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Multirate and Multistage Filters

Decimation, interpolation, rate conversion, and filter banks

Multirate filters are digital filters that change the sample rate of a digital signal without introducing aliasing or imaging in the rate-converted signal. These filters are categorized as decimators that reduce the sample rate, interpolators that increase the sample rate, and rate converters that do a combination of both. For details on these rate conversion operations and their effect on the signal in time and frequency domains, see Overview of Multirate Filters. DSP System Toolbox™ offers MATLAB® System objects and Simulink® blocks that implement decimators, interpolators, and rate converters. Advanced filter technologies such as channelizers, channel synthesizers, two-channel halfband filter banks, and multilevel filter banks use these filters as building components.

You can implement a multirate filter with a large rate conversion factor efficiently in two or more stages rather than in one single stage. When the design is long (contains many coefficients) and costly (requires many multiplications and additions per input sample), the multistage approach is more efficient to implement compared to the single-stage approach. For more details, see Overview of Multistage Filters.

The designMultistageDecimator and designMultistageInterpolator functions in DSP System Toolbox automatically determine the optimal configuration of the filter, which includes determining the number of stages and the rate conversion factor for each stage. An optimal configuration leads to the least computational effort and you can measure the cost of such an implementation using the cost function. For an example, see Multistage Rate Conversion.

Objects

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dsp.FarrowRateConverterPolynomial sample rate converter with arbitrary conversion factor
dsp.FIRDecimatorPolyphase FIR decimator
dsp.FIRHalfbandDecimatorHalfband decimator
dsp.FIRHalfbandInterpolatorHalfband interpolator
dsp.FIRInterpolatorPolyphase FIR interpolator
dsp.FIRRateConverterSample rate converter
dsp.IIRHalfbandDecimatorDecimate by factor of two using polyphase IIR
dsp.IIRHalfbandInterpolatorInterpolate by a factor of two using polyphase IIR
dsp.ComplexBandpassDecimatorExtract a frequency subband using a one-sided (complex) bandpass decimator
dsp.DigitalDownConverterTranslate digital signal from intermediate frequency (IF) band to baseband and decimate it
dsp.DigitalUpConverterInterpolate digital signal and translate it from baseband to IF band
dsp.FilterCascadeCreate cascade of filter System objects
dsp.SampleRateConverterMultistage sample rate converter
dsp.CICCompensationDecimatorCompensate for CIC decimation filter using FIR decimator
dsp.CICCompensationInterpolatorCompensate for CIC interpolation filter using FIR interpolator
dsp.CICDecimatorDecimate signal using cascaded integrator-comb (CIC) filter
dsp.CICInterpolatorInterpolate signal using cascaded integrator-comb filter
dsp.ChannelizerPolyphase FFT analysis filter bank
dsp.ChannelSynthesizerPolyphase FFT synthesis filter bank
dsp.DyadicAnalysisFilterBankDyadic analysis filter bank
dsp.DyadicSynthesisFilterBankReconstruct signals from subbands
dsp.SubbandAnalysisFilterDecompose signal into high-frequency and low-frequency subbands
dsp.SubbandSynthesisFilterReconstruct signal from high-frequency and low-frequency subbands

Functions

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coeffsReturns the filter System object coefficients in a structure
costEstimate cost of implementing filter System object
cascadeCascade of filter system objects
freqzFrequency response of discrete-time filter System object
fvtoolVisualize frequency response of DSP filters
infoInformation about filter System object
measureMeasure frequency response characteristics of filter System object
outputDelayDetermine output delay of single-rate or multirate filter
polyphasePolyphase decomposition of multirate filter
designMultirateFIRMultirate FIR filter design
designMultistageDecimatorMultistage decimator design
designMultistageInterpolatorMultistage interpolator design
fdesign.decimatorDecimator filter specification object
fdesign.interpolatorInterpolator filter specification
fdesign.rsrcRational-factor sample-rate converter specification

Blocks

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Farrow Rate ConverterPolynomial sample-rate converter with arbitrary conversion factor
FIR DecimationFilter and downsample input signals
FIR Halfband DecimatorDecimate signal using polyphase FIR halfband filter
FIR Halfband InterpolatorInterpolate signal using polyphase FIR half band filter
FIR InterpolationUpsample and filter input signals
FIR Rate ConversionUpsample, filter, and downsample input signals
IIR Halfband DecimatorDecimate signal using polyphase IIR halfband filter
IIR Halfband InterpolatorInterpolate signal using polyphase IIR halfband filter
Complex Bandpass DecimatorExtract a frequency subband using a one-sided (complex) bandpass decimator
Digital Down-ConverterTranslate digital signal from Intermediate Frequency (IF) band to baseband and decimate it
Digital Up-ConverterInterpolate digital signal and translate it from baseband to Intermediate Frequency (IF) band
Sample-Rate ConverterMultistage sample-rate conversion
CIC Compensation DecimatorCompensate for CIC filter using FIR decimator
CIC Compensation InterpolatorCompensate for CIC filter using FIR interpolator
CIC DecimationDecimate signal using cascaded integrator-comb filter
CIC InterpolationInterpolate signal using cascaded integrator-comb filter
ChannelizerPolyphase FFT analysis filter bank
Channel SynthesizerPolyphase FFT synthesis filter bank
Dyadic Analysis Filter BankDecompose signals into subbands with smaller bandwidths and slower sample rates or compute discrete wavelet transform (DWT)
Dyadic Synthesis Filter BankReconstruct signals from subbands with smaller bandwidths and slower sample rates or compute inverse discrete wavelet transform (IDWT)
Two-Channel Analysis Subband FilterDecompose signal into high-frequency and low-frequency subbands
Two-Channel Synthesis Subband FilterReconstruct signal from high-frequency and low-frequency subbands

Topics

Sample and Frame Rates in Multirate Models

Multirate Filters

Multistage Filters

Filter Banks

Dataflow

Delay and Latency