1. EE599-020 Audio Signals and Systems
Psychoacoustics
Kevin D. Donohue Electrical and Computer Engineering University of Kentucky

2. Psycho Psychoacoustics – study of the sensations produced by sounds.
Psychophysics – study of relationship between magnitude of stimulus and magnitude of sensory response or sensation.

3. Psychometric Function
A particular human response to a stimulus can be considered a signal. A psychometric function maps a stimulus measure into a probability that a particular human response will occur.

4. Psychometric Experiment
Response: Human hears a change in pitch
Stimulus: A change in the tonal frequency with measure being the frequency difference between the tone in Hertz
Design an experiment to estimate the psychometric function indicating the smallest tonal interval from 1000 Hz that can be detected by a human. Run experiment using a yes/no test and plot the estimated psychometric function.

5. Response Model of Yes-No Test
Assume human has an internal axis r on which the stimulus is mapped to a response (recall definition of random variable!).
Assume a stimulus will map to this internal axis according to a Gaussian distribution with mean (  ) proportional to the stimulus measure (strength) and standard deviation (  ) representing intra- and inter-subject variability of the responses.

6. Internal Decision Criterion
Consider the types of errors for user response and derive expressions for their the probabilities.

7. Compute Decision Criterion
The response for a given stimulus is modeled by a Gaussian distribution with mean 6 and standard deviation 1, find the decision criterion threshold where the human would have the correct response 92% of the time. If “no stimulus” is modeled by the same distribution with a mean of zero, what is the false alarm (false positive) rate?
Hint: Use the inverse CDF, also use Z-score transformation and standard error function (inverse).

8. Limitations with Yes/No Tests
The Yes/No test involves the internal criteria that subjects use to decide whether the stimulus is present. For subjects with similar low level auditory functions this criteria can vary depending on how liberal (aggressive) or conservative the subject is in making positive decisions. It can even vary in the same subject depending on mood or concentration level.
A 2 alternative forced choice test is typically used reduce the effects of the various internal criteria and emphasize the auditory systems detection capability.
Describe the difference in false positive errors between aggressive and conservative subjects in a Yes/No test?

9. 2AFC Test
The 2 alternative forced choice (2AFC) tests present a subject with 2 intervals. One contains the stimulus and the other does not.
The subject must decide (guess in cases where they don’t know) which interval contains the stimulus.
The resulting psychometric function plots strength of stimulus measure vs. probability of choosing the correct interval.

10. 2AFC Test
What is the probability of a correct response when the subject is guessing in a 2AFC?

11. 2 AFC Trials - Staircase Method
For a typical psychoacoustic the test stimuli are presented in sequence with increasing or decreasing values depending on the accuracy of subject response.
A standard staircase method uses equal increments and decrements in the stimulus measure with turn around rules designed to converge on a specific probability threshold.
The convergence probability is where the probability of turning down is equal to the probability of turning up (.5).

12. 2 AFC Trials – Staircase Rules
The “1-up n-down” rule operates to increase the stimulus one unit after one incorrect decision and to decrease the stimulus one unit after n consecutive correct decisions.
The convergence probability is determine from the place where the turn down probability (n consecutive correct decisions) is .5:

13. 2 AFC Trials – Staircase Rules
What is the convergence probability for a 1-up 2-down rule?
What are all possible sequences that result in the staircase sequence turning up? What is the probability of it turning up?
What are all possible sequences that result in the staircase sequence turning down? What is the probability of it turning down?

14. 2 AFC Test for Loudness
Modify the mfile for the yes/no pitch example to test subjects with a 2 AFC test to estimate the internal threshold on how much signal power (in dB) increase results in deciding when a test tone of 1000 Hz is louder than a reference tone of 1000 Hz at 75 dB. Use a 1-up 4-down rule.
Note: Unless you have a SPL meter you cannot determined where 75 dB is. However this adjustment can be done with the speaker volume and should not affect the mfile. You will need to use the “sound” command rather than the “soundsc” command in Matlab so you can adjust the amplitude of the sine wave and have that directly impact the change in volume. Volume change should happen in equal increments of dB.

15. Homework Problems
For the staircase rule 1-up and 3-down, indicate all possible decision sequences that would cause the staircase to go up and all possible sequences that result in the sequence going down (let I indicate incorrect decision and C indicate correct decision).
Compute the convergence probability in this case verify that the probabilities of the up and down turnarounds are both .5.