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Types of Sound:
- Simple: only one frequency
- Complex: multiple frequencies
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Three dimensions of sound:
- Time: how long a sound, or a component of a sound, lasts.
- Frequency: the rate at which particles in an object vibrate.
- Amplitude: the magnitude at which the particles in an object vibrate.
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Frequency can be...
- Periodic: regularly repeating. Characterized by a fundamental frequency (f0) and perhaps harmonics (integer multiples of the f0)
- Aperiodic: not regularly repeating. Composed of multiple frequencies that bear no integer relationship to one another.
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Ways to Display Sound
Given that sound has three dimensions (time, frequency, amplitude), and we are limited to two-dimensional space, the formats for displaying sound employ two of the three dimensions
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A waveform shows which teo dimensions of sound
amplitude and time
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A spectrum displays what two dimensions of sound
- amplitude y and frequency x
- Discrete: shows energy at specific frequency locations. Indicative of period sounds.
- Continuous: shows energy at multiple, continuous frequency locations. Indicative of aperiod (noise) sounds.
- This shows that at this instant in time, these are the characteristics.
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Frequency Response Curve:
amplitude x frequency characteristics of a resonant system.
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A spectogram shows which aspects of sound
- Frequency and time
- (amplitude conveyed by the darkness of the energy)
- Narrowband: good frequency resolution, poor temporal resolution
- Wideband: good temporal resolution, poor frequency resolution
- primarily a showing of frequency and time.
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Wide band shows the resonances of the vocal tract
does well showing characteristics of driven system.
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Narrow bands do not show this well
does show the characteristics of the driving force well.
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An acoustic filter is
a software program that transmits (passes) energy that is frequency selective.
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Acoustic Filter
Frequemcy Range
- Low-pass: block frequencies above a certain point, pass frequencies below that point.
- High-pass : block frequencies below a certain point, pass frequencies above that point.
- Band-pass : block frequencies above and below certain points, pass frequencies between those points.
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Acoustic Filters
Tuning (pertains to band pass filters)
- Sharply tuned (narrowband): pass a narrow band of frequency. Have good frequency resolution, poor temporal resolution
- Broadly tuned (wideband): pass a broad range of frequencies. Have good temporal resolution, poor frequency resolution
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Acoustic filters are useful in
the analysis of the frequency and amplitude characteristics of sound
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Narrowband filter
- characterized by good frequency resolution, but poor temporal resolution
- Used in generating a narrowband spectrogram or spectrum
- Useful for showing frequency and amplitude of the driving force (source) in a forced vibration.
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Wideband filter:
- characterized by good temporal resolution, but poor frequency resolution
- Used in generating a wideband spectrogram or spectrum
- Useful for showing frequency and amplitude of the driven system (filter) in a forced vibration.
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Why do filters display the frequency and temporal resolutions that they do?
- Frequency and time are inversely related (f = 1/T)
- Increasing the frequency resolution (narrowband) requires more samples for analysis, reducing temporal resolution.
- Decreasing the frequency resolution (wideband) requires less samples for analysis, increasing temporal resolution.
- Increasing the number of samples analyzed (window length) reduces the bandwidth, decreasing the number of samples analyzed increases the bandwidth.
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Window length = sampling rate/bandwidth
- Window length is the number of samples analyzed
- Sampling rate is the number of times/second that the computer is sampling the acoustic signal
- Bandwidth is the width (in frequency) of the band pass filter.
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If sampling rate = 16000 (samples/sec), and the bandwidth = 250 Hz, window length = 64 samples (points)
If sampling rate = 16000 (samples/sec), and the bandwidth = 40 Hz, window length = 400 samples (points)
Below are the spectrogram settings in WaveSurfer for bandwidth and window length.
- For CD quality they use 44100 sampling speed.
- For us, we typically use 16000 sampling seed.
- So a sample of 40 Hz. F = 1/T. 40 = 1/.025. So we measure at 16000 sampling rate. So 16000 * .025 = 400. This means that we would need 400 pts to specify what the filter is.
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Relationship between filter bandwidth and frequency resolution
- If you have a wide window, it has a narrow frequency.
- If you have a narrow window, it has a wide frequency.
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Relationship between filter bandwidth and temporal resolution
- wide band - vertical
- narrow band - horizontal
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