Signals and Systems - Electrical Engineering

11.5 FIR Filter Design 687

FIGURE 11.23
Low-pass FIR filters using (a)
rectangular and (b) Hamming
windows.

−0.1 051015 20

0

0.1

0.2

0.3

h

[n

]

n

ω/π

0 0.5 1

− 100

− 80

− 60

− 40

− 20

0

20log10|

H

(e

jω

)|(dB)

− 100

− 80

− 60

− 40

− 20

0

20log10|

H

(e

jω

)|(dB)

0 0.5 1

ω/π

0 0.5 1

0

0.2

0.4

0.6

0.8

1

ω/π

|H

(e

jω

)|

ω/π

0 0.5 1

−8

−6

−4

−2

0

<H

(e

jω

)

−10

−5

0

<H

(e

jω

)

0 0.5 1

0

0.2

0.4

0.6

0.8

1

ω/π

0 0.5 1

ω/π

|H

(e

jω

)|

051015 20

0

0.1

0.2

0.3

h

[n

]

n

(b)

(a)

%%%%%%%%%%%%%%%%

% Example 11.13---FIR filter from ‘fir’

%%%%%%%%%%%%%%%%

M = 14;wc = 0.2;wo = 1;wind = 4;

[b] = fir(M,wc,wo,wind);

[H,w] = freqz(b,1,256);

The results are shown in Figure 11.24. Notice the symmetry of the impulse response with respect

toM/ 2 =7 gives a linear phase in the passband of the high-pass filter. The second lobe of the gain

in dB is about−50 dB.