designMultirateFIR

Multirate FIR filter design

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Syntax

B = designMultirateFIR(L,M)

B = designMultirateFIR(L,M,P)

B = designMultirateFIR(L,M,TW)

B = designMultirateFIR(L,M,P,Astop)

B = designMultirateFIR(L,M,TW,Astop)

B = designMultirateFIR(___,'SystemObject',flag)

Description

example

B= designMultirateFIR(L,M)designs a multirate FIR filter with interpolation factorLand decimation factorM. The outputBis the vector of designed FIR coefficients. To design a pure interpolator, setMto 1. To design a pure decimator, setLto 1.

example

B= designMultirateFIR(L,M,P)designs a multirate FIR filter with half-polyphase lengthP. By default, the half-polyphase length is12.

B= designMultirateFIR(L,M,TW)designs a multirate FIR filter with interpolation factorL,大量毁灭的因素M, and normalized transition widthTW.

example

B= designMultirateFIR(L,M,P,Astop)designs a multirate FIR filter with stopband attenuationAstop. By default, the stopband attenuation is 80 dB.

B= designMultirateFIR(L,M,TW,Astop)designs a multirate FIR filter with interpolation factorL,大量毁灭的因素M, normalized transition widthTW, and stopband attenuationAstop, specified in dB.

B= designMultirateFIR(___,'SystemObject',flag)returns a vector of filter coefficientsBif the flag is set tofalse, or a multirate filter System object™ if theflagis set totrue.

Examples

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Design an FIR Interpolator

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To design an FIR Interpolator using thedesignMultirateFIRfunction, you must specify the interpolation factor of interest (usually greater than 1) and a decimation factor equal to 1. You can use the default half-polyphase length of 12 and the default stopband attenuation of 80 dB. Alternately, you can also specify the half-polyphase length and stopband attenuation values.

Design an FIR interpolator with interpolation factor set to 5. Use the default half-polyphase length of 12 and the default stopband attenuation of 80 dB.

b = designMultirateFIR(5,1); fvtool(b,'impulse')

Figure Impulse Response contains an axes object. The axes object with title Impulse Response contains an object of type stem.

Design an FIR Decimator

Open Live Script

To design an FIR Decimator using thedesignMultirateFIRfunction, you must specify the decimation factor of interest (usually greater than 1) and an interpolation factor equal to 1. You can use the default half-polyphase length of 12 and the default stopband attenuation of 80 dB. Alternately, you can also specify the half-polyphase length and stopband attenuation values. Design an FIR decimator with decimation factor set to 3, and half-polyphase length set to 14. Use the default stopband attenuation of 80 dB.

b = designMultirateFIR(1,3,14); fvtool(b,'impulse');

Figure Impulse Response contains an axes object. The axes object with title Impulse Response contains an object of type stem.

Design an FIR Rate Converter

Open Live Script

To design an FIR Rate Converter using thedesignMultirateFIR功能,您必须指定插值和decimation factors of interest (usually greater than 1). In addition, you can specify either the half-polyphase length and stopband attenuation values, or the normalized transition width and stopband attenuation values.

Design an FIR rate converter with interpolation factor set to 3, decimation factor set to 4, half-polyphase length set to 14, and stopband attenuation set to 90 dB.

b = designMultirateFIR(3,4,14,90); impz(b,1)

Figure contains an axes object. The axes object with title Impulse Response contains an object of type stem.

Design an FIR rate converter with interpolation factor set to 3, decimation factor set to 4, normalized transition width set to 0.2, and stopband attenuation set to 90 dB.

bTW = designMultirateFIR(3,4,0.2,90); impz(bTW,1)

Figure contains an axes object. The axes object with title Impulse Response contains an object of type stem.

Design a dsp.FIRInterpolator System object

Open Live Script

Set the'SystemObject'flag totruein thedesignMultirateFIRfunction to design a multirate filter object. The design parameters specified in the function determine the type of System object the function designs.

In this example, the function designs a polyphase FIR interpolator System object™. For more details, seedsp.FIRInterpolator.

Create adsp.FIRInterpolatorobject with the interpolation factor equal to 5, transition width equal to 0.01, and stopband attenuation equal to 60 dB. Set the'SystemObject'flag totrueto design a multirate filter object.

firInterp = designMultirateFIR(5,1,0.01,60,'SystemObject',true); fvtool(firInterp)

Figure Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB) contains 2 objects of type line.

Compute the cost of implementing the filter.

cost(firInterp)

ans =struct with fields:NumCoefficients: 582 NumStates: 145 MultiplicationsPerInputSample: 582 AdditionsPerInputSample: 578

Measure the frequency response characteristics of the filter object.

measure(firInterp)

ans = Sample Rate : N/A (normalized frequency) Passband Edge : 0.195 3-dB Point : 0.19884 6-dB Point : 0.2 Stopband Edge : 0.205 Passband Ripple : 0.016474 dB Stopband Atten. : 60.1827 dB Transition Width : 0.01

Input Arguments

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`L`—Interpolation factor
positive scalar integer

Interpolation factor, specified as a positive scalar integer. To design a decimator only, setLto1.

Example:2

`M`—Decimation factor
positive scalar integer

Decimation factor, specified as a positive scalar integer. To design an interpolator only, setMto1.

Example:2

`P`—Half-polyphase length
12(default) |positive scalar integer

Half-polyphase length, specified as a positive scalar integer that is greater than or equal to 1.

Example:12

Example:20

`TW`—Normalized transition width
real scalar in the range (0 1)

Normalized transition width of the multirate FIR filter, specified as a real scalar in the range (0 1).

`Astop`—Stopband attenuation
90(default) |nonnegative scalar

Stopband attenuation in dB, specified as a nonnegative real scalar greater than or equal to0.

Example:0.0

Example:80.5

`flag`—System object flag
`false`(default) |`true`

System object flag set to:

false–– Function returns a vector of filter coefficients.
true–– Function returns one of the following multirate filter System objects:
- dsp.FIRInterpolator–– WhenL> 1 andM= 1.
- dsp.FIRDecimator–– WhenL= 1 andM> 1.
- dsp.FIRRateConverter–– WhenL> 1 andM> 1.

Data Types:logical

Output Arguments

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`B`— Coefficients
real-valued vector

Multirate FIR filter coefficients, returned as a real-valuedN-length vector.

If bothLandMare equal to 1, thenNequals 1.

IfL> 1 orM> 1, thenNis given by $N = {\begin{matrix} 2 P R + 1 \\ 2 P R \end{matrix} \begin{array}{l} M > L > 1 and \mod (P L, M) \neq 0 \\ otherwise \end{array}$ , wherePis the half-polyphase length andRis defined by the following equations:

IfL> 1,R=L.
IfL= 1,R=M.

For more details, see theAlgorithmssection.

When the'SystemObject'flag is set totrue, the function returns one of the following multirate filter System objects:

dsp.FIRInterpolator–– WhenL> 1 andM= 1.
dsp.FIRDecimator–– WhenL= 1 andM> 1.
dsp.FIRRateConverter–– WhenL> 1 andM> 1.

Data Types:double

Algorithms

designMultirateFIRdesigns anR^thband Nyquist FIR filter using a Kaiser window vector to window the truncated impulse response of the FIR filter.

的filter lengthNis defined as one of the following:

$N = {\begin{matrix} 2 P R + 1 \\ 2 P R \end{matrix} \begin{array}{l} M > L > 1 and \mod (P L, M) \neq 0 \\ otherwise \end{array}$

Pis the half-polyphase length andRis defined as explained inB.

的truncated impulse responsed(n)is delayed byN/2样品的因果。的truncated and delayed impulse response is given by:

$d (n - N / 2) = \frac{\sin (w_{c} (n - N / 2))}{π (n - N / 2)}, n = 0, \dots, \frac{N}{2}, \dots, N$

where $w_{c} = π / R$ .

For everyR^thband, the impulse response of the Nyquist filters is exactly zero. Because of this property, when Nyquist filters are used for pure interpolation, the input samples remain unaltered after interpolating.

A Kaiser window is used because of its near-optimum performance while providing a robust way of designing a Nyquist filter. The window depends on two parameters: lengthN+ 1 and shape parameterβ.

的Kaiser window is defined by:

$w (n) = \frac{I_{0} (β \sqrt{1 - {(\frac{n - N / 2}{N / 2})}^{2}})}{I_{0} (β)}, 0 \leq n \leq N,$

whereI₀is the zeroth-order modified Bessel function of the first kind.

的shape parameter β is calculated from:

$β = {\begin{array}{l} 0.1102 (A_{s t o p} - 8.7) & if A_{s t o p} \geq 50 \\ 0.5842 {(A_{s t o p} - 21)}^{0.4} + 0.07886 (A_{s t o p} - 21) & if 21 < A_{s t o p} < 50 \\ 0 & if A_{s t o p} \leq 21, \end{array}$

whereA_stopis the stopband attenuation in dB.

的windowed impulse response is given by

$h (n) = w (n) d (n - N / 2) = w (n) \frac{\sin (w_{c} (n - N / 2))}{π (n - N / 2)}, n = 0, \dots, \frac{N}{2}, \dots, N$

h(n)forn = 0,..,N/2,...Nare 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

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

的function must return a vector of coefficients. Setting the'SystemObject'flag totrueis not supported for code generation.
的inputs to the function must be constants when generating code for transition width-based filter design. In this design, you cannot specify the polyphase length (and therefore the filter length) and the function determines this value iteratively.
While generating code from thedesignMultirateFIRfunction, if you specify the inputs to the function as:
- Constants –– The third argument (if specified) is either treated as the transition width or the half polyphase length. If the value of the third argument is less than 1, then it is treated as the transition width. Otherwise, the third argument is treated as the half-polyphase length. This behavior is consistent with the behavior of the function.
  % Transition width equals 0.1codegendesignMultirateFIR-args{coder.Constant(5),coder.Constant(4),coder.Constant(0.1)}designMultirateFIR_mex(5,4,.1)
  % Half-polyphase length equals 10codegendesignMultirateFIR-args{coder.Constant(5),coder.Constant(4),coder.Constant(10)}designMultirateFIR_mex(5,4,10)
- Nonconstants –– The third argument (if specified) is always treated as the half-polyphase length, irrespective of its value.
  For example, specify the third argument as 0.1 while generating the code. Even though the function treats a value less than 1 as the transition width, the generated code treats this value as the half-polyphase length.
  codegendesignMultirateFIR-args{5,4,0.1}
  While running the generated code, specify the third argument as a positive integer since the half-polyphase length input must be a positive integer.
  designMultirateFIR_mex(5,4,1)
  However, if you specify the third argument as a scalar less than 1, the function displays the following error message.
  designMultirateFIR_mex(5,4,0.1)
  Expected P to be a scalar with value >= 1.

版本历史

Introduced in R2016a

designMultirateFIR

Syntax

Description

Examples

Design an FIR Interpolator

Design an FIR Decimator

Design an FIR Rate Converter

Design a dsp.FIRInterpolator System object

Input Arguments

`L`—Interpolation factor
positive scalar integer

`M`—Decimation factor
positive scalar integer

`P`—Half-polyphase length
12(default) |positive scalar integer

`TW`—Normalized transition width
real scalar in the range (0 1)

`Astop`—Stopband attenuation
90(default) |nonnegative scalar

`flag`—System object flag
`false`(default) |`true`

Output Arguments

`B`— Coefficients
real-valued vector

Algorithms

References

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

版本历史

See Also

Functions

Objects

designMultirateFIR

Syntax

Description

Examples

Design an FIR Interpolator

Design an FIR Decimator

Design an FIR Rate Converter

Design a dsp.FIRInterpolator System object

Input Arguments

L—Interpolation factorpositive scalar integer

M—Decimation factorpositive scalar integer

P—Half-polyphase length12(default) |positive scalar integer

TW—Normalized transition widthreal scalar in the range (0 1)

Astop—Stopband attenuation90(default) |nonnegative scalar

flag—System object flagfalse(default) |true

Output Arguments

B— Coefficientsreal-valued vector

Algorithms

References

Extended Capabilities

C/C++ Code GenerationGenerate C and C++ code using MATLAB® Coder™.

版本历史

See Also

Functions

Objects

`L`—Interpolation factor
positive scalar integer

`M`—Decimation factor
positive scalar integer

`P`—Half-polyphase length
12(default) |positive scalar integer

`TW`—Normalized transition width
real scalar in the range (0 1)

`Astop`—Stopband attenuation
90(default) |nonnegative scalar

`flag`—System object flag
`false`(default) |`true`

`B`— Coefficients
real-valued vector

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.