The aim of this experiment is to

- become familiar with the TMS320C6748 hardware and software tools by outputting sinusoidal signals from the C6748 board and
- explore the design tradeoffs in signal quality vs. implementation complexity in computing values of sinusoidal signals.

Sinusoidal waveforms will be output by using two different methods:

- Interrupts
- Direct Memory Access

- OMAP-L138 Low-Cost Developer Kit (LCDK)
- Two BNC - stereo pin (DSP) cables

*Real-Time Digital Signal Processing from MATLAB to C with the TMS320C6x DSPs*(Jan. 2012) by Thad B. Welch, Cameron H. G. Wright and Michael G. Morrow,- Chapters 5 and 6 (except Section 5.5 Pseudonoise Sequences)
- Appendices A, B, C and D

*Software Receiver Design*by C. Richard Johnson, Jr., William A. Sethares and Andrew Klein- Sections 2.1-2.5
- Sections 3.1, 3.2, 3.4 and 3.6

- Course reader
- Lecture 1 slides on Generating Sinusoidal Signals
- Sampling the Unit Step handout
- Discrete-Time Periodicity handout
- Piano key frequencies go from 27.5 Hz to 4186 Hz.

- Lecture 2 slides on Introduction to Digital Signal Processors

- Lecture 1 slides on Generating Sinusoidal Signals

**Downloads**

Recitation slides Part 1 and Part 2 by Mr. Jinseok Choi, Mr. Sam Kanawati, Ms. Debarati Kundu and Mr. Shreyas Rao, The University of Texas at Austin

Lab instructions Part 1 and Part 2 by Mr. Jinseok Choi, Mr. Sam Kanawati, Ms. Debarati Kundu and Mr. Shreyas Rao, The University of Texas at Austin

Updated EDMA files as a zip archive (see 7-zip for a free zip program) for week 2 of lab

Design tradeoffs in computing sinusoidal signals by Prof. Brian L. Evans, The University of Texas at Austin (see slides 1-8 to 1-15)

LabVIEW transmitter demonstration by Dr. Zukang Shen to show how labs 1-6 fit together

Overview Slides by Prof. Steven Tretter, University of Maryland (from Jan. 2008 lab manual)

C code for casting float to short int by Prof. Brian L. Evans, The University of Texas at Austin

**Debugging and Troubleshooting Tips**

When connecting the USB cable from the PC to the C6748 DSP board, please use the USB port on the opposite side of the board from the power connector.

Here are troubleshooting tips for Code Composer Studio v5.

Here are troubleshooting tips if you see an incorrect sinusoid on the oscilloscope:

- Be sure that the output impedance of the signal generator is set to be high-Z.
- Check the implementation of the difference equation or lookup table method. One can use the printf function to print out the values of samples they generated so they can check the correctness.
- Be sure that the sampling rate is set properly in both the Interrupt Service Routine (ISR) and the configuration file. The sampling frequency specified in isr file is only used for computation.
- Check to see if interrupt is working. Even though the interrupt is not working, the oscilloscope could still show sinusoidal-like noise. This can be easily checked by measuring the magnitude of the waveform, and knowing that noise should have a very small magnitude.
- Be sure that in the generatetable function in the EDMA starter code, you have cast floating point calculations to Uint32. This is needed because the samples will be received by the McASP, which processes integers.
- In the second week of lab 2, students must not reset the board between the first part (talkthrough using EDMA) and the second part (sinusoidal generation using EDMA).
- Be sure to declare the array holding the lookup table as a global variable.

**Lab Report**

Please turn in one lab report per two-person team. Include the following sections in the Lab #2 report and in future reports:

**Introduction**: Briefly explain the theory and algorithms behind the programs that you wrote. The recitation slides might help you in writing this section.**Methods**: Describe the steps you took to implement the algorithms in*your own words*. This section should be brief (1-2 paragraphs).**Results**: Present the results you obtain for each task on the assignment sheet. This section should include illustrative oscilloscope screenshots of the DSP algorithms in action. Also include any code that you wrote or modified. Please do not include all of the boilerplate code from the textbook.**Discussion**: In this section, discuss the takeaway from each lab. You can mention any intuition that you developed. Also mention any problems that you faced and how you rectified them.**Assignment questions**: Please answer the questions asked in the assignment.

**Discrete-Time Resonator Implementation**

The Welch, Wright and Morrow book has C code in Section 5.4.4 to generate a sine wave using a discrete-time resonator.

The difference equation to generate sin(w_{0} n) u(n) is

y[n] = sin(w_{0}) x[n-1] + 2 cos(w_{0}) y[n-1] - y[n-2]

and the input signal x[n] is the discrete-time impulse.

At n = 0, we have x[n] = 1, x[n-1] = 0, y[n-1] = 0, y[n-2] = 0, which gives y[n] = 0)

At n = 1, we have x[n] = 0, x[n-1] = 1, y[n-1] = 0, y[n-2] = 0, which gives y[n] = sin(w_{0})

At n = 2; we have x[n] = 0, x[n-1] = 0, y[n-1] = sin(w_{0}), y[n-2] = 0, which gives y[n] = 2 cos(w_{0}) sin(w_{0}) = sin(2 w_{0}) when using the following trigonometric identity:

sin(x) cos(y) = 1/2 ( sin(x-y) + sin(x+y) )

**Issue #1**.
The code in Section 5.4.4 starts the difference equation at n = 2.
As a result, the code in the book will generate a shifted version
of sin(w_{0} n) u(n).

When w_{0} = pi/2, a shift in the sine wave by two samples will generate a negated sine wave:

sin(pi/2 (n - 2)) = sin((pi/2) n - pi) = -sin((pi/2) n)

When f_{0} = 2 kHz and f_{s} = 8 kHz, we have
w_{0} = 2 pi f_{0} / f_{s} = pi/2, and hence,
the shifted sine wave generated by the code in Welch, Wright and
Morrow looks like -sin(w_{0} n).

**Issue #2**.
The code in the book is inefficient and difficult to follow.
To improve efficiency and clarity, one could change

float y[3] = {0 , 1 , 0} ; .... CodecDataOut.Channel[LEFT] = A * sinf(theta) * y[0]; // scaleto

float y[3] = {0 , sinf(theta) , 0} ; .... CodecDataOut.Channel[LEFT] = A * y [0]; // scaleAnd, for additional efficiency, one could replace

`sinf(theta)`

and `cosf(theta)`

with constants because `theta`

is a constant.
There is no reason to call the sinf and cosf functions because the values can be computed offline for a constant theta. And, the whole point of using the difference equation in the first place is to avoid calling a math routine.

**Useful references**

Texas Instruments TMS320C6748 processor, board, and tools

- General overview of TMS320C6748
- Audio Codecs
- Code Composer Studio 5
- C6000 Optimizing C Compiler 7.4
- C6000 Programmer's Guide
- C674x DSP CPU and Instruction Set Reference Guide
- C6748 Evaluation Module Board