designMultirateFIR
Design and implement antialiasing and anti-imaging lowpass FIR filter
Description
designs a
multirate FIR filter. The output B
= designMultirateFIRB
is a vector of filter
coefficients. To implement the filter, you must assign the filter coefficients
B
to a multirate filter object.
The multirate FIR filter is an antialiasing and anti-imaging lowpass FIR filter used in digital rate conversion.
specifies options using one or more name-value arguments. (since R2024a)B
= designMultirateFIR(Name=Value
)
For example,
designs an FIR rate converter with the interpolation factor of 3, decimation factor
of 2, polyphase length of 24, and the stopband attenuation of 80 dB. As the
B
=
designMultirateFIR
(InterpolationFactor
=3,DecimationFactor
=2,SystemObject
=true)SystemObject
argument is true
, the
function returns a dsp.FIRRateConverter
System object™.
When you specify only a partial list of filter parameters, the function designs the filter by setting the other design parameters to their default values.
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
where, 2P is the polyphase length and R is defined by one of these equations:
R = L if L > 1
R = M if L = 1.
The function algorithm delays the truncated impulse response d(n) by N/2 samples to make it causal. The truncated and delayed impulse response is
where .
For every Rth band, the impulse response of the Nyquist filters is exactly zero. Because of this property, when the algorithm uses Nyquist filters for pure interpolation, the input samples remain unaltered after interpolating.
When designing a Nyquist filter, the algorithm uses a Kaiser window because of its near-optimum performance and ability to provide a robust design. 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 using
where Astop is the stopband attenuation in dB.
The windowed impulse response is
h(n) for n = 0,1,…,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 R2016aSee Also
Functions
designLowpassFIR
|designHighpassFIR
|designHalfbandFIR
|firnyquist
|rcosdesign
|fdesign.decimator
|fdesign.interpolator
|fdesign.halfband
|designMultistageDecimator
|designFracDelayFIR