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Signal Processing Front End

Signal Processing Front End. s k. Spectrum. Signal Processing Front End. Filterbank. MFCC. Linear Prediction Analysis. O = o (1) o (2).. o (T). Signal. A quantity who changes with the time. Continuous signal Discrete-Time signal Digital signal Digital Data: 00010101.

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Signal Processing Front End

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  1. Signal Processing Front End sk Spectrum Signal Processing Front End Filterbank MFCC Linear Prediction Analysis O=o(1)o(2)..o(T)

  2. Signal • A quantity who changes with the time. • Continuous signal • Discrete-Time signal • Digital signal • Digital Data: 00010101

  3. Discrete-time signal from Continuous Signal • Speech signal is a continuous signal. • In order to process the Speech signal in a computer we need to digitalized it.

  4. ~ S S S k d k ~ S (t) S(t) Quantizer Zero Order Holder Digitalization 1 2 3 4 5 SNR por cuantización Store

  5. Spectrum • Representation in the Frequency domain of a time signal. • Tools: • Fourier Transform (continuous signals) • Fourier Series (periodic continuous signals) • Discrete-Time Fourier Transform (Discrete Time Signals periodic and not-periodic) • Discrete Fourier Transform (Discrete Time Signals) • Fast Fourier Transform (Discrete Time Signals of length 2x)

  6. Spectral Analysis • Discrete-Time Fourier Transform (DTFT). • Short-Time Fourier Transform (STFT). • Windowing effects • Discrete Fourier Transform (DFT) • Short-Time Fourier Transform (STFT).

  7. Discrete-Time Fourier Transform • Discrete-Time Fourier Tranform (DTFT) Synthesis Definition • If is a periodic waveform (1) • DTFT Analysis Definition

  8. Short-Time Fourier Transform • Since speech signal change with the time, we we make a short-time analysis. • Hence the Short-Time Fourier Transform (STFT) is defined as: • Hence, the speech signal is multiplied in time by a window .

  9. Windowing Effects • is only an approximation to Effect: Smooth the spectrum

  10. Main lobe Side lobes 101-point FIR filters

  11. Narrow Bandwidth Analysis

  12. Wide Bandwidth Analysis

  13. Discrete Fourier Transform (DFT) • The spectrum is sampled, as follow: • By substituting it in 1 , the DFT is defined as follows: • The analysis DFT is as follows: • Time resolution depends on N. N samples in time corresponds to N samples in frequency

  14. STDFT DFT DFT DFT DFT o(1) o(2) o(3) o(4)

  15. Time-Frequency Representation: Sonogram

  16. Can we use all the Sampled Spectrum as our feature observations for the Automatic Speech Recognition task?

  17. Reducing the information • Filterbank Energy as Parameters • Formant Frequencies as Parameters • Cepstral Coefficients

  18. Filterbank • Uniform Filterbank • No-uniform Filterbank • Filterbank Front End

  19. Uniform Filterbank

  20. No-uniform Filterbank

  21. Filter-Bank Front End FB FB FB FB o(1) o(2) o(3) o(4)

  22. Can we found better parameters?

  23. Introduction Since excitation information is not needed for ASR (in English), it is desirable to separate the excitation information form the vocal tract information.

  24. We can think the speech spectrum as a signal, we can observer that is composed for the multiplication of a slow signal, and a fast signal, . We can filter the spectrum signal using linear filtering, however, the excitation and the speech signals are multiplied, and linear filters only useful to separate signals that are added.

  25. On the other hand, linear filtering is convenient to use because it is simple to implement. • Therefore, we transform this no-linear relationship to a linear relationship using a log transformation.

  26. In the log transform, we can filter out the excitation signal, and keep the vocal tract information. This is called the cepstrum spectrum. • If we only take into account the magnitude of the log transform we obtain the cepstrum. • Since the vocal tract information was in the slow signal spectrum, hence from the cepstrum, we keep the slower coefficients.

  27. CC DFT |.|2 Log() IDFT

  28. Cepstral Coefficients CC CC CC CC o(1) o(2) o(3) o(4)

  29. MFCC • If : • Instead of a IDFT used to obtain the cepstrum is used a Cosine Transform. • Instead of feeding to the Cosine Transform the Energy in each frequency, the output of a non-linear filterbank energy is used • we obtain the MFCC

  30. MFCC DFT Non-Uniform Filterbank |.|2 Log() Cosine Transform

  31. MFCC MFCC MFCC MFCC o(1) o(2) o(3) o(4)

  32. Sphinx: • $base_dir/preprocessing/adc2mfcc.8k.csh

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