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What is a complex wave?
any sound wave that is not sinusoidal

What is Fourier's Theorem?
complex waves consist of a series of simple sinusoids that can differ in amplitude, frequency, and phase (called Fourier series)

How can a Fourier series be derived?
Fourier Analysis

What is Fourier Analysis?
any complex wave can be decomposed to determine the amplitudes, frequencies, and phases of the sinusoidal components

How are sound waves classifed?

What is a periodic wave?
 a wave that repeats itself over time
 also called a periodic time function
 a sine wave is always periodic
 *pg 67 slide 5

Components of a complex periodic wave
 sinusoidal components cannot be selected at random they must satisfy an harmonic relation
 with an harmonic relation, each sinusoid in the series must be an integer multiple of the lowest in the series
 example: lowest = 215 Hz, components = 215, 430, 645, 860, etc

Harmonic series
 if harmonic relation is present, the series of components is called an harmonic series
 each of the components is called an harmonic
 *pg 68 slide 7

T = 8 ms; fundamental frequency = 125 Hz. What are the frequencies of the first five harmonics?
 1st (fundamental) = 125 Hz
 2nd = 250
 3rd = 375
 4th = 500
 5th = 625

What are the characteristics of a simple wave?
 pure tone
 sine wave
 one frequency

What are the characteristics of complex waves?
 2 or more pure tones of different frequency, amplitude, and phase added together
 most sounds are complex

What are harmonics?
 whole number multiples of fundamental frequency
 energy is expected but not required at each harmonic
 in theory, no limit to number of harmonics though effect of higher frequencies is not noticeable

*Summation of sine waves pg 68 and 69

What are aperiodic waves?
 waves that lack periodicity (book dropping, static)
 noisy, turbulent sounds (fricatives)
 pathologic voices
 you can't get fundamental frequency and harmonics
 *complex waves can be periodic or aperiodic

What are continuous aperiodic waves?
 more than 1 frequency
 no harmonic relationship
 continuous in time
 "shhhhh"

What are transient aperiodic waves?
 more than 1 frequency
 no harmonic relationship
 brief duration
 book dropping

What is a waveform?
 plot of changes in some variable as a function of time
 example: displacement, velocity, acceleration, pressure, etc as a function of time
 can calculate fundamental but cannot easily see all frequency components, or their amplitudes or starting phases
 graph of amplitude by time (sine wave)

What is an amplitude spectrum?
 a graphic alternative to the waveform
 also called the amplitude spectrum in the frequency domain
 graph of amplitude by frequency
 shows all component frequencies and their corresponding amplitudes
 series of discrete lines
 fundamental always has most amplitude
 *pg 69 slide 17 and 18

What is the spectral envelope?
the slope of a spectrum given by connecting the peaks of the vertical lines

What is an octave?
 doubling of frequncy
 ratio of 2:1 (up an octave) or 1:2 (down an octave)

What is a line spectrum?
 energy only at frequencies identified by vertical lines
 height of vertical line reflects amplitude

What is a continuous spectrum?
 energy present at all frequencies between certain frequency limits
 slope of envelope = 0 dB/octave (amp. at all freq., white noise)
 a slope of 0 dB/octave is not a requirement for continuous spectra

What is a phase spectrum?
 the phase spectrum in the frequency domain defines the starting phase as a function of frequency
 the combination of the amplitude spectrum and the phase spectrum defines the waveform completely in the frequency domain

What is a sawtooth wave?
 complex periodic wave
 energy at odd AND even integer multiples of fundamental
 spectral envelope slope of 6 dB/octave
 *pg 71 slide 25

What is a log scale?
a distorted scale that makes higher frequencies closer together in order to fit them all on

What is a square wave?
 complex periodic wave
 energy only at odd integer multiples of fundamental
 spectral envelope slope of 6 dB/octave
 *pg 72

What is a triangular wave?
 complex periodic wave
 energy only at odd integer multiples of fundamental
 spectral envelope slope of 12 dB/octave

What is a pulse train?
 a repetitious series of rectangularly shaped pulses
 each pulse has some width or duration (P_{d})
 complex periodic wave with harmonics at odd AND even integer multiples of the PRF (100, 200, 300, etc)
 amplitude spectrum shows lobes and valleys (nulls)
 nulls occur at integer multiples of reciprocal of P_{d }(nulls occur at 1/P_{d}, 2/P_{d}, 3/P_{d}, etc)
 1/T defines the pulse repeition frequency (PRF)
 *pg 7374

What is white/gaussian noise?
 an aperiodic waveform with equal energy in every frequency band 1 Hz wide: from .5 Hz to .5 Hz
 spectral envelope slope of 0 dB/octave
 starting phases in random array

Why is white noise called white noise?
analogous to white light equal energy in all light wavelengths

*Single pulse pg 74 slide 48

What is signaltonoise ratio?
 the ratio of signal level to noise level
 important for hearing and determining occupational hazards

How do you calculate signaltonoise ratio?
 signal level minus noise level
 positive S/N ratio indicates that signal exceeds noise
 negative S/N noise exceeds signal; S/N = 0 indicates that noise and signal are equal

What is resonance?
 the absorption and radiation of acoustical energy by a device
 frequency dependent

What is the principle of resonance?
 periodic force (vibrating fork) is applied to an elastic system (hard surface)
 system is forced to vibrate at frequency of applied force, not at natural frequency of the system
 the closer the frequency of the applied force to the natural frequency of the system, the greater the amplitude of vibration (loudness increases) less impedence

What is attenuation?
a decrease in amplitude

What determines an elastic system's natural/resonant frequency?
mass and stiffness

When is amplitude of vibration of elastic system greatest?
when driving frequency equals natural frequency of system

What is a resonance/filter curve?
 a frequencyselective elastic system
 it shows the relative amplitude of forced vibrations as a function of frequency that would be realized if driving forces of variable frequency, but constant amplitude, were applied (determines which frequencies will have what amplitude)

What are other names for a resonance curve?
 filter curve
 system transfer function
 amplitude response
 "frequency response"

What are the two components of impendance?
 resistance (R) energy dissipating
 reactance (X) energy storage

What components of impedance determine natural frequency?
 mass reactance and compliant reactance
 resistance is independent of frequency (does not contribute to determination of natural frequency)

What determines the shape of resonance curve, and location in frequency domain?
 impedence of resonant system: the relative contributions of resistance, mass reactance, and compliant reactance
 *pg 80 slide 20

What is a transfer function?
what we're passing things through

What are the effects of impedance on resonance curve?
 below center frequency (f_{c}) compliant dominant
 above center frequency mass dominant

What is admittance?
 refers to the inverse of impedance
 energy accepted, or admitted, to a system
 inversely proportional to Z
 measure in Mho (Z^{1})

Why is a narrow tuned system a better generator than a broad tuned system?
 lower resistance
 less damping
 longer free vibrations at natural frequency

Why is a broad tuned system a better receiver than a narrow tuned system?
 higher resistance
 more damping
 brief free vibrations
 can be forced to vibrate with maximum amplitude over a wide range of frequencies

What is impedance matching?
 apply vibrating force (driver) to elastic system (load): power transferred to system; system forced to vibrate
 maximum amplitude occurs at center freq. where Z is minimal and admittance is maximal
 maximum power transfer occurs when Z of driver = Z of load

What are examples of impedance matching?
 sounding board of a piano
 air cavity above the vocal folds: do not amplify sounds, Zs are matched, maximum transfer of power

*Frequencyselective systems: filters pg 82

What are the five principal parameters of filter curves?
 center (natural) frequency
 upper cutoff frequency
 lower cutoff frequency
 bandwidth
 attenuation (rejection) rate

Center frequency
 freqency corresponding to maximum amplitude of vibration
 mass reactance equals compliant reactance
 impedance is minimal
 admittance is maximal

Upper cutoff frequency
 that frequency above center frequency for which amplitude of response is 3 dB less than response at center frequency
 the 3dB down point or the halfpower point

Lower cutoff frequency
 that frequency below center frequency for which amplitude of response is 3 dB less than response at center frequency
 the 3dB down point or the halfpower point
 *pg 83

Bandwidth
 defines the passband of the system: the range of frequencies passed by the filter
 upper cutoff frequency minus lower cutoff frequency
 quantifies how narrowly or broadly tuned the filter is
 measured in Hz

Attenuation rate in dB/octave
 attenuation rate: rolloff rate, rejection rate
 the rate at which energy for frequencies less than or greater than center freqency is rejected (attenuated)
 the slope of the filter curve, expressed in dB/octave
 *pg 83 slide 42

What are filters?
 determines which frequencies will be attenuated
 change amplitudes

What are four types of filters?
 lowpass
 highpass
 bandpass
 bandreject

Lowpass filter
 passes energy below some upper cutoff frequency; attenuates energy above upper cutoff frequency
 bandwidth equals upper cutoff frequency
 no lower cutoff frequency (0 Hz)
 two parameters: upper cutoff frequency and attenuation rate

Highpass filter
 passes energy above some lower cutoff frequency; attenuates energy below lower cutoff frequency
 bandwidth = highest freq. in signal minus lower cutoff frequency
 mirror image of lowpass filter
 *need higher freq. even though there is no upper cutoff frequency
 two parameters: lower cutoff freq. and attenuation rate

Bandpass filter
 passes energy between some lower cutoff frequency and upper cutoff frequency; attenuates energy below lower cutoff frequency and above upper cutoff frequency
 all five parameters usefal (center freq, upper cutoff freq, lower cutoff freq, bandwidth, attenuation)
 bandwidth = upper cuttoff  lower cutoff
 frequency independent

What are two types of bandpass filters?
 bandpass
 constant percentage bandwidth
 *pg 85

Constant percentage bandwidth filter
 the bandwidth is always a constant percentage of the center frequency
 dependent on center frequency
 as center freq. increases, the bandwidth becomes more broad (louder, but not because amplitude increases)
 *pg 86

*Oneoctave filter and thirdoctave filter pg 87 slide 61

Bandreject filter
rejects energy between some lower cutoff frequency and upper cutoff frequency

White noise
 all frequencies are represented with some amplitude
 the more freq. packed together, the higher the amplitude
 has a pressure spectrum level slope of 0 dB
 *pg 90 slide 84

Pink noise
 pass white noise through a specific filter
 mimics industrial noise (high frequencies)
 attenuates high frequencies, lets low freq. pass through (opposite of white noise)
 has a pressure spectrum level slope of 3 dB/octave
 has an octaveband level slope of 0 dB

Undistorted signal
the system reproduces the waveform faithfully

Distorted signal
the shape of the waveform is altered

Frequency distortion
 change in amplitude
 *pg 93 slides 45

System transfer function
 the extent to which a signal can be expected to undergo frequency distortion
 also called amplitude response
 *pg 93 slide 6

Linear systems
 alter only the amplitudes and phases of a signal
 produce frequency distortion

InputOutput (I/O) function of linear system
 as input amplitude increases output amplitude increases proportionally
 output amplitude does not need to equal input amplitude; the change is a proportional one
 *pg 94 slides 89

What does transient mean?
someting in short duration

Transient distortion
the amplitude response of a sine wave is not really a line spectrum because its duration is finite

Acoustic uncertainty principle
 change in frequency multiplied by a change in time (always equals some constant, k=1)
 inversely proportional

What happens as you increase time in an amplitude response?
 more frequency smearing
 *an infinite duration is unrealistic (used in a hearing test)

What are effects of duration on amplitude response?
 energy spread to surrounding frequencies, and amplitude spectrum is continuous
 nulls at integer multiples of reciprocal of duration (100 ms) 1/.1 = +/ 10 Hz, 2/.1 = +/ 20 Hz, etc (like a pulse train)
 *pg 9495

Decay time
time it takes a signal to go from maximum amplitude to 10% of the maximum amplitude (20 ms)

Rise time
the time it takes a signal to go from 0 to 90% maximum amplitude (20 ms)


Amplitude distortion
 creates frequencies (change in frequency)
 *pg 95

What happens if some of the instananeous amplitudes of the input signal exceed the limits of linearity?
 the instantaneous amplitudes at or near max. amp. are "clipped off" output amp. is not proportional to input amp. the signal has been peak clipped; distortion
 more severe peak clipping, more severe distortion
 output gets messed up, amplitude distortion happens, frequencies are created (complex wave)

Why is amplitude distortion also called nonlinear distortion?
the distortion arose from operating on the nonlinear portion of the I/O function

What is another name for amplitude/nonlinear distortion?
harmonic distortion (if the input waveform is sinusoidal)

Percentage harmonic distortion
proportion of total energy that is undesired energy (important for hearing aids)

How do you calculate percentage harmonic distortion?
*pg 97 slide 25

Dynamic range
 difference between amplitude from ENF to its maximum amplitude
 range we need to stay inside of (linear range)

Electric noise floor (ENF)
background noise

Intermodulation distortion
 driving signal is complex (instead of sine wave)
 experience nonlinear distortion
 making a complex wave more complex (worse than harmonic distortion)

