Straightforward DSP Algorithm Suitable for GPU Computation Raul Hazas
Transcript of Straightforward DSP Algorithm Suitable for GPU Computation Raul Hazas
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Data flow analysis within a simplified DSP
structure provides insight into a likely GPUsuitable algorithm
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1. Introduction2. IIR Digital Filters and Biquad Structure
3. Data Flow across biquad structure
4. Previous work5. Proposed method
6. Experimental results
7. Conclusions
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Digital treatment of sequences resulting fromsampled physical phenomena has manyapplications: image and video processing
environmental and life sciences, etc.
DSP processing can consume vast amounts ofcomputing resources
Trend to migrate signal-processing chores tohighly integrated Graphical Processing Units(GPUs)
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Infinite Impulse Response digital filters are aparticular kind of filters that act on: current and past input signal samples,
past filter output values
+
=
= (1)
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To suit our analysis purposes, we take the Ztransform of the previous difference equation
=
+ =
2
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The polynomial fraction could be factored as
+ +
=
Where + .
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We could rearrange the filter structure if wefactor (4) as:
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We follow the flow of sequence across thestructure
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+ +
Then, takes its place as the input to thefeed-forward section
+ +
Where an apparent inner vector product istaking place
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There has been a greatdeal of previous workon the parallelimplementation of
digital filtering
Most of the speed-upefforts are hindered
because of datadependency problems
// u, a float is passed to this// section of the code// x and y arrays are initialized// to {0,0,0}
// initializationfloat sum = 0;int i=0;
// compute the valuefor(i=0;i
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Due to the simplicity of the biquad structure,we suggest:
For a given input sequence , replace thecontents at each memory location by thecontents of
Perform a vector inner product with the feed-forward coefficients
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Matlab and C++ programs were devised tocreate a series of input sequences consistingof a sampled sinusoid signal augmented withrandom values
C++ program was coded according to thealgorithm described before.
Filter coefficients were chosen from textbook
examples for low-pass (LPF), and high-pass(HPF) filters.
For Matlab we used: filter(bb,aa,x) function
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The output from theproposed filtercompletely matchesthe one returned by
Matlab The filters
characteristic behavioris portrayed by theintermediate sequence
Note: Output sequence lengthswere adjusted for comparison anddisplay
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Again, the filterscharacteristic behavioris portrayed by theintermediate sequence
Moreover, the feed-forward sectionreinforces the high-pass filteringperformance
Note: Output sequence lengthswere adjusted for comparison anddisplay
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We implemented a forthright filteringalgorithm
It behaves in agreement with industrystandard application
There are well-established approaches forGPU inner-vector product
We foresee uncoupling recursive operation
will be accomplished by taking advantage ofGPUs massive parallelism andsynchronization