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Digital Filtering Basics

Module by: Deania Fernandez

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

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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 htht and the output signal yt yt for input signal xtxt is given by the convolution integral

yt=∫0txt−uhudt y t t 0 t x t u h u

Similarly, digital filters are specified by its impulse hnhn and the output sequence ynyn for the input sequence (samples of input analog signal) xnxn by the discrete convolution

yt=∑k= 0 N −0hkxn−k y t k 0 N 0 h k x n k

The filter design problem is to design the impulse response hn 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 hn h n to implement filtering.

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