Finite Impulse Response Filters - Digital Signal Processing and Applications with the C6713 and C6416 DSK - page 134

3. Bandpass: C 0 = 2 - 1

sin n p - sin n p

2

Ú

()

2 1

CH n = cos p d =

(4.62) n d

n p

1

4. Bandstop: C 0 = 1 - ( -

1 )

2

sin n p - sin n p

1

1

Ú

()

Ú

()

1 2

CH n = cos p d + H n cos p d =

(4.63)

n d d

n p

0

2

2 are the normalized cutoff frequencies shown in Figure 4.4. Several
filter-design packages are currently available for the design of FIR filters, as dis-
cussed later. When we implement an FIR filter, we develop a generic program such
that the specific coefficients will determine the filter type (e.g., whether lowpass or
bandpass).

where 1 and

Exercise 4.4: Lowpass FIR Filter

We will find the impulse response coefficients of an FIR filter with N = 11, a sam-

pling frequency of 10 kHz, and a cutoff frequency f c = 1 kHz. From (4.60),

f
F

c

C == = 02 .

0 1

N

where F N = F s /2 is the Nyquist frequency and

sin 02 . n p

C = n = ± 12 , ± ,..., ± 5 (4.64)

n

n p

Since the impulse response coefficients h i = C Q - i , C n = C - n , and Q = 5, the impulse

response coefficients are

hh == 0 h h == 0 1514 .

0 10 3 7

hh == 0 0468 . h h == 0 1872 .

1 9 4 6

hh == 0 1009 . h = 0 2 . (4.65)

2 8 5

These coefficients can be calculated with a utility program (on the accompanying
CD) and inserted within a generic filter program, as described later. Note the sym-
metry of these coefficients about Q 11 for an FIR filter is low for a

practical design, doubling this number can yield an FIR filter with much better char-

= 5. While N =