designMultirateFIR
Multirate FIR filter design
Syntax
Description
Examples
Input Arguments
Output Arguments
Algorithms
designMultirateFIR
designs an
Rth band Nyquist FIR filter using a
Kaiser window vector to window the truncated impulse response of the FIR filter.
The filter length N is defined as one of the following:
P is the half-polyphase length and R is defined as explained in B.
The truncated impulse response d(n) is delayed by N/2 samples to make it causal. The truncated and delayed impulse response is given by:
where .
For every Rth band, the impulse response of the Nyquist filters is exactly zero. Because of this property, when Nyquist filters are used for pure interpolation, the input samples remain unaltered after interpolating.
A Kaiser window is used because of its near-optimum performance while providing a robust way of designing a Nyquist filter. The window depends on two parameters: length N + 1 and shape parameter β.
The Kaiser window is defined by:
where I0 is the zeroth-order modified Bessel function of the first kind.
The shape parameter β is calculated from:
where Astop is the stopband attenuation in dB.
The windowed impulse response is given by
h(n) for n = 0,..,N/2,...N are the coefficients of the multirate filter. These coefficients are defined by the interpolation factor, L, and decimation factor, M.
References
[1] Orfanidis, Sophocles J. Introduction to Signal Processing. Upper Saddle River, NJ: Prentice-Hall, 1996.
Extended Capabilities
Version History
Introduced in R2016a
See Also
Functions
firnyquist
|firhalfband
|rcosdesign
|fdesign.decimator
|fdesign.interpolator
|fdesign.halfband
|designMultistageDecimator
|designFracDelayFIR