Directform FIR polyphase decimator
hm = mfilt.firdecim(m)
hm = mfilt.firdecim(m,num)
hm = mfilt.firdecim(m)
returns
a directform FIR polyphase decimator object hm
with
a decimation factor of m
. A lowpass Nyquist filter
of gain 1 and cutoff frequency of π/m
is
designed by default. This filter allows some aliasing in the transition
band but it very efficient because the first polyphase component is
a pure delay.
hm = mfilt.firdecim(m,num)
uses
the coefficients specified by num
for the decimation
filter. This lets you specify more completely the FIR filter to use
for the decimator.
Make this filter a fixedpoint or singleprecision filter by
changing the value of the Arithmetic
property
for the filter hm
as follows:
To change to singleprecision filtering, enter
set(hm,'arithmetic','single');
To change to fixedpoint filtering, enter
set(hm,'arithmetic','fixed');
The following table describes the input arguments for creating hm
.
Input Argument  Description 

 Decimation factor for the filter. m specifies the amount
to reduce the sampling rate of the input signal. It must be an integer.
When you do not specify a value for 
 Vector containing the coefficients of the FIR lowpass
filter used for decimation. When 
This section describes the properties for both floatingpoint filters (doubleprecision and singleprecision) and fixedpoint filters.
Every multirate filter object has properties that govern the
way it behaves when you use it. Note that many of the properties are
also input arguments for creating mfilt.firdecim
objects.
The next table describes each property for an mfilt.firdecim
filter
object.
Name  Values  Description 


 Defines the arithmetic the filter uses. Gives you the
options 
 Integer  Decimation factor for the filter. 
 String  Reports the type of filter object. You cannot set this
property — it is always read only and results from your choice
of 
 Integers  Contains a value derived from the number of input samples
and the decimation factor — 
 Vector  Vector containing the coefficients of the FIR lowpass filter used for decimation. 

 Determines whether the filter states get restored to
zeros for each filtering operation. The starting values are the values
in place when you create the filter if you have not changed the filter
since you constructed it. 
 0 in  Differentiates between the adders in the filter that
work in full precision at all times ( 

 This property contains the filter states before, during, and after filter operations. States act as filter memory between filtering runs or sessions. Double is the default setting for floatingpoint filters in double arithmetic. 
This table shows the properties associated with the fixedpoint
implementation of the filter. You see one or more of these properties
when you set Arithmetic to fixed. Some of the properties have different
default values when they refer fixed point filters. One example is
the property PolyphaseAccum
which stores data
as doubles when you use your filter in doubleprecision mode, but
stores a fi
object in fixedpoint mode.
Note
The table lists all of the properties that a fixedpoint filter
can have. Many of the properties listed are dynamic, meaning they
exist only in response to the settings of other properties. To view
all of the characteristics for a filter at any time, use 
For further information about the properties of this filter
or any mfilt
object, refer to Multirate Filter Properties.
Name  Values  Description 

 Any positive or negative integer number of bits [32]  Specifies the fraction length used to interpret data output by the accumulator. This is a property of FIR filters. 
 Any integer number of bits [39]  Sets the word length used to store data in the accumulator. 
 fixed for fixedpoint filters  Setting this to 
 [true], false  Specifies whether the filter automatically chooses the
proper fraction length to represent filter coefficients without overflowing.
Turning this off by setting the value to 
 Any integer number of bits [16]  Specifies the word length to apply to filter coefficients. 
 [FullPrecision], SpecifyPrecision  Controls whether the filter automatically sets the output
word and fraction lengths, product word and fraction lengths, and
the accumulator word and fraction lengths to maintain the best precision
results during filtering. The default value, 
 Any positive or negative integer number of bits [15]  Specifies the fraction length the filter uses to interpret input data. 
 Any integer number of bits[16]  Specifies the word length applied to interpret input data. 
 Any positive or negative integer number of bits [32]  Determines how the filter interprets the filter output
data. You can change the value of 
 Any integer number of bits [39]  Determines the word length used for the output data.
You make this property editable by setting 
 saturate, [wrap]  Sets the mode used to respond to overflow conditions
in fixedpoint arithmetic. Choose from either 
 [  Sets the mode the filter uses to quantize numeric values when the values lie between representable values for the data format (word and fraction lengths).
The choice you make affects only the accumulator and output arithmetic. Coefficient and input arithmetic always round. Finally, products never overflow — they maintain full precision. 
 [true], false  Specifies whether the filter uses signed or unsigned fixedpoint coefficients. Only coefficients reflect this property setting. 

 This property contains the filter states before, during,
and after filter operations. States act as filter memory between filtering
runs or sessions. The states use 
To provide decimation, mfilt.firdecim
uses
the following structure. At the input you see a commutator that operates
counterclockwise, moving from position 0 to position 2, position 1,
and back to position 0 as input samples enter the filter.
The following figure details the signal flow for the direct
form FIR filter implemented by mfilt.firdecim
.
Notice the order of the states in the filter flow diagram. States
1 through 9 appear in the diagram above each delay element. State
1 applies to the first delay element in phase 2. State 2 applies to
the first delay element in phase 1. State 3 applies to the first delay
element in phase 0. State 4 applies to the second delay in phase 2,
and so on. When you provide the states for the filter as a vector
to the States
property, the above description
explains how the filter assigns the states you specify.
In property value form, the states for a filter hm
are
hm.states=[1:9];
Convert an input signal from 44.1 kHz to 22.05 kHz using decimation by a factor of 2. In the figure that appears after the example code, you see the results of the decimation.
m = 2; % Decimation factor. hm = mfilt.firdecim(m); % Use the default filter. fs = 44.1e3; % Original sample freq: 44.1kHz. n = 0:10239; % 10240 samples, 0.232 second long % signal. x = sin(2*pi*1e3/fs*n); % Original signalsinusoid at 1kHz. y = filter(hm,x); % 5120 samples, 0.232 seconds. stem(n(1:44)/fs,x(1:44)) % Plot original sampled at 44.1 kHz. hold on % Plot decimated signal (22.05 kHz) % in red. stem(n(1:22)/(fs/m),y(13:34),'r','filled') xlabel('Time (sec)');ylabel('Signal Value')