Introduction to Digital Signal Processing Using GNU Radio
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The document discusses digital signal processing using GNU Radio. It begins with an introduction to software-defined radio (SDR) and GNU Radio. It then demonstrates how to add a simple moving average filter in GNU Radio and analyzes the filter using back-of-the-envelope calculations. Specifically, it shows that the filter has a low-pass frequency response by examining how it averages input samples over time. The document thus provides an overview of SDR concepts and a hands-on example of creating and analyzing a basic filter using GNU Radio.
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Introduction to Digital Signal Processing Using GNU Radio
- 1. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 May 25, 2013
- 2. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks About the Author He is both a programmer and a communication engineer. He learned Python in 2000 and has used it extensively on improving his workflow ever since. He has been working in communication IC industry for more than eight years. His interests include communication engineering and engineering communication, which consists of fields from physical layer to MAC layer as well as typesetting. Blog: Random Notes, http://alberthuang314.blogspot.com/ LinkedIn: http://www.linkedin.com/in/alberthuang314 Email address: alberthuang314 AT gmail DOT com
- 3. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Outline 1 Introduction to SDR and GNU Radio 2 Adding a Filter in GNU Radio 3 Analyzing Filters 4 Concluding Remarks
- 4. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Software-Defined Radio Software-Defined Radio (SDR) is a radio communication system implemented (mostly) in software.
- 5. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Software-Defined Radio Software-Defined Radio (SDR) is a radio communication system implemented (mostly) in software. Application areas Military systems, space exploration, base stations, NVIDIA i500 LTE SDR modems, etc.
- 6. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Software-Defined Radio Software-Defined Radio (SDR) is a radio communication system implemented (mostly) in software. Application areas Military systems, space exploration, base stations, NVIDIA i500 LTE SDR modems, etc. Background knowledge required for SDR programmer Digital Signal Processing (the most fundamental knowledge) Programming Probability and Statistics Communication System
- 7. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Software-Defined Radio Software-Defined Radio (SDR) is a radio communication system implemented (mostly) in software. Application areas Military systems, space exploration, base stations, NVIDIA i500 LTE SDR modems, etc. Background knowledge required for SDR programmer Digital Signal Processing (the most fundamental knowledge) Programming Probability and Statistics Communication System This talk is going to illustrate how easy digital signal processing is! Don’t be hesitated!
- 8. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Introduction to GNU Radio GNU Radio is a free & open-source software development toolkit that provides signal processing blocks to implement software radios. Primarily written in Python with performance-critical signal processing components written in C++ [1]. C++ classes are wrapped by SWIG [2]. Python can be used to develop rapid prototype for SDR in an elegant and fast way. “Install GNU Radio 3.6.2 on MacOSX 10.8.2” http://goo.gl/mJQmA “A Glimpse into Developing Software-Defined Radio by Python” on SlideShare.net
- 9. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks GNU Radio Companion
- 10. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Top Block 1 #!/ us r / bin /env python 2 from PyQt4 import Qt 3 # Other imports are hidden 4 c l a s s top bl ock ( gr . top block , Qt . QWidget ) : 5 def i n i t ( s e l f ) : 6 # GUI−r e l a t e d s t u f f are hidden here 7 s e l f . samp rate = samp rate = 16000 8 # q t g u i s i n k s t u f f hidden 9 s e l f . t o p l a y o u t . addWidget ( s e l f . q t g u i s i n k x 10 s e l f . a n a l o g s i g s o u r c e x 1 = analog . s i g s o u r 11 samp rate , analog . GR COS WAVE, 8000 , 12 s e l f . connect (( s e l f . a n a l o g s i g s o u r c e x 1 , 0) 13 ( s e l f . a u d i o s i n k 0 , 0)) 14 s e l f . connect (( s e l f . a n a l o g s i g s o u r c e x 1 , 0) 15 ( s e l f . q t g u i s i n k x 0 , 0)) 16 17 i f name == ’ m a i n ’ : 18 tb = top bl ock () 19 tb . s t a r t () 20 tb . show () 21 tb . stop ()
- 11. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Adding a Simple Moving Average Filter 1 #!/ us r / bin /env python 2 from gnuradio import f i l t e r # Add t h i s l i n e i n t o top bl ock . p 3 # Other imports are hidden 4 c l a s s top bl ock ( gr . top block , Qt . QWidget ) : 5 def i n i t ( s e l f ) : 6 # GUI−r e l a t e d s t u f f are hidden here 7 s e l f . samp rate = samp rate = 44100 8 # q t g u i s i n k s t u f f hidden 9 s e l f . t o p l a y o u t . addWidget ( s e l f . q t g u i s i n k x 10 11 s e l f . a n a l o g s i g s o u r c e x 1 = analog . s i g s o u r 12 # ============================== 13 taps = (0. 25 , 0. 25 , 0. 25 , 0. 25) 14 s e l f . f l t = f i l t e r . f i r f i l t e r f f f (1 , taps ) 15 s e l f . connect (( s e l f . a n a l o g s i g s o u r c e x 1 , 0) 16 ( s e l f . f l t , 0)) 17 s e l f . connect (( s e l f . f l t , 0) , 18 ( s e l f . q t g u i s i n k x 0 , 0)) 19 s e l f . connect (( s e l f . f l t , 0) , 20 ( s e l f . a u d i o s i n k 0 , 0)) 21 22 # ==============================
- 12. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks What Is This Filter?! self.flt = filter.fir filter fff(1, (0.25, 0.25, 0.25, 0.25) ) FIR filter block Input: Float Output: Float Coefficients: Float Time domain equation: y[n] = 0.25x[n]+0.25x[n −1]+0.25x[n −2]+0.25x[n −3] x[n]: current input sample, x[n-1] previous one input sample, and so on... y[n]: current output sample It’s just adding/multiplying numbers together, right? Pretty easy, huh?
- 13. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Digital Frequency Digital frequency is not related to real frequency (yet). So forget about Hz right now. Normally mapped to [0, π] or [0, 1].
- 14. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Digital Frequency: Highest 0 1 2 3 4 5 6 7 8 9 10 -2 -1 0 1 2 Figure : π in [0, π], or 1 in [0, 1]
- 15. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Digital Frequency: Lowest or DC 0 1 2 3 4 5 6 7 8 9 10 -2 -1 0 1 2 Figure : 0
- 16. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Digital Frequency: Middle 0 1 2 3 4 5 6 7 8 9 10 -2 -1 0 1 2 Figure : π/2 in [0, π], or 0.5 in [0, 1]
- 17. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks How to Analyze This Filter? Back-of-the-Envelope Method Do fast calculation in the back of the envelope Handy to get a feel of this filter’s frequency response Discrete Fourier Transform (DFT) All transformations are giving us different perspectives DFT gives us frequency response of a filter z Transform Gives us more than just frequency response Also give us more thorough information, such as stability, etc.
- 18. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Back-of-the-Envelope Method Is the filter low pass filter, high pass filter, or?
- 19. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Back-of-the-Envelope Method Is the filter low pass filter, high pass filter, or? Let’s input these coefficients into Octave to tell us...
- 20. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Back-of-the-Envelope Method Is the filter low pass filter, high pass filter, or? Let’s input these coefficients into Octave to tell us... What if your Octave is not installed, like most of attendees here...
- 21. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Back-of-the-Envelope Method Is the filter low pass filter, high pass filter, or? Let’s input these coefficients into Octave to tell us... What if your Octave is not installed, like most of attendees here... Let’s use back-of-the-envelope method
- 22. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Back-of-the-Envelope Method Is the filter low pass filter, high pass filter, or? Let’s input these coefficients into Octave to tell us... What if your Octave is not installed, like most of attendees here... Let’s use back-of-the-envelope method Remember the filter time domain equation is y[n] = (x[n] + x[n − 1] + x[n − 2] + x[n − 3])/4
- 23. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Back-of-the-Envelope: Highest 0 1 2 3 4 5 6 7 8 9 10 -1 0 1 0 1 2 3 4 5 6 7 8 9 10 -1 0 1 Figure : π in [0, π], or 1 in [0, 1]
- 24. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Back-of-the-Envelope: Middle 0 1 2 3 4 5 6 7 8 9 10 -1 0 1 0 1 2 3 4 5 6 7 8 9 10 -1 0 1 Figure : π/2 in [0, π], or 0.5 in [0, 1]
- 25. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Back-of-the-Envelope: Lowest or DC 0 1 2 3 4 5 6 7 8 9 10 -1 0 1 0 1 2 3 4 5 6 7 8 9 10 -1 0 1
- 26. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Back-of-the-Envelope: Frequency Response 0 1 0 1
- 27. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Complete Frequency Response 0 0.5 1 1.5 2 2.5 3 3.5 −60 −50 −40 −30 −20 −10 0 dB radian/sample
- 28. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Transforming Time Domain Equations into z-Domain y[n] = x[n]+x[n−1]+x[n−2]+x[n−3] 4
- 29. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Transforming Time Domain Equations into z-Domain y[n] = x[n]+x[n−1]+x[n−2]+x[n−3] 4 Looking up z transform pairs in DSP textbook, and you will get... x[n − k]− > X[z] × z−k y[n]− > Y [z]
- 30. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Transforming Time Domain Equations into z-Domain y[n] = x[n]+x[n−1]+x[n−2]+x[n−3] 4 Looking up z transform pairs in DSP textbook, and you will get... x[n − k]− > X[z] × z−k y[n]− > Y [z] Y [z] = X[z]+X[z]×z−1+X[z]×z−2+X[z]×z−3 4
- 31. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Transforming Time Domain Equations into z-Domain y[n] = x[n]+x[n−1]+x[n−2]+x[n−3] 4 Looking up z transform pairs in DSP textbook, and you will get... x[n − k]− > X[z] × z−k y[n]− > Y [z] Y [z] = X[z]+X[z]×z−1+X[z]×z−2+X[z]×z−3 4 H[z] = Y [z] X[z] = 1+z−1+z−2+z−3 4 = B[z] A[z]
- 32. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Transforming Time Domain Equations into z-Domain y[n] = x[n]+x[n−1]+x[n−2]+x[n−3] 4 Looking up z transform pairs in DSP textbook, and you will get... x[n − k]− > X[z] × z−k y[n]− > Y [z] Y [z] = X[z]+X[z]×z−1+X[z]×z−2+X[z]×z−3 4 H[z] = Y [z] X[z] = 1+z−1+z−2+z−3 4 = B[z] A[z] Zeros are values to make |H[z]| = 0 and are roots of B[z] = 1 + z−1 + z−2 + z−3 = 0 (There are three zeros at z=1j, z=-1, and z=-1j) Poles are values to make |H[z]| = ∞ and are roots of A[z] = 0 (There isn’t any pole for this filter)
- 33. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Visualization of equations: z Plane
- 34. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Visualization of z Plane 1/3 “Logic will get you from A to Z (Plane); imagination will get you everywhere.” – Albert Einstein
- 35. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Visualization of z Plane 2/3 Imagine... Zeros drag surface to ground Poles bring surface up in the sky
- 36. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Visualization of z Plane 3/3 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −30 −20 −10 0 10 20 30
- 37. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks z Transform and Frequency Response −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −30 −20 −10 0 10 20 30 0 0.5 1 1.5 2 2.5 3 3.5 −60 −50 −40 −30 −20 −10 0 dB radian/sample
- 38. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Sampling Rate and Real Frequency [0, 1] −→ [0, 1 2 Fs] [0, π] −→ [0, 1 2Fs] Fs is sampling rate The highest digital frequency we can represent is 1, and it will be mapped to Fs 2 . Fs 2 plays an important role in digital signal processing, and is called Nyquist frequency. To sample 8kHz analog signals, you need Fs 2 ≥ 8 kHz, i.e. Fs ≥ 16 kHz to represent it. (Nyquist-Shannon sampling theorem)
- 39. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Demo: Seeing Is Believing No, in this case,
- 40. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Demo: Seeing Is Believing No, in this case, Hearing is believing!
- 41. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Concluding Remarks GNU Radio provides us a signal processing framework in Python. Digital signal processing seems not easy at first glance. By visualizing z plane and frequency response, DSP becomes easier to understand! Finally, don’t forget Fs ≥ 2 Finterest, where Finterest is the highest frequency for signal you’re interested in. With these visualization techniques, you can use gr filter design tool in GNU Radio to design filter without analyzing it.
- 42. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks Q & A
- 43. Introduction to Digital Signal Processing Using GNU Radio Albert Chun-Chieh Huang PyCon Taiwan 2013 Introduction to SDR and GNU Radio Adding a Filter in GNU Radio Analyzing Filters Concluding Remarks References “GNU Radio Project Wiki.” [Online]. Available: http://gnuradio.org/redmine/projects/gnuradio/wiki “SWIG - Simple Wrapper and Interface Generator.” [Online]. Available: http://swig.org J. Mitola, III, “Software radios-survey, critical evaluation and future directions,” in Telesystems Conference, 1992. NTC-92., National, 1992, p. 13.