Digital Signal Processing Basics
In an FIR filter computation, products of 16-bit fixed-point data and coefficients are represented in 32 bits, and 256 of these products are added up. Which of the following is the minimum accumulator width that guarantees no overflow during the computation?
- A32 bits
- B33 bits
- C40 bits
Show answer and explanation
Answer: C. 40 bits
Adding two 32-bit products can increase the magnitude by up to 1 bit, and adding 256 = 2⁸ of them by up to 8 bits. An accumulator of 32 + log₂256 = 32 + 8 = 40 bits therefore cannot overflow even in the worst case. Some typical 16-bit fixed-point DSPs have 40-bit accumulators, with 8 guard bits added to the 32-bit product. When the result is finally brought back to 16 bits, rounding and saturating arithmetic keep it within range.
- A. With the same 32 bits as the product, adding just two products can overflow.
- B. A 1-bit margin guarantees only the sum of two products.
- C. Correct. 256 = 2⁸, so 8 guard bits are added for 40 bits.