Speech Analysis

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Speech Analysis
EEM.ssr Speaker Speech Recognition

• by
• Dr Philip Jackson

lecturer in speech audio Centre for Vision,
Speech Signal Processing, Department of
Electronic Engineering.
http//www.ee.surrey.ac.uk/Teaching/Courses/eem.ss
r
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Whats the point of analysing speech?

• Speech analysis, or speech processing, transforms
  a speech waveform into a representation that is
  suitable for extracting its features
• Human visual inspection
• e.g., by a speech scientist, speech therapist, or
  forensic phonetician
• Computer analysis
• e.g., for automatic speech recognition, speaker
  recognition, or paralinguistic processing

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And what does that mean?

• Suitable could be
• amenable to human visual inspection
• using a small number of bits per second (for
  transmission or storage)
• compatible with the models in a speech recognizer
• in line with our understanding of human auditory
  processing

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Cochlear section

• Cochlea, or inner ear, has a spiral form
• vestibular canal
• basilar membrane
• tympanic canal
• auditory nerve

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Response of the cochlea
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Basilar membrane

• sound enters at the stapes
• travels along the basilar membrane
• vibrates at matching position
• activates auditory nerves

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Short-term spectrum

• Represents the distribution of power with respect
  to frequency over a time interval centred at
  time, t, like a vertical slice through the
  spectrogram
• From a source-filter perspective, it gives us
  some information about the shape of the vocal
  tract at time t
• From a human speech perception view, it provides
  similar information to that sent from the cochlea
  to the auditory nerve

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Computing the ST-spectrum

• Analogue-to-Digital (A/D) Conversion
• convert the analogue signal from the microphone
  into a digital signal
• Windowing
• select a short section of speech, centred at time
  t, and smooth
• Frequency analysis
• estimate the distribution of power with respect
  to frequency

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Waterfall display
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Speech spectrogram
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Derived formant tracks
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A/D conversion

• Sampling measures the speech signal at regular
  intervals, n
• Quantisation encodes the signal xn with a
  discrete value

x
n
n
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Sample rate

• Nyquists theorem for a signal band-limited to B
  Hz, then a rate of 2B samples per second is
  needed to encode the signal faithfully
• Human ear sensitive up 20 kHz (hence 44 kHz rate
  for CDs)
• But for speech
• high-quality needs 10 kHz bandwidth, i.e., 20 kHz
  sample rate
• bandwidth can be reduced to 4 kHz (8 kHz rate),
  for telephone quality
• e.g., 8-bit PCM at 8kHz 64 kbps

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CD-quality fS 44 kHz
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High-quality speech fS 20 kHz
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Telephone speech fS 8 kHz
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Window functions
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Frequency analysis

• Discrete Fourier Transform (DFT) is applied to
  the windowed digital waveform x(n)n1,,N.
• With an N-sample window, an N-point complex
  spectrum is obtained X(k) k1,,N.
• The modulus squared gives the power spectrum,
  X2(k)
• The logarithm gives the log-power spectrum,
  logX2(k)

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Discrete Fourier transform

• over a finite period of time
• sampled at regular intervals

Forward transform
Inverse transform
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Frequency analysis

• Alternative methods include
• filter-bank analysis (based on a set of band-pass
  filters)
• approximations of the spectral envelope, e.g.,
  Linear predictive coding (LPC)

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Time-frequency resolution 1

• If the window is long then
• the time resolution is poor
• the number of points, N, is large
• there are N points in the spectrum
• so there is fine frequency resolution
• narrow-band frequency analysis, or narrow-band
  spectrum

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Narrow-band spectrum
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Time-frequency resolution 2

• If the window is short then
• the time resolution is good
• the number of points, N, is small
• there are N points in the spectrum
• so the frequency resolution is coarse
• broad-band frequency analysis, or broad-band
  spectrum

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Wide-band spectrum
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Time-frequency resolution 3

• In summary
• long window, narrow-band spectrum
• short window, broad-band spectrum.
• Indeed, the bandwidth-time product cannot exceed
  a half
• where and is the sample
  rate

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Wide-band and narrow-band spectrograms
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Mel-frequency filter bank

• Allocation of DFT bins to filters, spaced
  according to the Mel scale

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The real cepstrum

• Procedure for computing cepstral coefficients
  from the magnitude spectrum

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Mel-frequency cepstrum

• Procedure for computing cepstral coefficients,
  based on the output from Mel-frequency binning

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Summary of Fourier analysis

• Fourier leads to frequency representation
• good for visualisation
• is reversible
• continuous and discrete time forms
• Wide- and narrow-band spectra obtained by
  adjusting frame size
• Windowing
• reduces spectral smearing
• allows for adaptation