# Examples of Digital Filters

Posted on Feb 7, 2014

Digital filters are incredibly powerful, but easy to use. In fact, this is one of the main reasons that DSP has become so popular. As an example, suppose we need a low-pass filter at 1 kHz. This could be carried out in analog electronics with the following circuit: For instance, this might be used for noise reduction or separating multiplexed sign

als. (Chapter 3 describes how to design these analog filters). As an alternative, we could digitize the signal and use a digital filter. Say we sample the signal at 10 kHz. A comparable digital filter is carried out by the following program: 100 `LOW-PASS WINDOWED-SINC FILTER 110 `This program filters 5000 samples with a 101 point windowed-sinc 120 `filter, resulting in 4900 samples of filtered data. 130 ` 140 ` `INITIALIZE AND DEFINE THE ARRAYS USED 150 DIM X `X[ ] holds the input signal 160 DIM Y `Y[ ] holds the output signal 170 DIM H `H[ ] holds the filter kernel 180 ` 190 PI = 3. 14159265 200 FC = 0. 1 `The cutoff frequency (0. 1 of the sampling rate) 210 M% = 100 `The filter kernel length 220 ` 230 GOSUB XXXX `Subroutine to load X[ ] with the input signal 240 ` 250 ` `CALCULATE THE FILTER KERNEL 260 FOR I% = 0 TO 100 270 IF (I%-M%/2) = 0 THEN H[I%] = 2*PI*FC 280 IF (I%-M%/2) <> 0 THEN H[I%] = SIN(2*PI*FC * (I%-M%/2) / (I%-M%/2) 290 H[I%] = H[I%] * (0. 54 - 0. 46*COS(2*PI*I%/M%) ) 300 NEXT I% 310 ` 320 `FILTER THE SIGNAL BY CONVOLUTION 330 FOR J% = 100 TO 4999 340 Y[J%] = 0 350 FOR I% = 0 TO 100 360 Y[J%] = Y[J%] + X[J%-I%] * H[I%] 370 NEXT I% 380 NEXT J% 390 ` 400 END As in this example, most digital filters can be implemented with only a few dozen lines of code. How do the analog and digital filters compare Here are the frequency responses of the two filters: Even though we designed the digital...

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