AN2182

Cutoff band filter

11/18

6

Cutoff band filter

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

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

The FIR coefficients correspond to h(n) where h is the continuous time response of the filter

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

following response:

Figure 7.

Ideal cut-band filter frequency response

If we consider

●

frequency F2

●

frequency F2

●

then, we can easily notice that

In the time domain, this gives

with n = 0.. N – 1 and where

●

N is the number of FIR coefficients

●

N – 1 is the FIR’s order

●

W is the window time response

In the case of a cutoff band filter, N should be odd because of the dirac, that is the FIR’s order

should be even.

F1

0

1

F2

-F1

-F2

Frequency

F1

0

1

F2

-F1

-F2

Frequency

Cut-band filter

Passband filter

H

C

f

()

1H

P

f

()

–

=

(8)

h

C

n

()

δ n N1

–

2

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

–

⎝⎠

⎛⎞

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

–

⎝⎠

⎜⎟

⎛⎞

–

=