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Types of Sound:
- Simple: only one frequency
- Complex: multiple frequencies
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.
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.
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
A waveform shows which teo dimensions of sound
amplitude and time
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.
Frequency Response Curve:
amplitude x frequency characteristics of a resonant system.
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.
Wide band shows the resonances of the vocal tract
does well showing characteristics of driven system.
Narrow bands do not show this well
does show the characteristics of the driving force well.
An acoustic filter is
a software program that transmits (passes) energy that is frequency selective.
- 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.
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
Acoustic filters are useful in
the analysis of the frequency and amplitude characteristics of sound
- 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.
- 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.
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.
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.
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.
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.
Relationship between filter bandwidth and temporal resolution
- wide band - vertical
- narrow band - horizontal