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LIN323 Notes - Topic 4.docx

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Marshall Chasin

TOPIC 4 – TEMPORAL AND FREQUENCY REPRESENTATIONS Spectra  Spectrogram: x=time, y=frequency  Spectrum: x=time, y=dB  Advantages of Spectra o Frequency or spectral domain: The domain where data pertaining to frequency information is apparent. This can be observed in the realm of speech acoustics with an FFT, LPC, or the result of application of a controlled bank of filters. A spectrum or a spectrogram. o Easy to see harmonic structure (F0) o Easy to see formant structure o Easy to see changes in frequency amplitude, time o Hard to perform this analysis  Advantages of Time based Representations o Temporal or time based domain: The domain where only time information is apparent such as a waveform. This is the natural output of a microphone and is the nature of the stored information on any media such as MP3, tape, or a CD. There is no readily apparent information to determine frequency information, but it can be calculated. o Easy to see changes in time o Easy to see amplitude o Easy to see phase o Hard to see frequency information o Hard to find F0 o Easy to perform this analysis o Easy to “parse” a sentence o Easy to see saturation effects (e.g. recording mistakes we might make) o Easy to see some recording/noise artifacts  Three ways to express temporal information as spectral information o Helmholtz resonators o A controlled bank of filters o Fourier Analysis (FFT) o Linear Predictive Coding (LPC) Helmholtz Resonators  A series of different sized brass spheres with a narrow neck on each one. The listener places each one up to the sound sources and listens to the resonator. If there is sound, there is energy characterized by that sphere in the sound source  Relative loudnesses heard are the relative intensities of the sound sources  Time consuming, subjective, and inaccurate  Can be done with guitar/piano strings Controlled Bank of Filters  Sound is converted to electricity using a microphone. The ac electric signal is routed through a series of filters – each one bring tuned to a small bandwidth. 1 o Output displayed as function of voltage  More objective than Helmholtz method and far less time consuming  Size of bandwidth will provide different types of information (e.g. wide vs. narrow)  E.g. Kay Spectrograph Fourier Analysis  The process of decomposing any complex waveform to determine the amplitudes, frequencies, and phases of the sine waves that makes up the complex wave. One of several methods to change information in the time domain, to equivalent spectral or frequency domain. o Based on the harmonics of F0 and builds up formant structure (F1 F2) o Cannot do sounds like explosion because there is no patterns o Infinite series calculations  Fast Fourier Transform (FFT) o A computerized technique for separating a complex waveform consisting of multiple frequencies into its individual frequency components. Based on the fundamental frequency and its harmonics. Useful for any signal such as speech or a sudden explosion. (-> low pressure to high pressure, short wavelength) o Converts time domain to frequency domain o Inverse Fourier Analysis: frequency → time domain Linear Predictive Coding  LPC: Another spectral analysis technique that expresses time domain information in the frequency domain. It is independent of the fundamental frequency and its hardmonics so the resulting frequency display looks smoother – easier to see formant frequencies. Based on the assumption that one can predict the values using a linear interpolation between any two points. Useful for slowly varying signals such as speech. o Based on time series analysis, also called “filter response” o Attempts to find regularities in the signal (fills in the blanks) o Assumes that there is alinear relationship o Not based on harmonic structure, but only the envelope of spectrum o Limited power to locate anti-resonances (e.g. nasals) and harmonic information o Better for finding exact formant frequencies than FFT FFT
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