FIR filter design - Continuous and Discrete Time Signals and Systems - page 701

For convenience, the specifications of the lowpass filter in Example 15.2 are
given by

pass-band edge frequency ( ω p ) = 3 π kradians/s,
stop-band edge frequency ( ω s ) = 4 π kradians/s,
maximum allowable pass-band ripple − 20 log 10 ( δ p ) = 25 dB,
i . e .δ p = 0 . 0562 ,
minimum stop-band attenuation − 20 log 10 ( δ s ) = 50 dB,
i . e .δ s = 0 . 0032 ,
sampling frequency ( f 0 ) = 8 ksamples/s.

Example 15.9
Design the lowpass FIR filter considered in Example 15.2 using the rectangular,
Bartlett, Hanning, Hamming, and Blackman windows. Sketch and compare the
magnitude response of the resulting FIR filters.

Solution
As shown in Example 15.2, the values of the normalized cut-off frequency
and the normalized transition bandwidth for the lowpass filter are given by
Ω n = 0 . 4375 and Ω n = 0 . 125, respectively.
Since the minimum stop-band attenuation is 50 dB, only the Hamming and
Blackman windows may be used for the filter design. The value of length N of
the FIR filters for the two windows is given by

Hamming window 6 . 6 N = 0 . 1250 ⇒ N = 6 . 6 / 0 . 125 = 52 . 8;

Blackman window 11 N = 0 . 1250 ⇒ N = 11 / 0 . 125 = 88 .

M ATLAB provides the fir1 function to derive the impulse response of the
FIR filter. The syntax for the fir1 function is given by

fir coeff. = fir1(order, norm cut off, type,window);

where the input argument order denotes the order of the FIR filter. For
an FIR filter of length N , the order is given by N - 1. The input argument
norm cut off specifies the normalized cut-off frequency of the FIR filter.
Its value should lie between zero and one. The input argument type specifies
the type of the FIR filter. Two possible choices for type are 'low' for the
lowpass FIR filter and 'high' for the highpass FIR filter. Finally, the input
argument window accepts coefficients w [ k ] of the window type being used
in the FIR filter design. Any of the elementary windows covered in Section