firhalfband
Halfband FIR filter design
Syntax
b = firhalfband(n,fp)
b = firhalfband(n,win)
b = firhalfband(n,dev,'dev')
b = firhalfband('minorder',fp,dev)
b = firhalfband('minorder',fp,dev,'kaiser')
b = firhalfband(...,'high')
b = firhalfband(...,'minphase')
Description
b = firhalfband(n,fp) designs
a lowpass halfband FIR filter of order n with an
equiripple characteristic. n must be an even integer. fp determines
the passband edge frequency, and it must satisfy 0 < fp <
1/2, where 1/2 corresponds to π/2 rad/sample.
b = firhalfband(n,win) designs
a lowpass Nth-order filter using the truncated, windowed-impulse response
method instead of the equiripple method. win is
an n+1 length vector. The ideal impulse response
is truncated to length n + 1, and then multiplied
point-by-point with the window specified in win.
b = firhalfband(n,dev,'dev') designs an Nth-order lowpass
halfband filter with an equiripple characteristic. Input argument dev sets
the value for the maximum passband and stopband ripple allowed.
b = firhalfband('minorder',fp,dev) designs
a lowpass minimum-order filter, with passband edge fp.
The peak ripple is constrained by the scalar dev.
This design uses the equiripple method.
b = firhalfband('minorder',fp,dev,'kaiser') designs a lowpass minimum-order
filter, with passband edge fp. The peak ripple
is constrained by the scalar dev. This design uses
the Kaiser window method.
b = firhalfband(...,'high') returns a highpass halfband
FIR filter.
b = firhalfband(...,'minphase') designs a minimum-phase
FIR filter such that the filter is a spectral factor of a halfband
filter (recall that h = conv(b,fliplr(b)) is a halfband filter). This can be useful for designing
perfect reconstruction, two-channel FIR filter banks. The minphase option for firhalfband is
not available for the window-based halfband filter designs — b
= firhalfband(n,win) and b = firhalfband('minorder',fp,dev,'kaiser') .
In the minimum phase cases, the filter order must be odd.
Examples
Design a Halfband Filter using halfband
This example designs a minimum order halfband filter with a specified maximum ripple.
b = firhalfband('minorder',.45,0.0001);
impz(b)
You can see that the impulse response is zero for every alternate sample.
References
[1] Saramaki, T, “Finite Impulse Response Filter Design,” Handbook for Digital Signal Processing. S.K. Mitra and J.F. Kaiser Eds. Wiley-Interscience, N.Y., 1993, Chapter 4.