Directform transposed FIR filter
hm = mfilt.firtdecim(m)
hm = mfilt.firtdecim(m,num)
hm = mfilt.firtdecim(m)
returns
a polyphase decimator mfilt
object hm
based
on a directform transposed FIR structure with a
decimation factor of m
. A lowpass Nyquist filter
of gain 1 and cutoff frequency of π/m
is
the default.
hm = mfilt.firtdecim(m,num)
uses
the coefficients specified by num
for the decimation
filter. num
is a vector containing the coefficients
of the transposed FIR lowpass filter used for decimation. If omitted,
a lowpass Nyquist filter with gain of 1 and cutoff frequency of π/m
is
the default.
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 

 Vector containing the coefficients of the FIR lowpass
filter used for interpolation. When 
 Decimation factor for the filter. 
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.firtdecim
objects.
The next table describes each property for an mfilt.firtdecim
filter
object.
Name  Values  Description 


 Specifies the arithmetic the filter uses to process data while filtering. 
 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. 
 Double, single [  The idea behind having both 

 Contains the filter states before, during, and after filter operations. States act as filter memory between filtering runs or sessions. 
This table shows the properties associated with the fixedpoint
implementation of the mfilt.firtdecim
filter.
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 info(hm) where 
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 and lattice
filters. IIR filters have two similar properties — 
 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 [  Sets the fraction length used to interpret the numerator coefficients. 
 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 

 Differentiates between the adders in the filter that
work in full precision at all times ( 
 [  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. 

 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 sample rate changes, mfilt.firtdecim
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. To keep
track of the position of the commutator, the mfilt
object
uses the property InputOffset
which reports the
current position of the commutator in the filter.
The following figure details the signal flow for the direct
form FIR filter implemented by mfilt.firtdecim
.
Notice the order of the states in the filter flow diagram. States
1 through 3 appear in the following diagram at each delay element.
State 1 applies to the third delay element in phase 2. State 2 applies
to the second delay element in phase 2. State 3 applies to the first
delay element in phase 2. 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=[1:3];
Demonstrate decimating an input signal by a factor of 2, in this case converting from 44.1 kHz down to 22.05 kHz. In the figure shown following the code, you see the results of decimating the signal.
m = 2; % Decimation factor. hm = mfilt.firtdecim(m); % Use the default filter coeffs. fs = 44.1e3; % Original sample freq: 44.1 kHz. n = 0:10239; % 10240 samples, 0.232 second long signal x = sin(2*pi*1e3/fs*n); % Original signalsinusoid at 1 kHz. y = filter(hm,x); % 5120 samples, 0.232 seconds. stem(n(1:44)/fs,x(1:44)) % Plot original sampled at 44.1 kHz. axis([0 0.001 1.2 1.2]); 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'); legend('Original signal','Decimated signal','location','best');