective: Time varying RMS amplitude Change in RMS over time Another perspective: Time varying RMS amplitude Windowing The window hops along the signal and an RMS measurement is computed at each stop. 7

8 AND STILL ANOTHER APPROACH quantifying how loud something is db = decibel =.1 bel db scale = a relative, logarithmic scale db Computation db = 20log Amplitude Reference amplitude This is used in a particular way to calculate sound pressure level. 8

9 20log Amplitude Reference amplitude 10log Amplitude Reference amplitude Used for db SPL and other computations We won t need to actually use this computation in 330, but you may see it in research. (Called Intensity Level ) db scale is logarithmic; not linear log(10) = log (10 1 ) = 1 log(100) = log (10 2 ) = 2 log (1000) = log (10 3 ) = 3 AND log(1) = log (10 0 ) = 0 9

10 Computation of Sound Pressure Level (SPL) e.g., in μpa units db SPL = 20 log amplitude of signal reference amplitude reference amplitude = threshold of human hearing = 20 μpa db SPL Scale Quietest: 20 μpa db = 20 log (.00002Pa/.00002Pa) = 20 log (1) = 20 x 0 = 0 db SPL Loudest bearable: 20 Pa db = 20 log (20Pa/.00002Pa) = 20 log (1,000,000) = 20 log (10 6 ) = 20 x 6 = 120 db SPL 10

11 Sound Threshold of pain Jet airplane Approaching subway train Shouting, singing Conversation Whisper Rustling of leaves Threshold of human hearing Sound pressure level (at 1 m from source) 130 db SPL 120 db SPL 100 db SPL 75 db SPL 60 db SPL 30 db SPL 20 db SPL 0 db SPL The db scale is much more convenient than the Pa scale: Approximate range of human perception (pressure) Quietest variation: 20 μpa (micropascal) Loudest variation: 20 Pa range = Pa to 20 Pa a very inconvenient range -- Pa units require as many as 5 decimal places -- μpa units may require very large numbers db SPL : values range from 0 to 120! 11

12 db Scale ANOTHER ADVANTAGE a log scale approximates human perception each 1 db step indicates about the same amount of increase in perceived loudness difference between 0 db and 20 db difference between 20 db and 40 db In Pa units, however, that is NOT the case A ratio of 4 Pa to 2 Pa difference of 2 Pa 20 log (4 Pa/2 Pa) = 20 log (2) = 20 x.3010 = 6.02 db B ratio of 6 Pa to 4 Pa also: difference of 2 Pa 20 log (6 Pa/ 4 Pa) = 20 log (1.5) = 20 x.1761 = 3.52 db In fact, the differences in A and B do not sound equivalent, even though both entail the same difference in Pa units the db scale better corresponds to hearing 12

13 Compute db SPL for a sound at.12 Pa db SPL = 20 log.!j KL.MMMMJKL = 20 log (6000) = 20 (3.778) = Pa is about db SPL 13

14 Re-order the results according to intensity. What general pattern do you observe in the mean intensities (in relation to the vowels) (column AM)? Can you offer any explanation? Source: Fairbanks, House, & Stevens (1950) Vowel What general pattern do you observe in the mean intensities? Can you offer any explanation? Intensity (db) æ 18.3 ɔ 17.6 ɑ 17.5 oʊ 16.8 eɪ 16.7 ɛ 16 u 15.7 ʌ 14.9 i 14.8 ʊ 14.1 ɪ 13.8 Source: Fairbanks, House, & Stevens (1950) 14

15 Vowel Intensity (db) A Practical Consequence speech recording: gain adjustment æ 18.3 ɔ 17.6 ɑ 17.5 oʊ 16.8 eɪ 16.7 ɛ 16 u 15.7 ʌ 14.9 i 14.8 ʊ 14.1 ɪ 13.8 Louder: hat, bad... Softer: hit, hood Source: Fairbanks, House, & Stevens (1950) 15

16 What general pattern do you observe in the normalized amplitudes? (multiple C tokens) (many different vowels) Source: Jongman et al. (2000) What general pattern do you observe in the normalized amplitudes? Segment Nzd Amp /ʒ/ -8.3 /z/ -9 /ʃ/ -9.9 /s/ -11 /v/ /ð/ -14 /f/ /θ/ Source: Jongman et al. (2000) 16