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T P S P S: Minimum Order of FIR High-Pass Digital Filter

This document determines the minimum order of a finite impulse response (FIR) high-pass digital filter given specific parameters. It provides the passband and stopband cutoff frequencies and passband ripple. It then calculates the transition bandwidth and determines that a Hann or Hamming window can be used based on the required stopband attenuation of 55dB. The order is calculated to be 685 for a Hann window and 731 for a Hamming window.

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Hafis Aikal Amran
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48 views3 pages

T P S P S: Minimum Order of FIR High-Pass Digital Filter

This document determines the minimum order of a finite impulse response (FIR) high-pass digital filter given specific parameters. It provides the passband and stopband cutoff frequencies and passband ripple. It then calculates the transition bandwidth and determines that a Hann or Hamming window can be used based on the required stopband attenuation of 55dB. The order is calculated to be 685 for a Hann window and 731 for a Hamming window.

Uploaded by

Hafis Aikal Amran
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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Given,

FT = 22.050kHz
fP = 500 Hz
fS = 400Hz
p = 0.02
s = 55dB

p=

= 0.045351473

= 0.036281179

= 0.0454

= 0.0363

Passband ripple, p

p = -20 log (1- p)


= -20 log (1-0.02)
= 0.175478486
= 0.1755 dB
Assume T=2;

p = tan (

= 0.07143

s = tan (

= 0.05705

Minimum order of FIR high-pass digital filter.


Known, s=55dB
The order of FIR high pass filter can be determined by using this table below:
Type of Window
Hann
Hamming
Blackman

Minimum Stopband
Attenuation
43.9dB
54.5dB
75.3dB

Transition Bandwidth, w
3.11/M
3.32/M
5.56/M

Table 1 : Window specifications table


From the table, the filter can be designed using Hann and Hamming as the minimum
stopband attenuation is lower than 55dB.
The order of Hann window :
w =

p-

= 0.0454-0.0363
= 9.1 x 10^-3
From the table,
w = 3.11/M
M= 3.11/(9.1 x 10^-3 )
= 341.758

N = 2M + 1
=2(341.758) + 1
= 684.52
N = 685

The order of Hamming window :


From the table,
w = 3.32/M
M= 3.32/(9.1 x 10^-3 )
= 364.835

N = 2M + 1
=2(364.835) + 1
= 730.67
N = 731

The order of Kaiser window :


Known, s=55dB
N=
=
= 720.25

= 720

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