ECE4703 Mid-term Exam B-16. Name: Box #:

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1 ECE4703 Mid-term Exam B-16 Name: Box #: The exam is worth 100 points with points per problem indicated. Please read through the entire exam in order to properly budget your time. Write neatly and show ALL your work. Clearly indicate your final answer by boxing or circling it. Attach your cheat sheet to your exam paper. Good luck! Remeber: NOWORK = NO POINTS! 1. (20 pts) The C6713 DSK is being used as a real-time signal generator. Below is the main code and serial port interrupt service routine. Answer the following questions assuming the indicated input signals are applied to the AIC23 Line-in input. Note: A page of trigonometric identities is attached at the end of the exam. void main() DSK6713_init(); hcodec = DSK6713_AIC23_openCodec(0, &config); MCBSP_FSETS(SPCR1, RINTM, FRM); MCBSP_FSETS(SPCR1, XINTM, FRM); MCBSP_FSETS(RCR1, RWDLEN1, 32BIT); MCBSP_FSETS(XCR1, XWDLEN1, 32BIT); DSK6713_AIC23_setFreq(hCodec, DSK6713_AIC23_FREQ_8KHZ); IRQ_globalDisable(); IRQ_nmiEnable(); IRQ_map(IRQ_EVT_RINT1,15); IRQ_enable(IRQ_EVT_RINT1); IRQ_globalEnable(); } while(1) } interrupt void serialportrcvisr() union Uint32 both; short ch[2];} linein,lineout; float left = 0.0, right = 0.0; linein.both = MCBSP_read(DSK6713_AIC23_DATAHANDLE); right = (float)(linein.ch[0])/normalize; left = (float)(linein.ch[1])/normalize; right = 0.5*(right + right); left = left * right; } lineout.ch[0] = (short)(right * NORMALIZE); lineout.ch[1] = (short)(left * NORMALIZE); MCBSP_write(DSK6713_AIC23_DATAHANDLE, lineout.both);

2 a) What should the scale factor NORMALIZE equal and why is it necessary? What are the maximum possible values for right and left? b) Assume that rr(t) and ll(t) are the signals input on the right and left channels of line-in respectively. rr(t) = 0.8*cos(2 2600t) and ll(t) = 0.8*cos(2 t) Use trigonometric identities to find simplified theoretical expressions for right and left. right = left = c) Assume the AIC23 anti-aliasing filter has the magnitude response shown below. Draw the magnitude spectra of the signals output to line-out of the AIC23. Completely label all amplitudes and frequencies. H(f) Fs = sampling frequency 0 db -80 db 0.8F N 1.2F N F s LEFT RIGHT

3 2. (20 pts) Below are the coefficient generated by fdatool for an IIR filter. const int NL = 5; const float NUM[5] = , , 0, , , }; const int DL = 5; const float DEN[5] = 1, , , , }; a) Draw a completely labeled block diagram of the Direct Form II implementation for the filter coefficients above. Write out the intermediate and output equations for this IIR Direct Form II filter.

4 b) Draw a completely labeled block diagram of the Direct Form II cascade of Second Order Stages implementation for the filter coefficients given below. Write out the intermediate and output equations for a single second order stage. #define MWSPT_NSEC 5 const int NL[MWSPT_NSEC] = 1,3,1,3,1 }; const float NUM[MWSPT_NSEC][3] = , 0, 0 1, , , 0, 0 1, , 1 1, 0, 0 } }; const int DL[MWSPT_NSEC] = 1,3,1,3,1 }; const float DEN[MWSPT_NSEC][3] = 1, 0, 0 1, , , 0, 0 1, , , 0, 0 } };

5 c) Discuss the relative strengths and weaknesses of Direct Form I, Direct Form II and Direct Form II SoS implementations for a given IIR filter.

6 3. (30 pts) For the questions below you are given the following infinite precision FIR filter coefficients. h = [h[0], h[1], h[2], h[3], h[4]] = [ ] a) Suppose you are required to store these filter coefficients in a signed char data type using Q-7 formatting, fill out the following table. Show your work. Orig. Coefficient Value Quantized Value (decimal) Quantized Value (binary) Quantization Error b) Show the fixed point binary (Q-7) calculation for y[0] assuming the 8-bit input sample x[0] = 64 and assuming the x history array was properly initialized to 0. y is also stored in a signed char. Binary y[0] Decimal y[0]

7 c) Your 8-bit fixed point FIR filter implementation will be using Extended Accumulation in an 16-bit signed integer (i.e. a short). Explain how you will have to scale your fixed point math in your implementation. Specifically, what scaling is required to complete your Q-7 multiplication and how will your code implement it? Also, what is the post-scaling required for your final sum in order to map the 16-bit extended precision accumulator variable to the 8-bit output variable, y? How did you arrive at this scale factor and how will you implement it?

8 4. (30 pts) Sperm whales hunt for their favorite prey, benthic squid, during deep foraging dives. During these dives, which can last over 40 min and reach depths of nearly 2 kilometers, the whales produce rhythmic patterns of echolocation clicks. Sperm whales echolocate on squid much like bats echolocate on mosquitos except that they are incredibly loud! Sperm whale clicks can be heard from as much as 10 nautical miles away. Impulsive sperm whale clicks are broad bandwidth signal with most of their enegry in the band from 2 khz to 18 khz. a) Assuming you were using a C6713 DSK with the AIC23 codec to process these signals, what best sampling frequency could you use? Why? b) Your task is to detect the occurrence of these sperm whale foraging clicks. You have decided to sample an ideal sinc function to implement a bandpass filter to try to capture as much of the signal energy in the 2-18kHz band as possible. The impulse response of your filter is exactly 3.4 ms long. Assuming the sampling rate you chose in Part (a), how many coefficients will your sperm whale filter have? Is your m filter an FIR or an IIR filter? How do you know? c) Our TMS320C6713 runs off a 225MHz clock. How many cycles between interrupts from the codec at the sampling frequency from Part (a)?

9 d) Assume that it takes your non-optimized filter code 32 cycles to calculate 1 floating point multiplication followed by 1 floating point add. Can a filter of the length of your bandpass filter, determined in Part (b), run in real-time at the sampling rate from Part (a)? Justify your answer. e) After Lab 4, you've managed to implement a fully optimized filter that can execute 1 floating point multiplication followed by 1 floating point add in just 5 cycles! Your sperm whale filter easily runs in real-time so you have decided to try and create a filter to detect the signal output on the left channel in Problem 1. It turns out that the signals are in Problem 1 pulsed. That is they are on for exactly 132 ms then off for between 5 to 45 seconds. You generate an FIR bandpass filter whose impulse response matches the on portion of the pusled signal. Can a fully optimized version of this bandpass filter run in real-time assuming the sampling frequency from Problem 1? Show all your work.