Digital Signal Processing Reference
In-Depth Information
-
2
x
10
4
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
x 10
4
-
2
x
10
4
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
-
2
x
10
4
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
2000
0
-2000
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
2000
-200
0
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
x
10
4
-
2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
x 10
4
Sample number
FIGURE 13.17
Four-subband compression for 16-bit speech data and SNR ΒΌ 27.5 dB.
13.4
WAVELET BASICS AND FAMILIES OF WAVELETS
Wavelet transform has become a powerful tool for signal processing. It offers time-frequency analysis
to decompose the signal in terms of a family of wavelets or a set of basic functions, which have a fixed
shape but can be shifted and dilated in time. The wavelet transform can present a signal with a good
time resolution or a good frequency resolution. There are two types of wavelet transforms: the
continuous wavelet transform (CWT) and the discrete wavelet transform (DWT). Specifically, the
DWT provides an efficient tool for signal coding. It operates on discrete samples of the signal and has
a relation with the dyadic subband coding described in
Section 13.2
.
The DWT resembles other
discrete transforms, such as the discrete Fourier transform (DFT) or the discrete cosine transform
(DCT). In this section, without getting too detailed with mathematics, we review the basics of the
Search WWH ::
Custom Search