October 2006
Intermediate to advanced
369 pages
8h 11m
English
Content preview from Digital Filters Design for Signal and Image Processing
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4.2. Different types of filters and filter specifications
Let us consider the example of an ideal low-pass filter of normalized gain and whose frequency is in relation to cut-off frequency (see Figure 4.1).
With an ideal filter, transmission is total in the passband and the stopband.
We write x as the normalized frequency in relation to the cut-off frequency:
NOTE.– x is also called the normalized angular frequency in relation to the cut-off angular frequency: 
Figure 4.1. Ideal low-pass filter
Figure 4.2. Low-pass filter corresponding to Figure 4.1, normalized in frequency and amplitude
In general, we will deduce normalized high-pass, band-pass and band-stop filters from normalized low-pass filters by applying frequency variable change formulae (see Figures 4.3, 4.4 and 4.5).
Obtaining the transfer function of the filter H(j2πf) from the transfer function of the normalized low-pass filter H(jx) follows the frequency transformation summarized in Table 4.1.
| Obtaining a filter | Transformation carried out from the transfer function of the normalized low-pass filter |
| High-pass with ... |
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