AN2182

High-pass filter

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4

High-pass filter

by determining a FIR h filter using the digital approach. The FIR coefficients correspond to h(n)

In the frequency domain, the ideal high-pass filter corresponding to these criteria has the

following response:

Figure 5.

Ideal high-pass filter frequency response

notice that

In the time domain, this gives

where N is the number of the filter’s coefficients, N–1 is the filter’s order and W is the window’s

time function.

In the case of a high-pass filter, N should be odd because of the dirac.

0

1

0

1

H

()

1H

()

–

=

(5)

h

H

n

()

δ n N1

–

2

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

–

⎝⎠

⎛⎞ 2

F

c

F

s

------

c 2F

c

n

N1

–

2

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

–

⎝⎠

⎛⎞ T

s

⎝⎠

⎛⎞

sin

–

⎝⎠

⎜⎟

⎛⎞

Wn

N1

–

2

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

–

⎝⎠

⎛⎞

⋅

=

(6)