Introduction to Digital Signal Processing Using GNU Radio

Introductionto DigitalSignal

ProcessingUsing GNU

Radio

AlbertChun-Chieh

HuangPyCon Taiwan

2013

Introductionto SDR andGNU Radio

Adding aFilter in GNURadio

AnalyzingFilters

ConcludingRemarks

Introduction to Digital Signal ProcessingUsing GNU Radio

Albert Chun-Chieh HuangPyCon Taiwan 2013

May 25, 2013


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AlbertChun-Chieh

HuangPyCon Taiwan

2013



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About the Author

He is both a programmer and a communication engineer.He learned Python in 2000 and has used it extensively onimproving his workflow ever since. He has been working incommunication IC industry for more than eight years. Hisinterests include communication engineering andengineering communication, which consists of fields fromphysical 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

http://alberthuang314.blogspot.com/

http://www.linkedin.com/in/alberthuang314


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AlbertChun-Chieh

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Outline

1 Introduction to SDR and GNU Radio

2 Adding a Filter in GNU Radio

3 Analyzing Filters

4 Concluding Remarks


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Software-Defined Radio

Software-Defined Radio (SDR) is a radio communicationsystem implemented (mostly) in software.


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Application areas

Military systems, space exploration, base stations, NVIDIAi500 LTE SDR modems, etc.


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AlbertChun-Chieh

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Application areas


Background knowledge required for SDR programmer

Digital Signal Processing (the most fundamentalknowledge)ProgrammingProbability and StatisticsCommunication System


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Application areas


Background knowledge required for SDR programmer

Digital Signal Processing (the most fundamentalknowledge)ProgrammingProbability and StatisticsCommunication System

This talk is going to illustrate how easy digital signalprocessing is! Don’t be hesitated!


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Introduction to GNU Radio

GNU Radio is a free & open-source software developmenttoolkit that provides signal processing blocks to implementsoftware radios.

Primarily written in Python with performance-criticalsignal processing components written in C++ [1].

C++ classes are wrapped by SWIG [2].

Python can be used to develop rapid prototype for SDR inan 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 byPython” on SlideShare.net

http://goo.gl/mJQmA


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GNU Radio Companion


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Top Block

1 #!/ us r / b in / env python2 from PyQt4 import Qt3 # Other impor t s a r e h i dden4 c l a s s t op b l o ck ( gr . top b l ock , 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 a r e h i dden he re7 s e l f . s amp ra te = samp ra te = 160008 # q t g u i s i n k s t u f f h i dden9 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 = ana log . s i g s o u r11 samp rate , ana l og .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) )1617 i f name == ’ ma i n ’ :18 tb = top b l o ck ( )19 tb . s t a r t ( )20 tb . show ( )21 tb . s top ( )


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Adding a Simple Moving Average Filter

1 #!/ us r / b in / env python2 from gnurad i o import f i l t e r # Add t h i s l i n e i n t o t op b l o ck . p3 # Other impor t s a r e h i dden4 c l a s s t op b l o ck ( gr . top b l ock , 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 a r e h i dden he re7 s e l f . s amp ra te = samp ra te = 441008 # q t g u i s i n k s t u f f h i dden9 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

1011 s e l f . a n a l o g s i g s o u r c e x 1 = ana log . s i g s o u r12 # ==============================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) )2122 # ==============================23 #s e l f . connect ( ( s e l f . a ud i o s ou r c e 0 , 0) ,


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What Is This Filter?!

self.flt = filter.fir filter fff(1, (0.25, 0.25, 0.25, 0.25) )

FIR filter blockInput: FloatOutput: FloatCoefficients: 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 inputsample, and so on...

y[n]: current output sample

It’s just adding/multiplying numbers together, right?Pretty easy, huh?


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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].


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Digital Frequency: Highest

0 1 2 3 4 5 6 7 8 9 10-2

-1

0

1

2

b

b

b

b

b

b

b

b

b

b

b

Figure : π in [0, π], or 1 in [0, 1]


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Digital Frequency: Lowest or DC

0 1 2 3 4 5 6 7 8 9 10-2

-1

0

1

2

b b b b b b b b b b b

Figure : 0


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Digital Frequency: Middle

0 1 2 3 4 5 6 7 8 9 10-2

-1

0

1

2

b

b

b

b

b

b

b

b

b

b

b

Figure : π/2 in [0, π], or 0.5 in [0, 1]


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How to Analyze This Filter?

Back-of-the-Envelope Method

Do fast calculation in the back of the envelopeHandy to get a feel of this filter’s frequency response

Discrete Fourier Transform (DFT)

All transformations are giving us different perspectivesDFT gives us frequency response of a filter

z Transform

Gives us more than just frequency responseAlso give us more thorough information, such as stability,etc.


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Is the filter low pass filter, high pass filter, or?


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Let’s input these coefficients into Octave to tell us...


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What if your Octave is not installed, like most ofattendees here...


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Let’s use back-of-the-envelope method


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Let’s use back-of-the-envelope method

Remember the filter time domain equation isy [n] = (x [n] + x [n − 1] + x [n − 2] + x [n − 3])/4


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Back-of-the-Envelope: Highest

0 1 2 3 4 5 6 7 8 9 10-1

0

1 b

b

b

b

b

b

b

b

b

b

b

0 1 2 3 4 5 6 7 8 9 10-1

0

1


Figure : π in [0, π], or 1 in [0, 1]


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Back-of-the-Envelope: Middle

0 1 2 3 4 5 6 7 8 9 10-1

0

1 b

b

b

b

b

b

b

b

b

b

b

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]


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Back-of-the-Envelope: Lowest or DC

0 1 2 3 4 5 6 7 8 9 10-1

0

1 b b b b b b b b b b b

0 1 2 3 4 5 6 7 8 9 10-1

0

1 b b b b b b b b b b b


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Back-of-the-Envelope: Frequency Response

0 10

1 b

b b


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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


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Transforming Time Domain Equations into

z-Domain

y [n] = x [n]+x [n−1]+x [n−2]+x [n−3]4


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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 youwill get...

x [n − k ]− > X [z]× z−k

y [n]− > Y [z]


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z-Domain

y [n] = x [n]+x [n−1]+x [n−2]+x [n−3]4


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


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z-Domain

y [n] = x [n]+x [n−1]+x [n−2]+x [n−3]4


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 ]


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z-Domain

y [n] = x [n]+x [n−1]+x [n−2]+x [n−3]4


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 ofB [z ] = 1 + z−1 + z−2 + z−3 = 0 (There are three zeros atz=1j, z=-1, and z=-1j)

Poles are values to make |H[z ]| = ∞ and are roots ofA[z ] = 0 (There isn’t any pole for this filter)


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Visualization of equations: z Plane


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Visualization of z Plane 1/3

“Logic will get you from A to Z (Plane); imaginationwill get you everywhere.” – Albert Einstein


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Imagine...

Zeros drag surface to groundPoles bring surface up in the sky


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−2−1.5

−1−0.5

00.5

11.5

2

−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

−30

−20

−10

0

10

20

30


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z Transform and Frequency Response

−2−1.5

−1−0.5

00.5

11.5

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


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Sampling Rate and Real Frequency

[0, 1] −→ [0, 12Fs ]

[0, π] −→ [0, 12Fs ]

Fs is sampling rate

The highest digital frequency we can represent is 1, and itwill be mapped to Fs

2 .Fs2 plays an important role in digital signal processing, andis called Nyquist frequency.

To sample 8kHz analog signals, you need Fs2 ≥ 8 kHz , i.e.

Fs ≥ 16 kHz to represent it. (Nyquist-Shannon samplingtheorem)


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Demo: Seeing Is Believing

No, in this case,


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Demo: Seeing Is Believing

No, in this case,Hearing is believing!


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Concluding Remarks

GNU Radio provides us a signal processing framework inPython.

Digital signal processing seems not easy at first glance.

By visualizing z plane and frequency response, DSPbecomes easier to understand!

Finally, don’t forget Fs ≥ 2 Finterest , where Finterest is thehighest frequency for signal you’re interested in.

With these visualization techniques, you can usegr filter design tool in GNU Radio to design filter withoutanalyzing it.


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Q & A


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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 evaluationand future directions,” in Telesystems Conference, 1992.NTC-92., National, 1992, p. 13.

http://gnuradio.org/redmine/projects/gnuradio/wiki

http://swig.org

Technology

Introduction to Digital Signal Processing Using GNU Radio