# AI News, Speech Processing for Machine Learning: Filter banks, Mel-Frequency Cepstral Coefficients (MFCCs) and What's In-Between

- On Thursday, October 4, 2018
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## Speech Processing for Machine Learning: Filter banks, Mel-Frequency Cepstral Coefficients (MFCCs) and What's In-Between

Speech processing plays an important role in any speech system whether its Automatic Speech Recognition (ASR) or speaker recognition or something else. Mel-Frequency

pre-emphasis filter is useful in several ways: (1) balance the frequency spectrum since high frequencies usually have smaller magnitudes compared to lower frequencies, (2) avoid numerical problems during the Fourier transform operation and (3) may also improve the Signal-to-Noise Ratio (SNR).

The pre-emphasis filter can be applied to a signal \(x\) using the first order filter in the following equation: \[y(t) = x(t) - \alpha x(t-1)\] which can be easily implemented using the following line, where typical values for the filter coefficient (\(\alpha\)) are 0.95 or 0.97, pre_emphasis = 0.97: Pre-emphasis has a modest effect in modern systems, mainly because most of the motivations for the pre-emphasis filter can be achieved using mean normalization (discussed later in this post) except for avoiding the Fourier transform numerical issues which should not be a problem in modern FFT implementations.

rationale behind this step is that frequencies in a signal change over time, so in most cases it doesn’t make sense to do the Fourier transform across the entire signal in that we would loose the frequency contours of the signal over time. To

A Hamming window has the following form: \[w[n] = 0.54 − 0.46 cos ( \frac{2πn}{N − 1} )\] where, \(0 \leq n \leq N - 1\), \(N\) is the window length.

This could be implemented with the following lines: The final step to computing filter banks is applying triangular filters, typically 40 filters, nfilt = 40 on a Mel-scale to the power spectrum to extract frequency bands. The

can convert between Hertz (\(f\)) and Mel (\(m\)) using the following equations: \[m = 2595 \log_{10} (1 + \frac{f}{700})\] \[f = 700 (10^{m/2595} - 1) \] Each filter in the filter bank is triangular having a response of 1 at the center frequency and decrease linearly towards 0 till it reaches the center frequencies of the two adjacent filters where the response is 0, as shown in this figure: Filter bank on a Mel-Scale This can be modeled by the following equation (taken from here): \[ H_m(k) =

\hfill 0 \hfill &

\hfill \dfrac{k - f(m - 1)}{f(m) - f(m - 1)} \hfill &

\hfill 1 \hfill &

\hfill 0 \hfill &

- On Tuesday, March 26, 2019

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