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update benchmarks and docs
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‎NWaves.Benchmarks/FftArrayVsSpan.cs ‎NWaves.Benchmarks/Fft/FftArrayVsSpan.cs

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‎NWaves.Benchmarks/FirFilterV2.cs ‎NWaves.Benchmarks/FirFilters/FirFilterV2.cs

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‎NWaves.Benchmarks/FirFiltersVersion2Vs5VsZi.cs ‎NWaves.Benchmarks/FirFilters/FirFiltersVersion2Vs5VsZi.cs

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‎NWaves.Benchmarks/FirFiltersVsBlockConvolvers.cs ‎NWaves.Benchmarks/FirFilters/FirFiltersVsBlockConvolvers.cs

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‎NWaves.Benchmarks/IirFilterLinq.cs ‎NWaves.Benchmarks/IirFilters/IirFilterLinq.cs

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‎NWaves.Benchmarks/IirFilterV2.cs ‎NWaves.Benchmarks/IirFilters/IirFilterV2.cs

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‎NWaves.Benchmarks/IirFilterV4.cs ‎NWaves.Benchmarks/IirFilters/IirFilterV4.cs

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‎NWaves.Benchmarks/IirFiltersVersion2Vs4Vs5VsZi.cs ‎NWaves.Benchmarks/IirFilters/IirFiltersVersion2Vs4Vs5VsZi.cs

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‎NWaves.Benchmarks/MedianFilters.cs ‎NWaves.Benchmarks/Misc/MedianFilters.cs

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‎NWaves.Benchmarks/MovingAverageFilters.cs ‎NWaves.Benchmarks/Misc/MovingAverageFilters.cs

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‎NWaves.Benchmarks/OfflineFilterForLoopVsLinq.cs ‎NWaves.Benchmarks/Misc/OfflineFilterForLoopVsLinq.cs

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‎NWaves.Benchmarks/Program.cs

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namespace NWaves.Benchmarks
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using BenchmarkDotNet.Running;
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namespace NWaves.Benchmarks
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{
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class Program
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{

‎NWaves.Benchmarks/README.md

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Benchmark results on a cheaper hardware:
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### IIR filters
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Different implementations of IIR filters are compared:
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- ```IirFilter``` (ver.0.9.2 of NWaves)
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- ```IirFilter``` (ver.0.9.4 of NWaves)
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- ```IirFilter``` (as of ver.0.9.5 of NWaves)
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- ```ZiFilter```
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```ZiFilter``` is noticeably faster than ```IirFilter``` in case when the number of zeros is equal to number of poles (e.g. BiQuad and Butterworth filters).
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In case of custom IIR filter (3 zeros and 1 pole) ```ZiFilter``` filtering is slower.
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``` ini
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BenchmarkDotNet=v0.13.0, OS=Windows 10.0.19043.1237 (21H1/May2021Update)
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Intel Pentium CPU G3460 3.50GHz, 1 CPU, 2 logical and 2 physical cores
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.NET SDK=5.0.100
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[Host] : .NET 5.0.0 (5.0.20.51904), X64 RyuJIT
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DefaultJob : .NET 5.0.0 (5.0.20.51904), X64 RyuJIT
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```
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| Method | Mean | Error | StdDev | Gen 0 | Gen 1 | Gen 2 | Allocated |
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|----------------------------- |----------:|---------:|---------:|---------:|---------:|---------:|----------:|
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| FilterVersion092BiQuad | 57.20 ms | 0.133 ms | 0.124 ms | 222.2222 | 222.2222 | 222.2222 | 19 MB |
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| FilterVersion094BiQuad | 63.14 ms | 0.147 ms | 0.138 ms | 250.0000 | 250.0000 | 250.0000 | 19 MB |
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| FilterVersion095BiQuad | 55.41 ms | 0.106 ms | 0.094 ms | 200.0000 | 200.0000 | 200.0000 | 19 MB |
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| FilterZiBiQuad | 41.44 ms | 0.130 ms | 0.122 ms | 307.6923 | 307.6923 | 307.6923 | 19 MB |
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| FilterVersion092Butterworth6 | 103.57 ms | 0.377 ms | 0.353 ms | 200.0000 | 200.0000 | 200.0000 | 19 MB |
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| FilterVersion094Butterworth6 | 108.64 ms | 0.309 ms | 0.274 ms | 200.0000 | 200.0000 | 200.0000 | 19 MB |
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| FilterVersion095Butterworth6 | 96.03 ms | 0.186 ms | 0.165 ms | 333.3333 | 333.3333 | 333.3333 | 19 MB |
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| FilterZiButterworth6 | 74.91 ms | 0.216 ms | 0.202 ms | 285.7143 | 285.7143 | 285.7143 | 19 MB |
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| FilterVersion092Custom | 56.77 ms | 0.175 ms | 0.164 ms | 222.2222 | 222.2222 | 222.2222 | 19 MB |
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| FilterVersion094Custom | 62.86 ms | 0.136 ms | 0.121 ms | 250.0000 | 250.0000 | 250.0000 | 19 MB |
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| FilterVersion095Custom | 54.71 ms | 0.101 ms | 0.090 ms | 200.0000 | 200.0000 | 200.0000 | 19 MB |
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| FilterZiCustom | 58.90 ms | 0.146 ms | 0.122 ms | 222.2222 | 222.2222 | 222.2222 | 19 MB |
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### FIR Filters
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Different implementations of FIR filters are compared:
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- ```FirFilter``` (ver.0.9.2 - 0.9.4 of NWaves)
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- ```FirFilter``` (as of ver.0.9.5 of NWaves)
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- ```ZiFilter```
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This benchmark demonstrates that the newer version of ```FirFilter``` is faster. ```ZiFilter``` is expectedly slower than ```FirFilter```.
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``` ini
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BenchmarkDotNet=v0.13.0, OS=Windows 10.0.19043.1237 (21H1/May2021Update)
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Intel Pentium CPU G3460 3.50GHz, 1 CPU, 2 logical and 2 physical cores
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.NET SDK=5.0.100
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[Host] : .NET 5.0.0 (5.0.20.51904), X64 RyuJIT
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DefaultJob : .NET 5.0.0 (5.0.20.51904), X64 RyuJIT
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```
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| Method | Mean | Error | StdDev | Gen 0 | Gen 1 | Gen 2 | Allocated |
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|------------------------- |----------:|----------:|----------:|---------:|---------:|---------:|----------:|
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| FilterVersion092Kernel5 | 9.782 ms | 0.1544 ms | 0.1444 ms | 234.3750 | 234.3750 | 234.3750 | 4 MB |
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| FilterVersion095Kernel5 | 9.697 ms | 0.1397 ms | 0.1307 ms | 187.5000 | 187.5000 | 187.5000 | 4 MB |
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| ZiFilterKernel5 | 11.069 ms | 0.2179 ms | 0.2140 ms | 281.2500 | 281.2500 | 281.2500 | 4 MB |
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| FilterVersion092Kernel35 | 51.575 ms | 0.0910 ms | 0.0807 ms | 300.0000 | 300.0000 | 300.0000 | 4 MB |
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| FilterVersion095Kernel35 | 36.210 ms | 0.0834 ms | 0.0780 ms | 285.7143 | 285.7143 | 285.7143 | 4 MB |
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| ZiFilterKernel35 | 68.211 ms | 0.0804 ms | 0.0752 ms | 250.0000 | 250.0000 | 250.0000 | 4 MB |
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### FFT
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Different FFTs are compared:
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- RealFft (single precision) : ```float[]``` and ```Span<float>```
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- RealFft64 (double precision) : ```double[]``` and ```Span<double>```
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- (Complex)Fft (single precision) : ```float[]``` and ```Span<float>```
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``` ini
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BenchmarkDotNet=v0.13.0, OS=Windows 10.0.19043.1237 (21H1/May2021Update)
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Intel Pentium CPU G3460 3.50GHz, 1 CPU, 2 logical and 2 physical cores
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.NET SDK=5.0.100
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[Host] : .NET 5.0.0 (5.0.20.51904), X64 RyuJIT
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DefaultJob : .NET 5.0.0 (5.0.20.51904), X64 RyuJIT
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```
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| Method | Mean | Error | StdDev | Gen 0 | Gen 1 | Gen 2 | Allocated |
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|---------------- |---------:|---------:|---------:|--------:|------:|------:|----------:|
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| FftArray | 14.25 ms | 0.023 ms | 0.021 ms | 15.6250 | - | - | 24,648 B |
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| FftSpan | 15.62 ms | 0.024 ms | 0.023 ms | - | - | - | - |
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| Fft64Array | 14.53 ms | 0.030 ms | 0.028 ms | 15.6250 | - | - | 49,224 B |
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| Fft64Span | 15.66 ms | 0.055 ms | 0.051 ms | - | - | - | - |
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| ComplexFftArray | 17.41 ms | 0.081 ms | 0.075 ms | - | - | - | 32,864 B |
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| ComplexFftSpan | 16.67 ms | 0.033 ms | 0.031 ms | - | - | - | - |
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### FIR filters vs. BlockConvolvers
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This benchmark demonstrates that OLS and OLA block covolvers are expectedly much faster than FIR filters for longer filter kernels.
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``` ini
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BenchmarkDotNet=v0.13.0, OS=Windows 10.0.19043.1237 (21H1/May2021Update)
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Intel Pentium CPU G3460 3.50GHz, 1 CPU, 2 logical and 2 physical cores
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.NET SDK=5.0.100
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[Host] : .NET 5.0.0 (5.0.20.51904), X64 RyuJIT
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DefaultJob : .NET 5.0.0 (5.0.20.51904), X64 RyuJIT
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```
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| Method | Mean | Error | StdDev | Gen 0 | Gen 1 | Gen 2 | Allocated |
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|--------------------- |----------:|----------:|----------:|---------:|---------:|---------:|----------:|
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| FirFilterKernel21 | 2.837 ms | 0.0093 ms | 0.0087 ms | 121.0938 | 121.0938 | 121.0938 | 391 KB |
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| OverlapAddKernel21 | 3.466 ms | 0.0052 ms | 0.0049 ms | 121.0938 | 121.0938 | 121.0938 | 391 KB |
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| OverlapSaveKernel21 | 3.452 ms | 0.0065 ms | 0.0061 ms | 121.0938 | 121.0938 | 121.0938 | 391 KB |
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| FirFilterKernel101 | 10.854 ms | 0.0208 ms | 0.0194 ms | 109.3750 | 109.3750 | 109.3750 | 391 KB |
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| OverlapAddKernel101 | 4.076 ms | 0.0069 ms | 0.0065 ms | 117.1875 | 117.1875 | 117.1875 | 391 KB |
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| OverlapSaveKernel101 | 4.035 ms | 0.0087 ms | 0.0081 ms | 117.1875 | 117.1875 | 117.1875 | 391 KB |
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| FirFilterKernel315 | 30.350 ms | 0.0446 ms | 0.0417 ms | 93.7500 | 93.7500 | 93.7500 | 392 KB |
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| OverlapAddKernel315 | 4.374 ms | 0.0082 ms | 0.0076 ms | 117.1875 | 117.1875 | 117.1875 | 392 KB |
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| OverlapSaveKernel315 | 4.329 ms | 0.0069 ms | 0.0062 ms | 117.1875 | 117.1875 | 117.1875 | 392 KB |
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### Moving average filters
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Recursive implementation of moving average filter (```MovingAverageRecursiveFilter```) is expectedly much faster than FIR subclass (```MovingAverageFilter```).
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``` ini
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BenchmarkDotNet=v0.13.0, OS=Windows 10.0.19043.1237 (21H1/May2021Update)
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Intel Pentium CPU G3460 3.50GHz, 1 CPU, 2 logical and 2 physical cores
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.NET SDK=5.0.100
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[Host] : .NET 5.0.0 (5.0.20.51904), X64 RyuJIT
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DefaultJob : .NET 5.0.0 (5.0.20.51904), X64 RyuJIT
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```
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| Method | Mean | Error | StdDev | Gen 0 | Gen 1 | Gen 2 | Allocated |
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|----------------------------- |---------:|----------:|----------:|---------:|---------:|---------:|----------:|
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| MovingAverageFilter | 9.167 ms | 0.1758 ms | 0.1726 ms | 218.7500 | 218.7500 | 218.7500 | 4 MB |
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| MovingAverageFilterRecursive | 3.856 ms | 0.0759 ms | 0.0779 ms | 218.7500 | 218.7500 | 218.7500 | 4 MB |
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### Median filters
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```MedianFilter``` is significantly faster than ```MedianFilter2```.
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``` ini
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BenchmarkDotNet=v0.13.0, OS=Windows 10.0.19043.1237 (21H1/May2021Update)
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Intel Pentium CPU G3460 3.50GHz, 1 CPU, 2 logical and 2 physical cores
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.NET SDK=5.0.100
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[Host] : .NET 5.0.0 (5.0.20.51904), X64 RyuJIT
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DefaultJob : .NET 5.0.0 (5.0.20.51904), X64 RyuJIT
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```
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| Method | Mean | Error | StdDev | Gen 0 | Gen 1 | Gen 2 | Allocated |
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|-------------- |----------:|----------:|----------:|---------:|---------:|---------:|----------:|
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| MedianFilter | 9.327 ms | 0.0201 ms | 0.0188 ms | 109.3750 | 109.3750 | 109.3750 | 391 KB |
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| MedianFilter2 | 14.030 ms | 0.0198 ms | 0.0185 ms | 109.3750 | 109.3750 | 109.3750 | 391 KB |

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