Introduction In this exercise, you will program in the Texas Instruments TMS320C55X DSP assembly language to create FIR filters. Begin by studying the assembly code for the basic FIR filter filtercode.asm.

filtercode.asm

The program filtercode.asm applies a FIR filter to the signal from input channel 1 and sends the resulting output to output channel 1. It also sends the original signal to output channel 2. First, create a work directory on your network drive for the files in this exercise and copy the filter folder from c:\ece609\55x\filter to your work directory. Then, use MATLAB to generate two 20-tap FIR filters. The first filter should pass signals from 4 kHz to 8 kHz; the second filter should pass from 8 kHz to 12 kHz. For both filters, allow a 1 kHz transition band on each edge of the filter passband. To create these filters, first convert these band edges to digital frequencies based on the 48 kHz sample rate of the system, then use the MATLAB Parks-McClellan equiripple design command firpm to generate this filter; you can type help firpm for more information. Use the save_coef command to save each of these filters into different files. (Make sure you reverse the vectors of filter coefficients before you save them.) Also save your filters in MATLAB, because you will need them later to generate test vectors. This can be done using the MATLAB save command. Once this is done, use the freqz command to plot the frequency response of each filter.

Part 1: Single-Channel FIR Filter For now, you will implement only the filter with a 4 kHz to 8 kHz passband. Edit filtercode.asm to use the coefficients for this filter by making three changes. First, the length of the FIR filter for this exercise is 20, not 8. Therefore, you need to change FIR_len1 to 20. FIR_len1 is set using the .set assembler directive, which assigns a number to a symbolic name. Second, you will need to ensure that the .copy directive brings in the correct coefficients. Change the filename to point to the file that contains the coefficients for your first filter. Third, you will need to modify the .align and .space directives appropriately. The TI TMS320C55x DSP requires that circular buffers, which are used for the FIR filter coefficient and state buffers, be aligned so that they begin at an address that is a multiple of a power of two greater than the length of the buffer. Since you are using a 20-tap filter (which uses 20-element state and coefficient buffers), the next greater power of two is 32. Therefore, you will need to align both the state and coefficient buffers to an address that is a multiple of 32. (16-element buffers would also require alignment to a multiple of 32.) This is done with the .align command. In addition, memory must be reserved for the state buffer. This is done using the .space directive, which takes as its input the number of bits of space to allocate. Therefore, to allocate 20 words of storage, use the directive .space 16*20 as shown below:

Assemble your code, load the output file, and run. Ensure that the filter implements the correct frequency response. After you have verified that this code works properly, proceed to the next step.

Part 2: Dual-Channel FIR Filters First, make a copy of your modified filtercode.asm file from Part 1. Work from this copy; do not modify your working filter from the previous part. You will use that code again later. Next, modify your code so that in addition to sending the output of your first filter (with a 4 kHz to 8 kHz passband) to output channel 1 and the unfiltered input to output channel 2, it sends the output of your second filter (with a 8 kHz to 12 kHz passband) to output channel 3. To do this, you will need to use the .align and .copy directives to load the second set of coefficients into data memory. You will also need to add instructions to initialize a pointer to the second set of coefficients and to perform the calculations for the second filter. Extra Credit Problem Two extra credit points will be awarded to you and your partner if you can implement the dual-channel system without using the auxiliary registers AR4 and AR5? Why is this more difficult? Renaming AR4 and AR5 using the .asg directive does not count! Using the techniques introduced in DSP Development Environment: Introductory Exercise for TI TMS320C55x, generate an appropriate test vector and expected outputs in MATLAB. Then, using the test-vector core file also introduced in DSP Development Environment: Introductory Exercise for TI TMS320C55x, find the system's output given this test vector. In MATLAB, plot the expected and actual outputs of the both filters and the difference between the expected and actual outputs. Why is the output from the DSP system not exactly the same as the output from MATLAB?

Part 3: Alternative Implementation for Symmetric FIR Filters An alternative method of implementing symmetric FIR filters uses the firsadd instruction. Recall that the impulse response of a linear phase FIR filters exhibits a symmetry about the midpoint. The symmetry can be exploited to reduce by 50 percent the number of multiplications per output sample. Modify your code from Part 1 to implement a single-channel filter with a 4 kHz to 8 kHz passband using the firsadd. The modication of your code from Part 1 for use with the firsadd instruction requires the states be broken up into two separate circular buffers. Refer to the firsadd instruction on page 5-152 in the Mnemonic Instruction Set manual.

Because states and coefficients are now treated differently than in your previous FIR implementation, you will need to modify the pointer initializations to

Two additional changes must be made before the code will compile successfully. Read the comments carefully and understand how the firsadd instruction works to make the necessary changes. Hints: check the accumulator usage (AC0, AC1, AC2) and determine what value should be sent to the output. Use the test-vector core file to find the output of this system given the same test vector you used to test the two-filter system. Compare the output of this code against the output of the same filter implemented using the mac instruction. Are the results the same? Why or why not? Ensure that the filtered output is sent to output channel 1, and that the unmodified output is still sent to output channel 2.

Student Evaluation The evaluation for Lab 1 is broken down as follows: 6 points: Prelab (must be ready to show the TA at the beginning of the lab period) 6 points: Working code: you must demonstrate that your code works using input from function generator and that it works using input from appropriate test vectors. Have an .asm file ready to demonstrate each of your three filters: single channel 20-tap; two channel system; single channel symmetric filter using firsadd. 3 points: Written quiz score: complete the short one-page quiz distributed by the TA. 2 extra credit points: As described above. The written quiz may cover signal processing material relating to FIR filters, including, but not limited to, the delay through FIR filters, generalized linear phase, and the differences between ideal FIR filters and realizable FIR filters. You may also be asked questions about digital sampling theory, including, but not limited to, the Nyquist sampling theorem and the relationship between the analog frequency spectrum and the digital frequency spectrum of a continuous-time signal that has been sampled. The written quiz may cover the code that you have written during the lab. You are expected to understand, in detail, all of the code in the files you have worked on, even if your partner or a TA wrote it. (You are not expected to understand the core file in detail). The quiz may ask you to explain various lines of code as part of the quiz. Other possible topics include: 2's complement fractional arithmetic, circular buffers, alignment, and the mechanics of either of the two FIR filter implementations. Your version of the quiz will be randomly selected from among several versions of the Lab 1 quiz.Use the TI documentation, specifically the Mnemonic Instruction Set manual. Also, feel free to ask the TAs to help explain the code that you have been given.