DSP Laboratory (EELE 4110) Lab#11 Implement FIR filters on TMS320C6711 DSK.

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Islamic University of Gaza Faculty of Engineering Electrical Engineering Department Spring-2011 DSP Laboratory (EELE 4110) Lab#11 Implement FIR filters on TMS320C6711 DSK.

1 Islamic University of Gaza Faculty of Engineering Electrical Engineering Department Spring-2011 DSP Laboratory (EELE 4110) Lab#11 Implement FIR filters on TMS320C6711 DSK. Theoretical Background Filtering is one of the most useful signal processing operations. Digital signal processors are now available to implement digital filters in real time. The TMS320C6x instruction set and architecture makes it well suited for such filtering operations. An analog filter operates on continuous signals and is typically realized with discrete components such as operational amplifiers, resistors, and capacitors. However, a digital filter, such as a finite impulse response (FIR) filter, operates on discrete-time signals and can be implemented with a digital signal processor such as the TMS320C6x. This involves use of an ADC to capture an external input signal, processing the input samples, and sending the resulting output through a DAC. Within the last few years, the cost of digital signal processors has been reduced significantly, which adds to the numerous advantages that digital filters have over their analog counterparts. These include higher reliability, accuracy, and less sensitivity to temperature and aging. Stringent magnitude and phase characteristics can be realized with a digital filter. Filter characteristics such as center frequency, bandwidth, and filter type can readily be modified. A number of tools are available to design and implement within a few minutes an FIR filter in real time using the TMS320C6xbased DSK. The filter design consists of the approximation of a transfer function with a resulting set of coefficients. Different techniques are available for the design of FIR filters, such as a commonly used technique that utilizes the Fourier series, as discussed in later on. General difference equation for any digital system: y n + a 1 y n 1 + a 2 y n a N y n (M 1) = b 0 x n + b 1 x n 1 + b 2 x n b M x n (N 1) M 1 y n = a k y n k k=1 + b k x n k M 1 The impulse response is given by: h n = a k h n k k=1 + b k δ n k

2 M 1 h n = a k h n k k =1 M 1 H z = a k z k H z k=1 + b k δ n k + b k z k Which give a transfer function of a form: k=0 b k z k H z = M a k z k k =1 For FIR Filter, h n = b o, b 1,, b M or H z = b k z k then, h n = b k δ n k = h k δ n k h n = h 0 δ n + h 1 δ n 1 + h 2 δ n h(n 1)δ n (N 1) h n = h k δ n k but, y n = x n h n = x n h k δ n k y n = h k x n δ n k y n = h k k=0 x n k (10.1)

3 FIR IMPLEMENTATION BY TMS320C6711 DSK: Within minutes, an FIR filter can be designed and implemented in real time. Several filter design packages are available for the design of FIR filters. A finite-duration impulse response filter has a system function of the form Hence the impulse response h(k) is H z = h(k)z k (11.1) h n = h(0), h(1),, h(n 1) and the difference equation representation is y n = b o x n + b 1 x n 1 + b 2 x n b x n (N 1) (11.2) y n = h k k=0 x n k (11.3) The FIR filter structures are always stable, and they are relatively simple compared to IIR structures. The difference equation (11.2) is implemented as a tapped delay line since there are no feedback paths. Let M=5 (i.e., a fourth-order FIR filter);then y n = h(0)x n + h(1)x n 1 + h(2)x n 2 + h(3)x n 3 + h(4)x n 4 (11.4) y n = b o x n + b 1 x n 1 + b 2 x n 2 + b 3 x n 3 + b 4 x n 4 The direct form structure is given in figure FIGURE Direct form FIR structure. The convolution equation (11.3) is used to program and implement these filters. We can arrange the impulse response coefficients within a buffer (array) so that the first coefficient, h(0), is at the beginning (first location) of the buffer (lower memory address).the last coefficient, h(n 1), can reside at the end (last location) of the coefficients buffer (higher-memory address).the delay samples are organized in memory so that the newest sample, x(n), is at the beginning of the samples buffer, while the oldest sample, x(n (N 1)), is at the end of the buffer. The coefficients and the samples can be arranged in memory as shown in Table 11.1.

4 Initially All the samples are set to zero. Time n The newest sample, x(n), at time n is acquired from an ADC and stored at the beginning of the sample buffer. The filter s output at time n is computed from the convolution equation (11.4). y n = h(0)x n + h(1)x n 1 + h(2)x n 2 + h(3)x n 3 + h(4)x n 4 The delay samples are then updated, so that x(n k) = x(n + 1 k) can be used to calculate y(n + 1), the output for the next unit of time, or sample period Ts. All the samples are updated except the newest sample. For example, x(n 1) = x(n), and x(n (N 1)) = x(n (N 2)).This updating process has the effect of moving the data (down) in memory (see Table 11.1, associated with time n + 1). Time n + 1 At time n + 1, a new input sample x(n + 1) is acquired and stored at the top of the sample buffer, as shown in Table The output y(n + 1) can now be calculated as y n + 1 = h 0 x n h 1 x n + + h N 1 x n N 2 and y n + 2 = h 0 x n h 1 x n h N 1 x n N 3 TABLE 11.1 Memory Organizations to Illustrate Update of Samples The samples are then updated for the next unit of time. Time n + 2 At time n + 2, a new input sample x(n + 2), is acquired. The output becomes y n + 2 = h 0 x n h 1 x n h N 1 x n N 3. This process continues to calculate the filter s output and updating the delay samples at each unit of time (sample period).

5 Example 11.1: FIR Filter Implementation: Bandstop (FIR) Step(1) Design a BSF using graphical user interface (GUI) filter designer FDATool.The filter s characteristics are shown in figure FIGURE Design BSF(2.7kHz) using FDATool. Export the coefficients of the filter (File Export) to workspace under the variable of name (Num) FIGURE Export the filter coefficients.

6 Step(2) To get the header file " bs2700.cof " we write the m-function getfircof(name,h,y,n) function x=getfircof(name,h,y,n) %x=getfircof('file_name.cof','array_name',filter_coefficient,factor) N=length(y); i=0:n-1; y=y*2^n; y=round(y) fid = fopen(name,'w'); % open/create file fprintf(fid,'#define N %d\n',n); fprintf(fid,'short '); % print array type fprintf(fid,h); % print array name fprintf(fid,'[%d]={',n); % [N]={ fprintf(fid,'%d, ',y(1:n-1)); % print N-1 points fprintf(fid,'%d ',y(n)); % print Nth point fprintf(fid,'};\n'); % print closing bracket fclose(fid); % close file Note: getfircof(name,h,y,n) FIGURE getfircof function name: is the name of the coefficient file,e.g: 'bs2700.cof' which will be included in the C program. h: is the name of the coefficient array inside the *.cof file. y: is the name of the filter coefficient that we export from FDATool. n: is a factor to make scaling for the filter, for n=15,y=round(y*2^15). getfircof('bs2700.cof','h',num,15) After we evaluate the above line, then we get (bs2700.cof ) the FIR coefficients file. This coefficient file, which contains 89 coefficients (filter order=88), represents an FIR bandstop (notch) filter centered at 2700Hz. #define N 89 short h[89]={-14, 23, -9, -6, 0, 8, 16, -58, 50, 44, -147, 119, 67, -245, 200, 72, -312, 257, 53, -299, 239, 20, -165, 88, 0, 105, -236, 33, 490, - 740, 158, 933, 1380, 392, 1348, -2070, 724, 1650, , 1104, 1776, , 1458, 1704, 29494, 1704, 1458, -3122, 1776, 1104, -2690, 1650, 724, -2070, 1348, 392, -1380, 933, 158, -740, 490, 33, -236, 105, 0, 88, -165, 20, 239, -299, 53, 257, -312, 72, 200, -245, 67, 119, -147, 44, 50, -58, 16, 8, 0, -6, -9, 23, - 14 }; FIGURE Coefficients for a FIR bandstop filter (bs2700.cof).

7 Step(3) Write the C source program FIR.c (figure 11.6), which implements an FIR filter. It is a generic FIR program, since the coefficient file included, bs2700.cof,specifies the filter s characteristics. //Fir.c FIR filter. Include coefficient file with length N #include "bs2700.cof" //coefficient file 2700Hz int yn = 0; //initialize filter s output short dly[n]; //delay samples interrupt void c_int11(){ //ISR short i; dly[0] = input_sample(); //newest top of buffer yn = 0; //initialize filter s output for (i = 0; i< N; i++) yn += (h[i] * dly[i]); //y(n) += h(i)* x(n-i) for (i = N-1; i > 0; i--) dly[i] = dly[i-1]; output_sample(yn >> 15); return; } void main(){ comm_intr(); while(1); } bottom of buffer //update delays with data move //scale output filter //init DSK, codec, McBSP //infinite loop FIGURE Generic FIR program (FIR.c). A buffer dly[n] is created for the delay samples. The newest input sample, x(n), is acquired through dly[0] and stored at the beginning of the buffer. The coefficients are stored in another buffer, h[n], with h[0] at the beginning of the coefficients buffer. The samples and coefficients are then arranged in their respective buffer, as shown in Table Two for loops are used within the interrupt service routine The first loop implements the convolution equation with N coefficients and N delay samples, for a specific time n. At time n the output is y(n) = h(0)x(n) + h(1)x(n 1) + + h(n 1)x(n (N 1)). The second loop The delay samples are then updated within the second loop to be used for calculating y n at time n + 1, or y n + 1. The newly acquired input sample always resides at the beginning of the samples buffer. The memory location that contained the sample x(n) now contains the newly acquired sample x(n + 1). The output y(n + 1) at time n + 1 is then calculated. This scheme uses a data move to update the delay samples.

8 Shift operator >> Shift right, << Shift left For example: y dec y bin y>>1 (Shift right) bin y>> y dec y bin y>>2 (Shift right) bin y>> Comment, shift the sequence y to right by n samples is equal to divided y by 2^n y >> n = y and y << n = y 2n 2n Other example: y dec y>> = = 1799 So yn >> 15 used to divided yn by 2^15. Step(4) Create a new project on CCS,add all support files and the Fir.c source file. Build your project and load the.out file. Now we are ready to test the functionality of the designed filter. Step(5) Using MATLAB, to generate different sine signals with different frequencies fo=1000; % choose different freq fs=8000; Ts=1/fs; t=(0:9999)/fs; % t=nts x=sin(2*pi*fo*t) ; sound(x) wavwrite(x,fs,'1khz.wav'); %Export the tone to wave file FIGURE generate sine wave

9 Use the program in figure 11.7 to generate sine tones with frequencies shown in figure 11.8 FIGURE sine tones Step(6) Connect the devices as shown in figure 11.9 FIGURE Components connection Step(7) Run the CCS project and test the response of the filter to the sine waves shown in figure 11.8 Comment:

Example 11.2: Effects on Voice Using Three FIR Lowpass Filters (FIR3LP) Figure 11.14 shows a listing of the program FIR3lp.

10 Example 11.2: Effects on Voice Using Three FIR Lowpass Filters (FIR3LP) Figure shows a listing of the program FIR3lp.c, which implements three FIR lowpass filters with cutoff frequencies at 600, 1000, and 1500Hz, respectively. The three lowpass filters were designed with MATLAB s FDATOOL to yield the corresponding three sets of coefficients. This example expands on the generic FIR program in Example The coefficients file LP600.cof represents an 81-coefficient FIR lowpass filter with a 600Hz cutoff frequency, using the Kaiser window function(figure 11.11). FIGURE Design LPF using FDATool. getfircof('lp600.cof','hlp600',num,15) Repeat for Fc=1000Hz and 1500Hz getfircof('lp1000.cof','hlp1000',num,15) getfircof('lp1500.cof','hlp1500',num,15) the other two coefficients file are shown in figure (11.12) and (11.13)

11 //lp600.cof FIR lowpass filter coefficients using Kaizer window #define N 81 short hlp600[81]={0, -13, -28, -41, -47, -41, -21, 12, 52, 89, 114, 114, 84, 25, -55, -141, -211, -242, -220, -136, 0, 166, 326, 439, 467, 384, 186, -104, -437, -742, -937, -948, -717, -222, 518, 1439, 2444, 3410, 4212, 4742, 4928, 4742, 4212, 3410, 2444, 1439, 518, - 222, -717, -948, -937, -742, -437, -104, 186, 384, 467, 439, 326, 166, 0, -136, -220, -242, -211, -141, -55, 25, 84, 114, 114, 89, 52, 12, -21, -41, -47, -41, -28, -13, 0 }; FIGURE Coefficient file for a FIR lowpass filter with 600-Hz cutoff frequency (lp600.cof). //lp1000.cof FIR lowpass filter coefficients using Kaizer window #define N 81 short hlp1000[81]={0, -20, -35, -29, 0, 41, 67, 54, 0, -71, -113, - 90, 0, 114, 179, 141, 0, -173, -271, -212, 0, 258, 403, 314, 0, - 383, -601, -472, 0, 588, 937, 751, 0, -1001, -1675, -1438, 0, 2439, 5201, 7379, 8205, 7379, 5201, 2439, 0, -1438, -1675, -1001, 0, 751, 937, 588, 0, -472, -601, -383, 0, 314, 403, 258, 0, -212, -271, - 173, 0, 141, 179, 114, 0, -90, -113, -71, 0, 54, 67, 41, 0, -29, - 35, -20, 0 }; FIGURE Coefficient file for a FIR lowpass filter with 1000-Hz cutoff frequency (lp1000.cof). //lp1500.cof FIR lowpass filter coefficients using Kaizer window #define N 81 short hlp1500[81]={0, 26, 25, -16, -49, -22, 47, 71, 0, -92, -80, 49, 143, 61, -126, -184, 0, 226, 191, -114, -330, -139, 284, 409, 0, -500, -424, 255, 741, 317, -660, -979, 0, 1304, 1181, -776, , -1316, 3668, 9616, 12275, 9616, 3668, -1316, -2560, -776, 1181, 1304, 0, -979, -660, 317, 741, 255, -424, -500, 0, 409, 284, -139, -330, -114, 191, 226, 0, -184, -126, 61, 143, 49, -80, -92, 0, 71, 47, -22, -49, -16, 25, 26, 0 }; FIGURE Coefficient file for a FIR lowpass filter with 1500-Hz cutoff frequency (lp1500.cof). LP_number selects the desired lowpass filter to be implemented. For example, if LP_number is set to 1, h[1][i] is equal to hlp600[i] (within the for loop in the function main), which is the address of the first set of coefficients. LP_number can be changed to 2 or 3 to implement the or 1500-Hz lowpass filter, respectively. With the GEL file FIR3LP.gel (Figure 11.15), one can vary LP_number from 1 to 3 and slide through the three different filters.

12 //FIR3LP.c FIR using three lowpass coefficients with three different BW #include "lp600.cof" //coeff file 600 Hz #include "lp1000.cof" //coeff file 1500 Hz #include "lp1500.cof" //coeff file 3000 Hz short LP_number = 1; //start with 1st LP filter int yn = 0; //initialize filter s output short dly[n]; //delay samples short h[3][n]; //filter characteristics 3xN interrupt void c_int11(){ //ISR short i; dly[0] = input_sample(); //newest top of buffer yn = 0; //initialize filter output for (i = 0; i< N; i++) yn +=(h[lp_number][i]*dly[i]); //y(n) += h(lp#,i)*x(n-i) for (i = N-1; i > 0; i--) bottom of buffer dly[i] = dly[i-1]; //update delays with data move output_sample(yn >> 15); //scale output filter return; //return from interrupt } void main(){ short i; for (i=0; i<n; i++){ dly[i] = 0; //init buffer h[1][i] = hlp600[i]; //start addr of LP600 coeff h[2][i] = hlp1000[i]; //start addr of LP1000 coeff h[3][i] = hlp1500[i]; //start addr of LP1500 coeff } comm_intr(); //init DSK, codec, McBSP while(1); //infinite loop } FIGURE FIR program to implement three different FIR lowpass filters using a slider for selection (FIR3LP.c). /*FIR3LP.gel Gel file to step through 3 different LP filters*/ menuitem "Filter Characteristics" slider Filter(1,3,1,1,filterparameter) /*from 1 to 3,incr by 1*/ {LP_number = filterparameter; /*for 3 LP filters*/ } FIGURE GEL file for selecting one of three FIR lowpass filter coefficients (FIR3LP.gel). Build this project as FIR3LP. Use the.wav file as input and observe the effects of the three lowpass filters on the input voice. With the lower bandwidth of 600Hz, using the first set of coefficients, the frequency components of the speech signal above 600 Hz are suppressed. Connect the output to a speaker or a spectrum analyzer to verify such results, and observe the different bandwidths of the three FIR lowpass filters.

DSP Laboratory (EELE 4110) Lab#10 Finite Impulse Response (FIR) Filters

Islamic University of Gaza OBJECTIVES: Faculty of Engineering Electrical Engineering Department Spring-2011 DSP Laboratory (EELE 4110) Lab#10 Finite Impulse Response (FIR) Filters To demonstrate the concept