1. Complex Auditory Stimuli
Complex periodic waves
Complex aperiodic waves

2. Complex Periodic Waves
Addition of sine waves
See next slide for examples
Always repeat themselves over time
… and therefore have a period.
Always have a fundamental frequency
Fundamental is the largest common denominator of a group of component frequencies
Always have harmonic frequencies
Harmonics are are whole number multiples of the fundamental
e.g., 1f, 2f, 3f, etc.

3. Periodic Complex Waves

4. Periodic Complex Waves

5. Periodic Complex Waves

6. How are complex periodic waves displayed?
Waveform
Amplitude Spectrum (line spectrum)

7. How are complex periodic waves displayed?
Several examples of a line spectrum. The lower figure represents the vowel / i /.

8. Fundamental Frequency
See earlier slide. Largest common denominator of a group of component frequencies.
E.g., If the the component frequencies are 500, 550, 1000, 1050, the largest number that can be evenly divided would be 50. Therefore, 50 Hz would be the fundamental.
It would also have the same pitch as a 50 Hz tone.

9. Harmonics
Harmonics are whole number multiples of the fundamental (fo). The fundamental is always the first harmonic (1f).
May be determined by dividing the fo into the component frequency.
In the previous example the component frequencies would equal the following harmonics.
500 Hz = 10xf (i.e., 10th Harmonic)
550 Hz = 11xf
1000 Hz = 20xf
1050 Hz = 21xf

10. Harmonics Relationship between harmonics and overtones.
Overtones are a musical term and are related to harmonics.

11. Complex Aperiodic Waves
Frequencies are random
Do not repeat over time
Do not have a fundamental frequency
Do not have harmonics

12. How are complex aperiodic waves displayed?
Waveform
Amplitude spectrum (continuous spectrum)

13. How are complex aperiodic waves displayed?

14. How is Sound Analyzed? Spectrogram (aka sonogram) Sound level meter
Oscilloscope and frequency counter
Fourier and real time analyses

15. Spectrogram

16. Sound Level Meter

17. Sound Level Meter Sound Pressure Level (linear)
dBA, dBB, dBC (weighted scales)

18. Sound Level Meter dBA, dBB, dBC (weighted scales)
Used primarily for industrial, community, and aviation applications.
dBA scale has greatest amount of attenuation in low frequencies.
dBB scale somewhat inbetween dBA and dBC.
dBC scale has least amount of attenuation in high frequencies.

19. Other Methods of Analysis
Oscilloscope (displays waveform)

20. Other Methods of Analysis
Frequency Counter

21. Other Methods of Analysis
Fourier Analysis
A method of mathematically changing a waveform to an amplitude spectrum
Real Time Analysis or Fast Fourier Transform (FFT).
Fourier analysis in real time

22. Summary