Finite Impulse Response Filters - Introduction to Digital Signal Processing and Filter Design - page 289

Magnitude response of an equiripple, linear phase FIR filter

10

0

10

−

N = 195

20

−

30

−

40

−

50

−

60

−

− 70

− 80

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized frequency

Figure 5.22 Magnitude response of an equiripple FIR bandpass filter.

It should also be remembered that the Remez algorithm is restricted to filters
of order greater than 3. It is interesting to note that the bandpass filter of order
195, using the Fourier series and the Hamming window achieves a higher stop-
band attenuation than does a bandpass filter of the same length, using the Remez
algorithm.

5.7 FREQUENCY SAMPLING METHOD

In the methods considered above for the design of linear phase FIR filters, the
magnitude response was specified as constant over disjoint bands, and the transi-
tion bands were “don't care” regions. In this section, we discuss briefly the MAT-
LAB function fir2 that designs a linear phase filter with multistage magnitudes

b=fir2(N, F, M)
b=fir2(N, F, M, window)
b=fir2(N, F, M, window, npt)

and so on. As input parameters for this function, N is the order of the filter and
F is the vector of frequencies between 0 and 1 at which the magnitudes are
specified. In the vector F , we include the end frequencies 0 and 1 and list the
magnitudes at these frequencies in the vector M , so the lengths of F and M are the
same. The argument npt is the number of gridpoints equally spaced between 0
and 1; the default value is 512. Frequencies at the edge of adjacent bands can be
included and will appear twice in the vector F indicating a jump discontinuity.