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Complex Auditory Stimuli

• Complex periodic waves• Complex aperiodic waves

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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.

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Periodic Complex Waves

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Periodic Complex Waves

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Periodic Complex Waves

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How are complex periodic waves displayed?

• Waveform• Amplitude Spectrum (line spectrum)

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How are complex periodic waves displayed?• Several

examples of a line spectrum. The lower figure represents the vowel / i /.

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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.

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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

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Harmonics

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

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Complex Aperiodic Waves

• Frequencies are random• Do not repeat over time• Do not have a fundamental frequency

• Do not have harmonics

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How are complex aperiodic waves

displayed?• Waveform

• Amplitude spectrum (continuous spectrum)

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How are complex aperiodic waves

displayed?

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How is Sound Analyzed?

• Spectrogram (aka sonogram)• Sound level meter• Oscilloscope and frequency counter

• Fourier and real time analyses

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Spectrogram

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Sound Level Meter

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Sound Level Meter

• Sound Pressure Level (linear)• dBA, dBB, dBC (weighted scales)

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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.

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Other Methods of Analysis

• Oscilloscope (displays waveform)

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Other Methods of AnalysisFrequency Counter

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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

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Summary