digital low pass FIR filter design where the cut off frequency is stuck at around -6db

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Lawrence Card 2016-3-2

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回答： Jess Stuart 2020-10-2

I am designing a digital FIR filter using Matlab to the specification of a 5KHz cut off frequency, however, no matter what order number(N), sampling frequency(fs) or window I use, I cannot get the cut off frequency(fc) below -6dB (to -3dB)?

Is this a quirk with MatLab or am I doing something wrong?

If I use an odd order number: 5KHz is around -15dB If I use an even order number: 5KHz is around -6dB

I have attached a screenshot of my frequency response at the moment. The code used to produce it is below:

%filter parameters 
fc = 5000; %5KHz cut off freq
fs = 20000; 
N = 18; 
h = fir1((N-1), (fc/fs)*2, 'low',bartlett(N), 'noscale'); 
fvtool(h, 'Fs', fs)

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Star Strider 2016-3-2

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The cutoff frequency is defined as the half-power point, corresponding to -6 dB. If you want the filter to be -3 dB down at a certain frequency, the firls function would be worth considering.

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Lawrence Card 2016-3-3

Ok, I understand, the key thing is the difference between power and amplitude which is what I was overlooking by assuming a rule for power whilst using amplitude.

Thanks for your explanations!

Star Strider 2016-3-4

My pleasure!

I’m not certain most signal processing textbooks even discuss the half-power point. The DSP text I use as a reference doesn’t specifically list it in the index. I learned about it early on in the course of studying for my Amateur Extra Class amateur radio ticket (this was back in the vacuum tube, log table and slide rule days), when it was the only way to specify filter passbands, and signals were all thought of in terms of power.

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