Frequency Warping and Its Applications on Signal Processing
Date Issued
2004
Date
2004
Author(s)
Lee, Kai-Ting
DOI
en-US
Abstract
The applications of frequency warping on signal processing have been discussed extensively. Conventionally, computing the discrete Fourier transform that is equivalent to sampling of the z transform of the input sequence at equally spaced angles around the unit circle. However, in some applications, it is better to sample it at unequally spaced angles.
Spectral analysis plays an important role in the field of signal process. In this thesis, we first introduce unequal bandwidth spectral analysis, which utilizes digital frequency warping. Here we use allpass maps to achieve frequency warping. We can fulfill any desired warping by selecting the warped parameter of the allpass filter. Moreover, in order to recover the original signal efficiently, the frequency warping is implemented by Laguerre filter instead. Then, the concept of frequency warping is then extended to discrete Fourier transform (DFT), discrete cosine transform (DCT) and discrete wavelet transform (DWT), i.e., applying the idea of nonuniform frequency resolution to these common transforms.
Warped discrete Fourier transform (WDFT) is mainly applied to spectral analysis. In the application of sinusoidal parameter estimation of noise-corrupted data, using WDFT is more efficient than using DFT. In addition, we can design tunable finite impulse response (FIR) filter and warped filter bank. DCT has been used in the standard of image compression of joint photograph experts group (JPEG) at present. Provided that WDCT is used in image compression, we will obtain better performance than ordinary DCT. However, the method has a defect of high computation complexity. If we further modify the image compression algorithm in the rate-distortion sense, not only the computation load will be reduced but the performance will also be improved.
Subjects
頻率變形
frequency warping
Type
thesis
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