Selectivity of filter based on filter length

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moonnightingale

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I have written this code for two filter lengths (L)

h770=[];
L=10;
fs=8000;
fb=770;
h770 = (2/L)*cos(2*pi*fb*(0:L-1)/fs);
ww=0pi/256)i;
ff=ww/(2*pi)*fs;
H=freqz(h770,1,ww);
subplot(2,1,1)
plot(ff,abs(H));
title('Magnitude response for L=10 for h770')
grid on;

L=100;
h770 = (2/L)*cos(2*pi*fb*(0:L-1)/fs);
H=freqz(h770,1,ww);
subplot(2,1,2)
plot(ff,abs(H));
title('Magnitude response for L=100 for h770')
grid on;

Now the book asks, Notice the selectivity of filters based on filter length. Think about how this selectivity is used to pass one component while rejecting or attenuating the others.

Kindly explain this to me what he mean by selectivity.
 

Selectivity is associated with Q (quality factor). The higher the Q, the steeper the rolloff curve.

The 'components' mentioned in the book refers to frequencies of signals applied to the coil. A frequency within the selectivity band will get passed. Others are rejected or attenuated.

Usually selectivity involves a center frequency. An inductor by itself does not have a center frequency (except for the rogue self-resonance due to internal capacitance between windings). So maybe it's assumed the coil is in a circuit where a center frequency is relevant.

Here's an internet article that deals with coil dimensions, Q, filter selectivity, etc. It says you can maximize Q by making the coil length equal to its diameter (single layer coil).
 

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