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
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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[4999] `X[ ] holds the input signal 160 DIM Y[4999] `Y[ ] holds the output signal 170 DIM H[100] `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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