dsp.SampleRateConverter - Multistage sample rate converter - MATLAB (original) (raw)

Multistage sample rate converter

Description

The SampleRateConverter System object™ converts the sample rate of an incoming signal.

To convert the sample rate of a signal:

1. Create the dsp.SampleRateConverter object and set its properties.
2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

This object supports C/C++ code generation and SIMD code generation under certain conditions. For more information, see Code Generation.

Creation

Syntax

Description

`src` = dsp.SampleRateConverter creates a multistage FIR sample rate converter System object, src, that converts the sample rate of each channel of an input signal.

`src` = dsp.SampleRateConverter(`Name=Value`) returns a multistage FIR sample rate converter System object, src, with properties and options specified by one or more Name-Value pair arguments.

example

Properties

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Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and therelease function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, seeSystem Design in MATLAB Using System Objects.

Specify the two-sided bandwidth of interest (after rate conversion) as a positive scalar expressed in Hz. This property sets the two-sided bandwidth of the information-carrying portion of the signal that you wish to retain.

Specify the sample rate of the input signal as a positive scalar expressed in Hz. The input sample rate must be greater than the bandwidth of interest.

Specify the maximum allowed tolerance for the sample rate of the output signal as a positive scalar between 0 and 1.

The output rate tolerance allows for a simpler design in many cases. The actual output sample rate varies but is within the specified range. For example, ifOutputRateTolerance is specified as 0.01, then the actual output sample rate is in the range given byOutputSampleRate ± 1%.

Specify the sample rate of the output signal as a positive scalar expressed in Hz. The output sample rate must be greater than the bandwidth of interest.

Specify the stopband attenuation as a positive scalar expressed in dB. This property is the minimum amount by which any aliasing involved in the process is attenuated.

Usage

Syntax

Description

[y](#mw%5F40d81e9e-4eec-4fe6-8ef6-66eb97106c1c) = src([x](#d126e334133)) designs one or more multirate FIR filters and then uses the filters to convert the rate of each channel (column) of the real or complex input signal x to the output sampling rate.

example

Input Arguments

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Input signal, specified as a vector or a matrix of size_P_-by-Q. The number of input rows_P_ can be arbitrary and does not have to be a multiple of the overall decimation factor. You can determine the decimation factor using the getRateChangeFactors function. The object treats each column ofx as a separate channel.

This object supports variable-size input signals, that is, the frame length (number of rows) of the signal can change even when the object is locked. However, the number of channels (columns) must remain constant.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

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Resampled signal, returned as a vector or a matrix. The output frame size depends on the input frame size P and the rate conversion factors of the individual filter stages. For more information on these filter stages, use thegetFilters function.

The number of output channels (columns) is the same as the number of input channels.

Data Types: single | double
Complex Number Support: Yes

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

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Examples

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Convert the sample rate of an audio signal from 44.1 kHz (CD quality) to 96 kHz (DVD quality).

Note: The dsp.AudioFileWriter System object™ is not supported in MATLAB Online.

FsIn = 44.1e3; FsOut = 96e3;

SRC = dsp.SampleRateConverter(Bandwidth=40e3,... InputSampleRate=FsIn,OutputSampleRate=FsOut);

[L,M] = getRateChangeFactors(SRC); FrameSize = 10*M;

AR = dsp.AudioFileReader('guitar10min.ogg', ... SamplesPerFrame=FrameSize); AW = dsp.AudioFileWriter('guitar10min_96k.wav', ... SampleRate=FsOut);

Convert 100 frames of audio signal. Release all objects.

for n = 1:100 x = AR(); y = SRC(x); AW(y); end

release(AR); release(AW); release(SRC);

Plot the input and output signals. The latency of the sample rate converter introduces a delay in the output signal.

tx = (0:length(x)-1)./FsIn; ty = (0:length(y)-1)./FsOut; figure subplot(2,1,1) plot(tx,x(:,1),'.') hold on plot(ty,y(:,1),'--') ylim([-0.25 0.25]); xlim([0 0.005]) xlabel('Time (s)') legend('Input samples','Output samples','Location','best') title('Channel 1') subplot(2,1,2) plot(tx,x(:,2),'.') hold on plot(ty,y(:,2),'--') ylim([-0.25 0.25]); xlim([0 0.005]) xlabel('Time (s)') legend('Input samples','Output samples','Location','best') title('Channel 2')

Use the outputDelay function to determine this delay value. To account for this delay, shift the output by this delay value.

[delay,,] = outputDelay(SRC,Fc=0)

tx = (0:length(x)-1)./FsIn; ty = (0:length(y)-1)./FsOut; figure subplot(2,1,1) plot(tx,x(:,1),'.') hold on plot(ty-delay,y(:,1),'--') xlim([0 0.005]) xlabel('Time (s)') legend('Input samples','Output samples','Location','best') title('Channel 1') subplot(2,1,2) plot(tx,x(:,2),'.') hold on plot(ty-delay,y(:,2),'--') xlim([0 0.005]) xlabel('Time (s)') legend('Input samples','Output samples','Location','best') title('Channel 2')

Zoom in to see the difference in sample rates.

figure subplot(2,1,1) plot(tx,x(:,1),Color=[0.6 0.6 0.6]) hold on plot(tx,x(:,1),'ro') plot(ty-delay,y(:,1),'b.') xlim([0.0105 0.0107]) legend('Interpolated input','Input samples','Output samples') title('Channel 1') subplot(2,1,2) plot(tx,x(:,2),Color=[0.6 0.6 0.6]) hold on plot(tx,x(:,2),'ro') plot(ty-delay,y(:,2),'b.') xlim([0.0105 0.0107]) legend('Interpolated input','Input samples','Output samples') title('Channel 2')

Create a multistage sample rate converter with default properties. The converter converts from 192 kHz to 44.1 kHz in three stages.

src = dsp.SampleRateConverter

src = dsp.SampleRateConverter with properties:

    InputSampleRate: 192000
   OutputSampleRate: 44100
OutputRateTolerance: 0
          Bandwidth: 40000
StopbandAttenuation: 80

Use src to convert the sample rate of a noisy sinusoid. The sinusoid has a frequency of 20 kHz and is sampled for 0.1 s.

f = 20e3;

FsIn = src.InputSampleRate; FsOut = src.OutputSampleRate;

t1 = (0:1/FsIn:0.1-1/FsIn)';

sIn = sin(2pif*t1) + randn(size(t1));

Estimate the power spectral density of the input.

hsa = spectrumAnalyzer(SampleRate=FsIn,... Method='welch',YLimits=[-40 40]); hsa(sIn) release(hsa)

Convert the sample rate of the signal. Estimate the power spectral density of the output.

sOut = src(sIn);

hsb = spectrumAnalyzer(SampleRate=FsOut,... Method='welch',YLimits=[-40 40]); hsb(sOut) release(hsb)

A signal output from an A/D converter is sampled at 98.304 MHz. The signal has a bandwidth of 20 MHz. Reduce the sample rate of the signal to 22 MHz, which is the bandwidth of 802.11 channels. Make the conversion exactly and then redo it with an output rate tolerance of 1%.

SRC1 = dsp.SampleRateConverter(Bandwidth=20e6, ... InputSampleRate=98.304e6,OutputSampleRate=22e6, ... OutputRateTolerance=0); SRC2 = dsp.SampleRateConverter(Bandwidth=20e6,... InputSampleRate=98.304e6,OutputSampleRate=22e6, ... OutputRateTolerance=0.01);

Use the cost method to determine the cost of each sample rate conversion. The zero-tolerance process requires more than 500 times as many coefficients as the 1% process.

c1 = struct with fields: NumCoefficients: 84779 NumStates: 133 MultiplicationsPerInputSample: 27.0422 AdditionsPerInputSample: 26.0684

c2 = struct with fields: NumCoefficients: 150 NumStates: 127 MultiplicationsPerInputSample: 22.6667 AdditionsPerInputSample: 22.1111

Find the integer upsampling and downsampling factors used in each conversion.

[L1,M1] = getRateChangeFactors(SRC1)

[L2,M2] = getRateChangeFactors(SRC2)

Compute the actual sample rate of the output signal when the sample rate conversion has a tolerance of 1%.

getActualOutputRate(SRC2)

Create a multistage sample rate converter with default properties, corresponding to the combined three filter stages used to convert from 192 kHz to 44.1 kHz. Determine its overall decimation and interpolation factors.

src = dsp.SampleRateConverter;

[L,M] = getRateChangeFactors(src);

Create a two-channel random signal. Specify a number of samples equal to the decimation factor. Call the object twice on the signal.

x = randn(M,2);

y1 = src(x); y2 = src(x);

no = all(y2==y1)

no = 1×2 logical array

0 0

The output is different because the internal states of src have changed. Use reset to reset the converter and call the converter again. Verify that the output is unchanged.

reset(src)

y3 = src(x);

yes = all(y3==y1)

yes = 1×2 logical array

1 1

Create a multistage sample rate converter with default properties, corresponding to the combined three filter stages used to convert from 192 kHz to 44.1 kHz. Compute and display the frequency response.

src = dsp.SampleRateConverter; [H,f] = freqz(src); plot(f,20*log10(abs(H)))

Compute and display the frequency response over the range between 20 Hz and 44.1 kHz.

f = 20:10:44.1e3; [H,f] = freqz(src,f); plot(f,20*log10(abs(H)))

Create src, a multistage sample rate converter with default properties. src converts between 192 kHz and 44.1 kHz. Find the individual filters that are cascaded together to perform the conversion.

src = dsp.SampleRateConverter; c = getFilters(src);

Visualize the frequency response of the decimator used in the first stage of the process.

m = c.Stage1;

[h,w] = freqz(m); plot(w/pi,20*log10(abs(h))) xlabel('\omega / \pi') ylabel('Magnitude (dB)')

Create a multistage sample rate converter with default properties, corresponding to the combined three filter stages used to convert from 192 kHz to 44.1 kHz.

src = dsp.SampleRateConverter

src = dsp.SampleRateConverter with properties:

    InputSampleRate: 192000
   OutputSampleRate: 44100
OutputRateTolerance: 0
          Bandwidth: 40000
StopbandAttenuation: 80

Display information about the design.

ans = 'Overall Interpolation Factor : 147 Overall Decimation Factor : 640 Number of Filters : 3 Multiplications per Input Sample: 27.667188 Number of Coefficients : 8631 Filters:
Filter 1: dsp.FIRDecimator - Decimation Factor : 2 Filter 2: dsp.FIRDecimator - Decimation Factor : 2 Filter 3: dsp.FIRRateConverter - Interpolation Factor: 147 - Decimation Factor : 160 '

Get the actual output sample rate for conversion between 192 kHz and 44.1 kHz when given a tolerance of 1%.

src = dsp.SampleRateConverter; src.OutputRateTolerance = 0.01; FsOut = getActualOutputRate(src)

Create src, a multistage sample rate converter with default properties. src combines three filter stages to convert from 192 kHz to 44.1 kHz. Determine its overall interpolation and decimation factors.

src = dsp.SampleRateConverter; [L,M] = getRateChangeFactors(src)

Create a multistage sample rate converter with default properties, corresponding to the combined three filter stages used to convert from 192 kHz to 44.1 kHz. Visualize the stages.

src = dsp.SampleRateConverter; visualize(src)

Algorithms

• The general multistage sample rate converter performs a multistage decimation, a single-stage sample rate conversion, and a multistage interpolation. Actual designs include at most two of these steps.
• The procedure automatically determines the optimal number of decimation or interpolation stages. In special cases, the algorithm can perform a decimation or interpolation in a single stage.
• The algorithm always attempts to start by reducing the sample rate. This decreases the amount of computation required. The decimation step ensures that the intermediate sample rate does not go below the bandwidth of interest and that the block does not filter out any information.
• Each individual stage uses halfband or Nyquist filters to minimize the number of nonzero coefficients.
• The algorithm allows transition-band aliasing because it decreases the implementation cost. It keeps the signal within the bandwidth of interest alias free up to the value specified by the StopbandAttenuation property.

Extended Capabilities

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Usage notes and limitations:

• See System Objects in MATLAB Code Generation (MATLAB Coder).
• The getRateChangeFactors function supports C and C++ code generation.
• This object supports SIMD code generation using Intel® AVX2 code replacement library under these conditions:
  • For upsampling, the ratio of output sample rate to input sample rate must be an integer.
  • For downsampling, the ratio of input sample rate to output sample rate must be an integer.
  • Input signal has a data type of single ordouble.
    The SIMD technology significantly improves the performance of the generated code. For more information, see SIMD Code Generation. To generate SIMD code from this object, see Use Intel AVX2 Code Replacement Library to Generate SIMD Code from MATLAB Algorithms.
• In the code you generate from this object, the resampled signal output is a fixed-size signal if the input signal is fixed size and is a multiple of the decimation factor. If the input is not a multiple of the decimation factor or if the input is a variable-size signal, then the resampled signal output is of variable-size.

Version History

Introduced in R2014b

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The dsp.SampleRateConverter object now supports the filterAnalyzer function and the Filter Analyzer app. Using this app, you can now visualize the frequency response of the overall filter and the response of the individual filter stages of the dsp.SampleRateConverter object.

The visualizeFilterStages function has been renamed tovisualize. Existing instances of this function continue to run. For new instances, use visualize.

The visualize function now launches a MATLAB® figure to visualize the filter stages of the sample rate converter.

This object supports an input signal with an arbitrary frame length, so the input frame length does not have to be a multiple of the decimation factor.

See Also

Functions

• cost | freqz | getActualOutputRate | getFilters | info | visualize | getRateChangeFactors

Objects

• dsp.FarrowRateConverter

Blocks

• Sample-Rate Converter

Topics

• Efficient Sample Rate Conversion Between Arbitrary Factors
• Multirate Filtering in MATLAB and Simulink
• Design of Decimators and Interpolators
• Digital Up and Down Conversion for Family Radio Service in MATLAB