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0 - 1 © 2010 Texas Instruments Inc Practical Audio Experiments using the TMS320C5505 USB Stick “Sine Waves” Texas Instruments University Programme Teaching Materials

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Chapter 4 - Slide 2 © 2010 Texas Instruments Inc Sine Waves

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Chapter 4 - Slide 3 © 2010 Texas Instruments Inc Introduction DSP can be used to generate sine waves Sine waves can be used in audio to: –Generate musical tones and complex waveforms –Generate tones for touch phones (DTMF) –Modulate audio signals (alien voices) –Control audio effects (chorus/phasing/flanging).

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Chapter 4 - Slide 4 © 2010 Texas Instruments Inc Objectives To generate sine waves from 10Hz to 16000Hz. To introduce the Texas Instruments library of DSP functions DSPLIB.

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Chapter 4 - Slide 5 © 2010 Texas Instruments Inc Knowledge Required Some understanding of fixed-point and floating-point numbers is required. Details of two useful articles from are given in the References Section.www.cnx.org

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Chapter 4 - Slide 6 © 2010 Texas Instruments Inc Sine Wave and FFT A sine wave is a pure tone. It only contains one frequency:

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Chapter 4 - Slide 7 © 2010 Texas Instruments Inc Complex Waveform and FFT A complex waveform has several frequency components:

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Chapter 4 - Slide 8 © 2010 Texas Instruments Inc Generating Sine Waves There are 3 main ways to generate sine waves: –Look-up Table –Recursive Equation –Taylor Expansion.

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Chapter 4 - Slide 9 © 2010 Texas Instruments Inc Look-up Table This is the simplest way to generate a sine wave. Put known values into a table: Values are read using an offset e.g. sinetable[3];

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Chapter 4 - Slide 10 © 2010 Texas Instruments Inc About Look-up Tables Advantages: –Fast to implement –Values are always accurate Disadvantages: –Can only be used for exact divisions of sampling frequency.

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Chapter 4 - Slide 11 © 2010 Texas Instruments Inc Recursive Equation Uses the following mathematical equation: The next sine output is derived from the previous values We shall look at this in more detail in Chapter 7, Infinite Impulse Response (IIR) filters.

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Chapter 4 - Slide 12 © 2010 Texas Instruments Inc Taylor Series A sine function can be implemented as a geometric series: where x is the input in radians. This method is used by the Texas Instruments DSP Library DSPLIB.

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Chapter 4 - Slide 13 © 2010 Texas Instruments Inc About Taylor Series Advantages: –Can generate any frequency Disadvantages: –Not as accurate as look-up table because there are rounding errors –Care needs to be taken to avoid overflow during multiplications.

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Chapter 4 - Slide 14 © 2010 Texas Instruments Inc C Code Implementation

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Chapter 4 - Slide 15 © 2010 Texas Instruments Inc Sine Function in C As standard, C comes with the function sin(x) in “ math.h ”. This uses floating-point maths. It is not efficient for real-time applications. A better way is to use DSPLIB.

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Chapter 4 - Slide 16 © 2010 Texas Instruments Inc Introducing DSPLIB

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Chapter 4 - Slide 17 © 2010 Texas Instruments Inc About DSPLIB Texas Instruments provides a library containing a whole range of useful functions used in DSP: Fast Fourier Transform (FFT) Sine, Cosine and Tangent Exponentials and logs. Each function is optimised for the processor, in this case the TMS320C55xx.

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Chapter 4 - Slide 18 © 2010 Texas Instruments Inc DSP LIB Headers When using DSPLIB, you need to add the two following #include statements to your code:

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Chapter 4 - Slide 19 © 2010 Texas Instruments Inc DSPLIB Library The library file 55xdsph.lib must be present in the build. DSPLIB for TMS320C5505 USB Stick.

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Chapter 4 - Slide 20 © 2010 Texas Instruments Inc DSPLIB Sine Function Is written in TMS320C55xx assembly language. The function takes 3 parameters: –Parameter 1. Address of location containing the frequency –Parameter 2. Address of location to store calculated sine –Parameter 3. Always 1.

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Chapter 4 - Slide 21 © 2010 Texas Instruments Inc Scaling the sine() function Need to convert frequency in Hz to value for sine () function. Use a scaling factor of

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Chapter 4 - Slide 22 © 2010 Texas Instruments Inc Magic Numbers Where did the magic number come from? The TMS320C5505 is a 16-bit fixed-point processor that uses: – to represent – –32767 to represent –1.000 Here represents decimal. We shall now look at how this magic number was obtained.

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Chapter 4 - Slide 23 © 2010 Texas Instruments Inc DSPLIB sine() function The DSPLIB function sine() calculates the sine of an angle. The input to the function is a fixed-point number that represents an angle: – 0 => 0 o – => 90 o – => 180 o – 2 * => 360 o

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Chapter 4 - Slide 24 © 2010 Texas Instruments Inc Sine 90 o To generate a waveform using 4 values we use: –sin 0 o –sin 90 o –sin 180 o –sin 270 o. If Fs = Hz, the frequency generated will be: –48000/4 = Hz.

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Chapter 4 - Slide 25 © 2010 Texas Instruments Inc Sine 45 o To generate a waveform using 8 value use: –sin 0 o –sin 45 o –sin 90 o –sin 135 o etc. If Fs = Hz, the frequency generated will be: –48000/8 = 6000 Hz.

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Chapter 4 - Slide 26 © 2010 Texas Instruments Inc Generate 1 Hz Sine Wave To generate a 1 Hz sine wave we work backwards: –48000/value = 1 Hz –value = 1/48000 There corresponding angle will be: – 360 o /48000 = o To implement a 1 Hz sine wave we use: 0 o, o, o, o, o etc.

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Chapter 4 - Slide 27 © 2010 Texas Instruments Inc Fixed-Point Implementation For 1 Hz we require each angle to be multiples of: – 360 o /48000 = o For 1 Hz using fixed-point using DSPLIB we require: –2 * / 48000

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Chapter 4 - Slide 28 © 2010 Texas Instruments Inc Scaling Factor We can use the value for 1 Hz as a scaling factor to calculate other frequencies: SCALING FACTOR = 360 o /48000 = o For 2 Hz: – 2 * SCALING FACTOR = 2 * 360 o /48000 = o For 10 Hz: – 10 * SCALING FACTOR = 10 * 360 o /48000 = o

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Chapter 4 - Slide 29 © 2010 Texas Instruments Inc Scaling Factor Calculation The fixed-point scaling factor is: In fixed-point maths, to divide by is awkward However, to divide by is easy because = 2 15 Example: To divide 3FFFFFFFh by 32768d shift right 15 places. Result = 7FFFh In C code, divide by is implemented as >> 15.

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Chapter 4 - Slide 30 © 2010 Texas Instruments Inc Scaling Factor Calculation The fixed-point scaling factor is derived as follows: The divide by is implemented as >>15 Here 2/32768 is implemented as >>14. The scaling factor used is therefore

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Chapter 4 - Slide 31 © 2010 Texas Instruments Inc Introduction to Laboratory

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Chapter 4 - Slide 32 © 2010 Texas Instruments Inc USB Stick Setup TMS320C5505 USB to PC Headphones USB Stick

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Chapter 4 - Slide 33 © 2010 Texas Instruments Inc Installing the Application Use the code given in Application 4, Sine Waves Follow the steps previously given in Chapter 1 to set up the new project.

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Chapter 4 - Slide 34 © 2010 Texas Instruments Inc Create New Project

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Chapter 4 - Slide 35 © 2010 Texas Instruments Inc Files Used in Project

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Chapter 4 - Slide 36 © 2010 Texas Instruments Inc Console Sampling frequency and Gain are shown in the Console window.

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Chapter 4 - Slide 37 © 2010 Texas Instruments Inc Experiments

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Chapter 4 - Slide 38 © 2010 Texas Instruments Inc Change the Headphone Volume Reduce gain from to 5000.

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Chapter 4 - Slide 39 © 2010 Texas Instruments Inc Change the Frequencies Rather than 200 Hz and 500 Hz, use two musical notes: A = 440 Hz C = 523 Hz

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Chapter 4 - Slide 40 © 2010 Texas Instruments Inc Change the Sampling Frequency Change the sampling frequency to Hz. The output frequencies will have changed. You will need to alter the scaling factor in sinewaves.c

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Chapter 4 - Slide 41 © 2010 Texas Instruments Inc Questions What are 3 ways to generate sine waves? Which method is best suited to the TMS320C5505 USB Stick? What are 3 applications of sine waves?

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Chapter 4 - Slide 42 © 2010 Texas Instruments Inc References TMS320C55xx DSP Library Programmer’s Reference. SPRU 422. Digital Signal Processing with C and the TMS320C30 by Rulph Chassaing. ISBN Fixed Point Arithmetic and Format (m10919) by Hyeokho Choi.www.cnx.org Fixed Point Arithmetic (m11054) by Hyeokho Choi.www.cnx.org

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