TABLE OF CONTENTS In the age of all-digital PLLs and software PLLs, increasing use of digital filters is made. This appendix is a short overview on digital filter design.
Analog filters are mostly described by their frequency response H( j ?) or by their transfer function H( s). [ Note: the frequency response of a network is often denoted H( j ?), but can also be written H( ?).] H( s) is defined to be
| (C.1) |  |
where O( s) is the Laplace transform of the output signal o( t) and I( s) is the Laplace transform of the input signal i( t). If the input signal is a delta function
the response of the filter is called impulse response h( t). Because I( s) = 1 in this case (refer also to App. B), we have
| (C.2) |  |
i.e., the transfer function H( s) of the analog filter is the Laplace transform of the impulse response h( t). This simple property is extensively used to build digital filters. Often digital filters are designed to have an impulse response similar to that of an analog filter. This is explained by Fig. C.1. Figure C.1a shows the impulse response h( t) of an analog filter; a low-pass filter has been chosen in this example. Of course,
