## Documentation Center |

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 integer-valued downsampling factor.
The decimation combines an FIR anti-aliasing 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.

`H = dsp.FIRDecimator ('PropertyName',PropertyValue,
...) ` returns an FIR decimator,

`H = dsp.FIRDecimator(DECIM,
NUM, 'PropertyName',PropertyValue,
...)` returns an FIR decimator,

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:

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 linear-phase 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('Output--Lowpass 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.

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