1. Renesas Electronics America Inc. © 2012 Renesas Electronics America Inc. All rights reserved. Class ID: You CAN Do Digital Filtering with an MCU! CC13B Kevin P King - Senior Staff Application Engineer

2. © 2012 Renesas Electronics America Inc. All rights reserved.2 Kevin P King Education Electrical Engineering, University of Lowell (Edward B Van Dusen Award for Academic Achievement) Thirty years of Embedded Design Experience (x86, HC05, HC11, 8051, Philips XA, Atmel AVR, Hitachi, Mitsubishi, etc.... Five years of Emulator design for MetaLink COP8, 68HC05, 68HC11, 8051 (multi-vendors), National CR16, Hitachi H8/500, etc... Multiple Quality Awards for Embedded Software & Hardware Development. Specialty is Embedded System Design - MCU firmware & hardware Senior Staff Application Engineer RX DSP Library Development Team Numerous Motor Control and Medical App notes 2010 Patent Award for Motor Control

3. © 2012 Renesas Electronics America Inc. All rights reserved.3 Renesas Technology & Solution Portfolio

4. © 2012 Renesas Electronics America Inc. All rights reserved.4 Microcontroller and Microprocessor Line-up Wide Format LCDs  Industrial & Automotive, 130nm  350µA/MHz, 1µA standby 44 DMIPS, True Low Power Embedded Security, ASSP 165 DMIPS, FPU, DSC 1200 DMIPS, Performance 1200 DMIPS, Superscalar 500 DMIPS, Low Power 165 DMIPS, FPU, DSC 25 DMIPS, Low Power 10 DMIPS, Capacitive Touch  Industrial & Automotive, 150nm  190µA/MHz, 0.3µA standby  Industrial, 90nm  200µA/MHz, 1.6µA deep standby  Automotive & Industrial, 90nm  600µA/MHz, 1.5µA standby  Automotive & Industrial, 65nm  600µA/MHz, 1.5µA standby  Automotive, 40nm  500µA/MHz, 35µA deep standby  Industrial, 40nm  200µA/MHz, 0.3µA deep standby  Industrial, 90nm  1mA/MHz, 100µA standby  Industrial & Automotive, 130nm  144µA/MHz, 0.2µA standby 2010 2012 32-bit 8/16-bit

5. © 2012 Renesas Electronics America Inc. All rights reserved.5 Challenge: “More and More Sensors are required by our “Smart” devices and reliable filtering is required to separate the signal from the noise.” Solution: “This lecture will introduce you to some of the basic concepts of Digital Filtering, low-cost Filter tools and help you avoid some of the more common pitfalls when implementing filters on the Renesas processor of their choice.” ‘Enabling The Smart Society’ Wireless Module Doctor, your patient is in distress

6. © 2012 Renesas Electronics America Inc. All rights reserved.6 Agenda System Block Diagram – analog filter FIR vs IIR Sampling theorem Anti-aliasing Oversampling Triggering skew ADC interrupt overhead Decimation Fixed point and floating point principles Fixed point vs. floating point benchmark Summary

7. © 2012 Renesas Electronics America Inc. All rights reserved.7 Example Filter Applications

8. © 2012 Renesas Electronics America Inc. All rights reserved.8 Filter Applications – The Boxcar Filter Very common to perform a “running” average Sum n samples, scale the output (usually divide by n) Recalculate each time one new sample comes in Very simple FIR called boxcar All coefficients equal to 1 Example of 8 kHz sampling rate, 8 tap FIR

9. © 2012 Renesas Electronics America Inc. All rights reserved.9 Filter Types - FIR Typically the gain = 1 Does not always have Decimation Decimation can be on front or back end X[n] – Input samples nD – Decimation Factor Y”[n] – Decimated Output B[n] – Coefficients (multiplies) Z -1 – Delay elements (storage array)

10. © 2012 Renesas Electronics America Inc. All rights reserved.10 Filter Types - IIR In addition to a forward path there is a feedback path X[n] – Input samples Y k [n] – Output b k [n] – Feed forward Coefficients (multiplies) -a k [n] – Feedback Coefficients (multiplies) Z -1 – Delay elements (storage array)

11. © 2012 Renesas Electronics America Inc. All rights reserved.11 FIR versus IIR* FIR Phase-linear Simple instructions, single loop Suited for Multi-rate (decimation or interpolation allows some calculations to be omitted) Desirable Numeric properties (finite-precision can usually be implemented using lower number of bits) Possible to implement with coefficients less then 1.0 May require more memory and calculations than the IIR Some responses are just impractical to implement in FIR IIR Less memory and calculations for a given filtering characteristic Arithmetic errors compounded by feedback Harder to implement using fixed point Not as easy to do multi-rate (decimation and interpolation) Not phase-linear * http://www.dspguru.com/dsp/faqs/fir/basics and http://www.dspguru.com/dsp/faqs/iirhttp://www.dspguru.com/dsp/faqs/fir/basicshttp://www.dspguru.com/dsp/faqs/iir

12. © 2012 Renesas Electronics America Inc. All rights reserved.12 Designing the Filter Programs like ScopeFIR, ScopeIIR or WinFilter simplify the task of designing a filter

13. © 2012 Renesas Electronics America Inc. All rights reserved.13 Identifying the Noise Programs like ScopeDSP allows inputting ADC data and running FFT

14. © 2012 Renesas Electronics America Inc. All rights reserved.14 Identifying the Noise The FFT clearly identifies a 1k,2K,4K and 8K component

15. © 2012 Renesas Electronics America Inc. All rights reserved.15 Sampling Theorem Nyquist-Shannon Sampling Theorem “If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.” 1hertz Sometimes this is incorrectly stated: To not lose information you must sample at twice the highest frequency you are concerned with in a signal Simply stated: A signal can only be properly sampled if it contains no frequencies greater than one-half the sampling frequency

16. © 2012 Renesas Electronics America Inc. All rights reserved.16 Aliasing Problem Record voice data and store Limit voice bandwidth to 4 kHz Sample at 8 kHz Problem - Audio contains energy above 4 kHz Anti-aliasing filter Adjust corner for 4 kHz

17. © 2012 Renesas Electronics America Inc. All rights reserved.17 Anti-aliasing filter - 12 dB is only an attenuation of 1/4

18. © 2012 Renesas Electronics America Inc. All rights reserved.18 Anti-aliasing filter

19. © 2012 Renesas Electronics America Inc. All rights reserved.19 Frequency Response of 8 Tap 4 kHz Filter -12dB line 20 dB attenuation at 8 kHz compared to 12 for analog filter

20. © 2012 Renesas Electronics America Inc. All rights reserved.20 Improved 4 kHz Filter By using 14 taps notice the improved attenuation at 6 kHz

21. © 2012 Renesas Electronics America Inc. All rights reserved.21 Oversampling and digital filtering Sample at 32 kHz instead of 8 kHz Only signals 16 kHz or greater will alias Could use simple RC or no anti-aliasing filter

22. © 2012 Renesas Electronics America Inc. All rights reserved.22 Oversampling and digital filtering Decimate results Store every 4 th sample Only calculate filter at 8 kHz

23. © 2012 Renesas Electronics America Inc. All rights reserved.23 Multi-rate and Decimation Temp cannot change more than 1 degree/ hour Required sampling rate for 1 degree logging Noise with 1 second period, averages out in 4 readings Sampling rate for noise x x x x x x x x x x x x x x x x Temperature x x x x

24. © 2012 Renesas Electronics America Inc. All rights reserved.24 ADC Considerations - Skew Problems: Interrupt Skew – 32 kHz requires sampling every 31.25 uS Software start ADC possibility of sample skew Other interrupts in the system Long instructions required to complete Solutions: Possible - Make the start interrupt highest system priority Preferred - Use ADC system that can be triggered by timer – Some devices may have to loop a timer to ADC trigger

25. © 2012 Renesas Electronics America Inc. All rights reserved.25 ADC Considerations - Overhead Problem: Interrupt Overhead Storing ADC Data – Assume ADC ISR takes 40 cycles context save + data save and pointer adjust + context restore Sampling at 32 kHz BW to store data = 1.28 million cycles Solutions: Use a DMA controller 4-5 cycles or less per transfer CPU BW to store data <200 thousand cycles

26. © 2012 Renesas Electronics America Inc. All rights reserved.26 ADC Considerations - Benchmark Example RX allows triggering ADC from GPT/MTU2/MTU3 (timer) DMAC transfers data to buffer HW assist to acquire/transfer data to buffer saves* ~3% at 200kHz rate / 5K samples ~13% at 400kHz rate / 5K samples ~26% at 500kHz rate / 5K samples * DevCon RX Performance lab

27. © 2012 Renesas Electronics America Inc. All rights reserved.27 Calculating the Filter Design 4 kHz, 8 tap, lowpass filter Sampling rate 32 kHz Passband 4 kHz Stopband 8 kHz Stopband attenuation 12 dB – actual 20 dB Passband ripple = 2 dB - actual 0.76 Coefficients: -0.074778857796693535 0.020358522095065112 0.200149797853876850 0.366925297165379800 0.200149797853876850 0.020358522095065112 -0.074778857796693535

28. © 2012 Renesas Electronics America Inc. All rights reserved.28 Implementing the Filter Could calculate the filter as: result=0; for (index = 0; index < taps; index++) { result += data[index] * coeff[index]; } The problem is the coefficients are all fractional values

29. © 2012 Renesas Electronics America Inc. All rights reserved.29 Options to Calculate the Filter Use an MCU with an FPU RH850 – 32 Bit RISC High Performance RISC RX600 – High Performance CISC SH2A like SH7269 – High Performance RISC Use Floating Point Libraries Can be very slow Use Fixed Point Math A little more complicated than floating point

30. © 2012 Renesas Electronics America Inc. All rights reserved.30 Floating Point Numbers Floating point value = (-1) sb + (1+Fraction) x 2 (exponent – bias) The exponent is expressed in biased form: e = E + bias Precision is function of fraction bits Floating supports a very large dynamic range ParameterSingle Precision Double Precision Total bit Width 32bits64bits Sign bit1bit Exponent field 8bits11bits Significand23bits52bits Precision24bits53bits Bias+127+1023 Emax+127+1023 Emin-126+1024 0313022 Significand part 23 bits (implied 1)Exponent 8 bitsS -2 8 2727 2626 2525 2424 23232 2121 2020 2 -1 2 -2 2 -3 2 -4 2 -5 2 -6 2 -7 2 -8 2 -9 2 -10 2 -11 2 -12 2 -13 2 -14 2 -15 2 -16 2 -17 2 -18 2 -19 2 -20 Radix point 2 -21 2 -22 2 -23 23

31. © 2012 Renesas Electronics America Inc. All rights reserved.31 Floating Point Hardware Single Precision Min Value = 5.88 x 10e-39, Max value = 3.4 x 10e+38 Double Precision Min Value = ~2.0 x 10e-308, Max value = ~2.0 x 10e+307 0313022 Significand part 23 bits (implied 1)Exponent 8 bitsS -2 8 2727 2626 2525 2424 23232 2121 2020 2 -1 2 -2 2 -3 2 -4 2 -5 2 -6 2 -7 2 -8 2 -9 2 -10 2 -11 2 -12 2 -13 2 -14 2 -15 2 -16 2 -17 2 -18 2 -19 2 -20 Radix point 2 -21 2 -22 2 -23 23 031 Significand part 32/52 bits (implied 1) 23232 2121 2020 32636251 Significand part 20/52 bits (implied 1) Exponent 11 bits S -2 12 2 11 2 10 2929 2828 2727 2626 2525 2424 2 -1 2 -2 2 -3 2 -4 2 -5 2 -6 2 -7 2 -8 2 -9 2 -10 2 -11 2 -12 2 -13 2 -14 2 -15 2 -16 2 -17 2 -18 2 -19 Radix point 52 2 -32 2 -33 2 -34 2 -35 2 -36 2 -37 2 -38 2 -39 2 -40 2 -41 2 -42 2 -43 2 -44 2 -45 2 -46 2 -47 2 -48 2 -49 2 -50 2 -51 2 -28 2 -29 2 -30 2 -31 2 -24 2 -25 2 -26 2 -27 2 -20 2 -21 2 -22 2 -23

32. © 2012 Renesas Electronics America Inc. All rights reserved.32 Fixed Point Fraction value is shifted (multiplied) by a value to make an integer Example – Represent 19. 78 using 16 bit fixed point – 1 bit for the sign – 19 requires 5 bits in binary – 10 bits left to represent fraction – Multiply the value by 1024 (shift left 10) – Could allocate more bits for integer and less for fraction Example : Calculate a 4 tap box filter using fixed point Assume ADC samples are – 0x100 (256), 0x200 (512), 0x120(288), 0x150(336) Coefficients are all 0.25 Solution – Scale coefficients to be integers by multiplying by 4 (shift left 2) – Multiply coefficients time ADC values 1*0x100 + 1 *0x200 + 1*0x120 + 1 *0x150 = 0x570 (1392) – Restore proper scaling (shift right 2) = 0x15C (348) S2424 23232 2121 2020 2 -1 2 -2 2 -3 2 -4 2 -5 2 -6 2 -7 2 -8 2 -9 2 -10

33. © 2012 Renesas Electronics America Inc. All rights reserved.33 Precision Requirements How many bits of coefficient are required? Do not want round-off error to cause an LSB error For 10 bit ADC need 10 bits coefficient Each tap could accumulate error – Additional bits depends on number taps – 8 taps – add 3 LSB – 16 taps – add 4 LSB – Etc…

34. © 2012 Renesas Electronics America Inc. All rights reserved.34 Pop Quiz: Assuming: 12 bit ADC, 7 tap FIR filter QUESTION: Is 16 bit Fixed Point enough resolution? 8 taps – add 3 LSB, for a total of 15 bits Don’t forget the sign bit! 16 bit total

35. © 2012 Renesas Electronics America Inc. All rights reserved.35 Some Benchmark Results Using RL78/G14 (16 bit, 32 MHz MCU ) 8 Tap Filter – 216 cycles (27 cycles per tap) 22 Tap Filer – 594 cycles (27 cycles per tap) 8 taps at 8 kHz = ~1.73 million cycles (approximately 5.4% BW @ 32 MHz) Each tap calculation requires Multiply Sum Two Pointer Increments

36. © 2012 Renesas Electronics America Inc. All rights reserved.36 A MAC Really Helps Really need a MAC RX has RMPA (software MAC), RL78 has MACH Unit – RL78 200 samples/64 Tap Filter – 354,000 cycles – RX 200 samples/64 Tap Filter – 33,000 cycles RX average 2.6 cycles per tap* RL78 average 27.6 cycles per tap* *From DSP and DSCL library test results

37. © 2012 Renesas Electronics America Inc. All rights reserved.37 Circular Buffer Bottleneck Most DSPs can handle circular buffers, MCUs typically do not Inefficient to put pointer check in loop X0X1X2X3 C0C1C2C3 X1X2X3X4 C0C1C2C3 New Data Circular Buffer Implementation X4 Classical Implementation

38. © 2012 Renesas Electronics America Inc. All rights reserved.38 Double Coefficient Loops X0X1X2X3 C0C1C2C3 C0C1C2C3 X4X1X2X3 C0C1C2C3 Loop1 C0C1C2C3 X4X5X2X3 C0C1C2C3 Loop2 Loop3 C0C1C2C3

39. © 2012 Renesas Electronics America Inc. All rights reserved.39 IIR Filters

40. © 2012 Renesas Electronics America Inc. All rights reserved.40 IIR Since round-off error in output feeds back IIR requires greater precision 16 bit precision typically sufficient for FIR IIR requires 32 bit precision 1 Floating point simplifies math

41. © 2012 Renesas Electronics America Inc. All rights reserved.41 Why use IIR Design 5 kHz bandpass Sampling rate 44 kHz Center Frequency - 5 kHz Passband - 1 kHz Stopband attenuation 40 dB Passband ripple = 2 dB FIR filter requires 59 taps: IIR filter only requires 17 taps (13 non-zero) Forward coefficients – 1,0,-4,0,6,0,-4,0,1 Feedback coefficients -0.9027953874, 5.5279871696, -16.3895992764 29.9415524963, -36.6655508659, 30.7172057969 -17.2497536574. 5.9688037639

42. © 2012 Renesas Electronics America Inc. All rights reserved.42 Some Benchmark Results Calculating the previous filter Using RX 59 tap FIR – 645 Cycles (6.45 uS @ 100 MHz) – 28% BW if run @ 44 kHz RX 17 tap IIR – 353 cycles (3.53 uSec @ 100 MHz) – 15% BW if run @ 44 kHz Tools like the RX DSP Library and RL78 DSC Library help simplify the calculations / implementation.

43. © 2012 Renesas Electronics America Inc. All rights reserved.43 Summary System Block Diagram – analog filter FIR vs IIR Sampling theorem Anti-aliasing Oversampling Triggering skew ADC interrupt overhead Decimation Fixed point and floating point principles Fixed point vs. floating point benchmark

44. © 2012 Renesas Electronics America Inc. All rights reserved.44 Questions? Questions?

45. © 2012 Renesas Electronics America Inc. All rights reserved.45 Challenge: “More and More Sensors are required by our “Smart” devices and reliable filtering is required to separate the signal from the noise.” “This lecture will introduce them to some of the basic concepts of Digital Filtering, low-cost Filter tools and help you avoid some of the more common pitfalls when implementing on the Renesas processor of their choice.” Do you agree that we accomplished the above statement? ‘Enabling The Smart Society’ in Review…

46. © 2012 Renesas Electronics America Inc. All rights reserved.46 Please utilize the ‘Guidebook’ application to leave feedback or Ask me for the paper feedback form for you to use… Please Provide Your Feedback…

47. © 2012 Renesas Electronics America Inc. All rights reserved.47 Appendix: Additional Information

48. © 2012 Renesas Electronics America Inc. All rights reserved.48 Resources ScopeFir and ScopeDSP http://www.iowegian.com/ http://www.dspguru.com/ The Scientist and Engineer's Guide to Digital Signal Processing, copyright ©1997-1998 by Steven W. Smith. For more information visit the book's website at: www.DSPguide.com C. E. Shannon, "Communication in the presence of noise", Proc. Institute of Radio Engineers, vol. 37, no. 1, pp. 10–21, Jan. 1949. Reprint as classic paper in: Proc. IEEE, vol. 86, no. 2, (Feb. 1998) C. E. ShannonReprint as classic paper in: Proc. IEEE, vol. 86, no. 2, (Feb. 1998) http://www.winfilter.20m.com Signal Processing tfor Communications (http://www.sp4comm.org/ )http://www.sp4comm.org/

49. © 2012 Renesas Electronics America Inc. All rights reserved.49 A visual look at Aliasing x(t) = cos(2 π * 8400t) solid line Fs = 8000Hz 400 Hz (dots) not distinguishable from 8000Hz

50. Renesas Electronics America Inc. © 2012 Renesas Electronics America Inc. All rights reserved.