Straightforward DSP Algorithm Suitable for GPU Computation Raul Hazas

8/10/2019 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:

5


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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

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Straightforward DSP Algorithm Suitable for GPU Computation Raul Hazas