Motorola MCF5281, MCF5282 user manual General Operation, Infinite Impulse Response IIR Filter

Models: MCF5282 MCF5281

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General Operation

N – 1N – 1

y(i) = a(k)y(i – k) + b(k)x(i – k)

k = 1

k = 0

Figure 3-2. Infinite Impulse Response (IIR) Filter

Here, the output y(i) is determined by past output values and past input values. This is the general form of an infinite impulse response (IIR) filter. A finite impulse response (FIR) filter can be obtained by setting coefficients a(k) to zero. In either case, the operations involved in computing such a filter are multiplies and product summing. To show this point, reduce the above equation to a simple, four-tap FIR filter, shown in Figure 3-3,in which the accumulated sum is a sum of past data values and coefficients.

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y(i) = b(k)x(i – k) = b(0)x(i) + b(1)x(i – 1) + b(2)x(i – 2) + b(3)x(i – 3)

k = 0

Figure 3-3. Four-Tap FIR Filter

3.3General Operation

The MAC speeds execution of ColdFire integer multiply instructions (MULS and MULU) and provides additional functionality for multiply-accumulate operations. By executing MULS and MULU in the MAC, execution times are minimized and deterministic compared to the 2-bit/cycle algorithm with early termination that the OEP normally uses if no MAC hardware is present.

The added MAC instructions to the ColdFire ISA provide for the multiplication of two numbers, followed by the addition or subtraction of the product to or from the value in an accumulator. Optionally, the product may be shifted left or right by 1 bit before addition or subtraction. Hardware support for saturation arithmetic can be enabled to minimize software overhead when dealing with potential overflow conditions. Multiply-accumulate operations support 16- or 32-bit input operands of the following formats:

Signed integers

Unsigned integers

Signed, fixed-point, fractional numbers

The EMAC is optimized for single-cycle, pipelined 32x32 multiplications. For word- and longword-sized integer input operands, the low-order 40 bits of the product are formed and used with the destination accumulator. For fractional operands, the entire 64-bit product is calculated and either truncated or rounded to the most-significant 40-bit result using the round-to-nearest (even) method before it is combined with the destination accumulator.

MOTOROLA

Chapter 3. Enhanced Multiply-Accumulate Unit (EMAC)

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Motorola MCF5281, MCF5282 user manual General Operation, Infinite Impulse Response IIR Filter