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Digital Filtering Basics

Module by: Deania Fernandez. E-mail the author

Summary: In this module, the basics of digital filtering is discussed.

Figure 1
Figure 1 (ScreenHunter_017.jpg)

You should be familiar with analog filters, which takes an analog input signal and output analog signal. Digital filters, with the sampling device and digital-to-analog converter, can do the same job as analog filters. Analog filters are specified by its impulse response h⁢tht and the output signal y⁢t yt for input signal x⁢txt is given by the convolution integral

y⁢t=∫0tx⁢t−u⁢h⁢udt y t t 0 t x t u h u

Similarly, digital filters are specified by its impulse h⁢nhn and the output sequence y⁢nyn for the input sequence (samples of input analog signal) x⁢nxn by the discrete convolution

y⁢t=∑k= 0 N −0h⁢k⁢x⁢n−k y t k 0 N 0 h k x n k

The filter design problem is to design the impulse response h⁢n h n so that the digital filter, together with the sample and D/A converter, performs the same processing as the analog filters. There are many possible ways to pick h⁢n h n to implement filtering.

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