Package: dsp
Polyphase FIR decimator
The FIRDecimator
object resamples vector or
matrix inputs along the first dimension. The object reseamples at
a rate M times slower than the input sampling rate,
where M is the integervalued downsampling factor.
The decimation combines an FIR antialiasing filter with downsampling.
The FIR decimator object uses a polyphase implementation of the FIR
filter.
To resample vector or matrix inputs along the first dimension:
Define and set up your FIR decimator. See Construction.
Call step
to resample the vector
or matrix inputs according to the properties of dsp.FIRDecimator
.
The behavior of step
is specific to each object in
the toolbox.
H = dsp.FIRDecimator
returns
an FIR decimator, H
, which applies an FIR filter
with a cutoff frequency of 0.4*pi
radians/sample
to the input and downsamples the filter output by factor of 2. This System object™ supports
variablesize input.
H = dsp.FIRDecimator ('
returns an FIR decimator, PropertyName'
,PropertyValue
,
...) H
, with
each property set to the specified value.
H = dsp.FIRDecimator(DECIM,
NUM, '
returns an FIR decimator, PropertyName
',PropertyValue
,
...)H
, with
the integervalued DecimationFactor
property set
to DECIM
, the Numerator
property
set to NUM
, and other specified properties set
to the specified values.

Decimation factor Specify the downsampling factor as a positive integer. The FIR
decimator reduces the sampling rate of the input by this factor. The
size of the input along the first dimension must be a multiple of
the decimation factor. The default is 

FIR filter coefficient source Specify the source of the numerator coefficients as one of 

FIR filter coefficients Specify the numerator coefficients of the FIR filter in powers of z^{–1}. The following equation defines the system function for a filter of length L: $$H(z)={\displaystyle \sum _{l=0}^{L1}{b}_{l}}{z}^{l}$$ To prevent aliasing
as a result of downsampling, the filter transfer function should have
a normalized cutoff frequency no greater than 1/ 

Filter structure Specify the implementation of the FIR filter as either 
clone  Create FIR decimator object with same property values 
freqz  Frequency response 
fvtool  Open filter visualization tool 
getNumInputs  Number of expected inputs to step method 
getNumOutputs  Number of outputs of step method 
impz  Impulse response 
isLocked  Locked status for input attributes and nontunable properties 
phasez  Unwrapped phase response 
release  Allow property value and input characteristics changes 
reset  Reset filter states of FIR decimator 
step  Decimate input by integer factor 
A polyphase implementation of an FIR decimator splits the lowpass FIR filter impulse response into M different subfilters, where M is the downsampling, or decimation factor. Let h(n) denote the FIR filter impulse response of length L and u(n) the input signal. Decimating the filter output by a factor of M is equivalent to the downsampled convolution:
$$y(n)={\displaystyle \sum _{l=0}^{L1}h}(l)u(nMl)$$
The key to the efficiency of polyphase filtering is that specific
input values are only multiplied by select values of the impulse response
in the downsampled convolution. For example, letting M=2,
the input values u(0),u(2),u(4), ... are
only combined with the filter coefficients h(0),h(2),h(4),...,
and the input values u(1),u(3),u(5),
... are only combined with the filter
coefficients h(1),h(3),h(5),....
By splitting the filter coefficients into two polyphase subfilters,
no unnecessary computations are performed in the convolution. The
outputs of the convolutions with the polyphase subfilters are interleaved
and summed to yield the filter output. The following MATLAB^{®} code
demonstrates how to construct the two polyphase subfilters for the
default order 35 filter in the Numerator
property
and the default DecimationFactor
property
value of two:
M = 2; Num = fir1(35,0.4); FiltLength = length(Num); Num = flipud(Num(:)); if (rem(FiltLength, M) ~= 0) nzeros = M  rem(FiltLength, M); Num = [zeros(nzeros,1); Num]; % Appending zeros end len = length(Num); nrows = len / M; PolyphaseFilt = flipud(reshape(Num, M, nrows).');
The columns of PolyphaseFilt
are subfilters
containing the two phases of the filter in Num
.
For a general downsampling factor of M , there
are M phases and therefore M subfilters.
Decimate a sum of sine waves with angular frequencies of π/4 and 2π/3 radians/sample by a factor of two. To prevent aliasing, the FIR decimator filters out the 2π/3 radians/sample component before downsampling:
x = cos(pi/4*[0:95]')+sin(2*pi/3*[0:95]'); H = dsp.FIRDecimator; y = step(H,x); % View group delay of default FIR filter fvtool(fir1(35,0.4),1,'analysis','grpdelay'); % Group delay of the default linearphase FIR filter % is 17.5 samples. Downsampling by a factor of % two expect an approx. 8.75 sample delay in the output % y with the initial filter states of zero subplot(211); stem(x(1:length(x)/2),'b','markerfacecolor',[0 0 1]); title('Input Signal'); subplot(212); stem(y,'b','markerfacecolor',[0 0 1]); title('OutputLowpass filtered and downsampled by 2');
The figure shows that the delay in the decimated output is consistent with the group delay of the filter when the initial filter states are zero.
Reduce the sampling rate of an audio signal by 1/2 and play it:
hmfr = dsp.AudioFileReader('OutputDataType',... 'single'); hap = dsp.AudioPlayer(22050/2); hfirdec = dsp.FIRDecimator; while ~isDone(hmfr) frame = step(hmfr); y = step(hfirdec, frame); step(hap, y); end release(hmfr); pause(0.5); release(hap);
This object implements the algorithm, inputs, and outputs described on the FIR Decimation block reference page. The object properties correspond to the block parameters, except:
Coefficient source – The
FIR decimator object does not support mfilt
objects.
Framing – The FIR decimator
object only supports Maintain input frame rate
Output buffer initial conditions – The FIR decimator object does not support this parameter.
Rate options – The FIR decimator object does not support this parameter.
Input processing The FIR decimator object does not support this parameter.