1. EE421, Fall 1998 Michigan Technological University Timothy J. Schulz 29-Sept, 1998EE421, Lecture 61 Lecture 6 - Sample Processing Methods l Basic building blocks: –adder –multiplier –delay x 1 (n) x 2 (n) x 1 (n) + x 2 (n) + x(n)ax(n) a x(n)x(n-1) z -1

2. EE421, Fall 1998 Michigan Technological University Timothy J. Schulz 29-Sept, 1998EE421, Lecture 62 Sample Processing Methods l Delay line State variables w 0 (n) = x(n) w 1 (n) = x(n-1) = w 0 (n-1) w 2 (n) = x(n-2) = w 1 (n-1) w 3 (n) = x(n-3) = w 2 (n-1) w0 := x w1 := w0 w2 := w1 w3 := w2 z -1 x(n) x(n-1)x(n-2)x(n-3)

3. EE421, Fall 1998 Michigan Technological University Timothy J. Schulz 29-Sept, 1998EE421, Lecture 63 Sample Processing Methods l Direct form realization z -1 + h0h0 h1h1 h2h2 h3h3 x(n)y(n)

4. EE421, Fall 1998 Michigan Technological University Timothy J. Schulz 29-Sept, 1998EE421, Lecture 64 Sample Processing Methods Algorithm considerations initialize all registers to zero store new sample: w0 := x compute filter output: y := h0*w0 + h1*w1 + h2*w2 + h3*w3 update all data registers: w3 := w2, w2 := w1, w1 := w0 wait for next sample order is important here!

5. EE421, Fall 1998 Michigan Technological University Timothy J. Schulz 29-Sept, 1998EE421, Lecture 65 Sample Processing Methods Hardware implementations DSP chips have the ability to carry out a multiply accumulate (MAC) operation in one clock cycle: y := y + h*x initialize all registers to zero store new sample in register: w0 := x initialize output: y := h3*w3 loop through state registers: w3 := w2 y := y + h2*w2 w2 := w1 y := y + h1*w1 w1 := w0 y := y + h0*w0 wait for next sample

6. EE421, Fall 1998 Michigan Technological University Timothy J. Schulz 29-Sept, 1998EE421, Lecture 66 Sample Processing Methods l Hardware considerations Shifting data from register to register can take a lot of time.

7. EE421, Fall 1998 Michigan Technological University Timothy J. Schulz 29-Sept, 1998EE421, Lecture 67 Sample Processing Methods l Hardware considerations An alternative is to use circular addressing:

8. EE421, Fall 1998 Michigan Technological University Timothy J. Schulz 29-Sept, 1998EE421, Lecture 68 Sample Processing Methods l Hardware considerations More on this when we develop hardware implementations in EE422.