Melfilterbanken

Melfilterbanken is a technique used in digital signal processing, particularly in the field of audio and speech processing. It is a method for transforming a signal from the time domain to the frequency domain, similar to the Fourier transform, but with a focus on the human auditory system.

The process begins with the application of a short-time Fourier transform (STFT) to the input signal, which converts the signal into a series of overlapping frames. Each frame is then multiplied by a window function to reduce spectral leakage. The resulting spectrum is then passed through a set of triangular filters, known as a mel filterbank, which are spaced according to the mel scale. This scale is designed to approximate the human ear's response more closely than the linear frequency scale used in the Fourier transform.

The mel scale is a perceptual scale of pitches judged by listeners to be equal in distance from one another. It is based on the fact that the human ear does not perceive frequencies linearly. Instead, it is more sensitive to changes in lower frequencies than in higher frequencies. The mel filterbank is designed to mimic this behavior, resulting in a more accurate representation of the signal's frequency content.

The output of the mel filterbank is a set of mel-frequency cepstral coefficients (MFCCs), which are used in various applications, including speech recognition, music information retrieval, and speaker identification. MFCCs are derived from the logarithm of the mel filterbank energies, and they provide a compact representation of the signal's spectral envelope.

In summary, melfilterbanken is a technique for transforming a signal into a set of mel-frequency cepstral coefficients, which are used in various audio and speech processing applications. It is based on the short-time Fourier transform and a set of triangular filters spaced according to the mel scale, which is designed to approximate the human ear's response more closely than the linear frequency scale.