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Chapter 18

Filter fundamentals

Two lessons in Part VII, Filter design. Read them in order, or start anywhere: a prerequisite is a link, never a gate.

Start with 18.1
0 of 2 read2 on the essential pathabout 35 minutes

Lessons in this chapter

Gain |H| from 0 to 4000 Hz: hatched forbidden zones above 1.05 and below 0.95 from 0 to 1000 Hz and above 0.01 from 1500 to 4000 Hz; the transition band, 1000 to 1500 Hz, is free. The dashed 4-point average curve fails, with crosses at 0.653 at 1000 Hz and 0.3182 at 1500 Hz. The solid 41-tap FIR curve passes: pass band worst 1.012, stop band worst 0.0095.Gain |H| from 0 to 4000 Hz: hatched forbidden zones above 1.05 and below 0.95 from 0 to 1000 Hz and above 0.01 from 1500 to 4000 Hz; the transition band, 1000 to 1500 Hz, is free. The dashed 4-point average curve fails, with crosses at 0.653 at 1000 Hz and 0.3182 at 1500 Hz. The solid 41-tap FIR curve passes: pass band worst 1.012, stop band worst 0.0095.

Lesson 1 Essential15 minYou are hereRead

Filter specifications

Draw the zones a filter's gain must avoid, quote them in dB, and see what a narrow transition costs in taps and delay.

Reading in kg against time from 0 to 4 s: 200 readings as small dots, off by noise of 0.2 kg RMS, and the true weight as a dashed line that steps from 0 to 1 kg at 2 s. The solid line is the 16-point average: noise left 0.050 kg, a 16-sample ramp at the jump, delay 7.5 samples (150 ms).Reading in kg against time from 0 to 4 s: 200 readings as small dots, off by noise of 0.2 kg RMS, and the true weight as a dashed line that steps from 0 to 1 kg at 2 s. The solid line is the 16-point average: noise left 0.050 kg, a 16-sample ramp at the jump, delay 7.5 samples (150 ms).

Lesson 2 Essential20 minYou are hereRead

Simple smoothing filters

Smooth a noisy scale three ways, with a moving average, an exponential moving average and a median, and see what each one costs.

After this chapter

Where to go next.

The chapters either side, and the rest of Part VII in the library.

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