Passband filter

AN2182

10/18

5

Passband filter

The aim of this section is to create a passband filter with a pass frequency F1, a cutoff

frequency F2> F1, and a gain G=1, by determining a FIR h filter using the digital approach.

In the frequency domain, the ideal passband filter corresponding to these criteria has the

following response:

Figure 6.

Ideal passband filter frequency response

This filter’s impulse response in the time domain is

Here, the same method described in the section entitled Low-pass filter is handled. Please refer

to this section for more details.

with n = 0.. N – 1 and where

●

N is the number of the FIR coefficients

●

N – 1 is the FIR’s order

●

W is the window time response

F1

0

1

Frequency

F2

-F1

-F2

ht

()

Hf

()e

2

πift

f

d

∞

–

∞

∫

e

2

πift

f

d

F2

–

F1

–

∫

e

2

πift

f

d

F1

F2

∫

+2F

2

c2F

2

t

() 2F

1

c2F

1

t

()

sin

–

sin

==

=

hn

()

2

F

2

F

s

-------c 2F

2

n

N1

–

2

-------------

–

⎝⎠

⎛⎞ T

s

⎝⎠

⎛⎞

sin

2

F

1

F

s

-------c 2F

1

n

N1

–

2

-------------

–

⎝⎠

⎛⎞ T

s

⎝⎠

⎛⎞

sin

–

⎝⎠

⎜⎟

⎛⎞

Wn

N1

–

2

-------------

–

⎝⎠

⎛⎞

⋅

=

(7)