Question

Observe that the number of bits needed to represent the scaled filter coefficients obtained in part 3 is greater than 16 bits. (a) Determine the maximum word size we can use for scaling the input sequence and represent the filter coefficients using 16 bit words without getting overflow when a 32 bit word is used for the output. (b) Use the Matlab function firscale2 to scale the filter coefficients using this word size for the input sequence. (c) Repeat part 5 using the revised scaled filter coefficients. The input for this part of the problem should be scaled to the new word size using fscale. (d) Repeat part 6 to compare the output for the convolution of the revised fixed point coefficients and the input scaled to the new word size with the output from the floating point implementation.

   Observe that the number of bits needed to represent the scaled filter coefficients
obtained in part 3 is greater than 16 bits.
(a) Determine the maximum word size we can use for scaling the input sequence
and represent the filter coefficients using 16 bit words without getting overflow when a 32 bit word is used for the output.
(b) Use the Matlab function firscale2 to scale the filter coefficients using this
word size for the input sequence.
(c) Repeat part 5 using the revised scaled filter coefficients. The input for this
part of the problem should be scaled to the new word size using fscale.
(d) Repeat part 6 to compare the output for the convolution of the revised fixed
point coefficients and the input scaled to the new word size with the output
from the floating point implementation.
Show more…
Digital Signal Processing. Principles, Algorithms and System Design
Digital Signal Processing. Principles, Algorithms and System Design
Winser Alexander and… 1st Edition
Chapter 6, Problem 7 ↓

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Step 1

First, let's consider the dynamic range of the filter coefficients. If the filter coefficients are scaled to a maximum value of 1, then the minimum value can be assumed to be -1. Therefore, the dynamic range of the filter coefficients is 2.  Show more…

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Observe that the number of bits needed to represent the scaled filter coefficients obtained in part 3 is greater than 16 bits. (a) Determine the maximum word size we can use for scaling the input sequence and represent the filter coefficients using 16 bit words without getting overflow when a 32 bit word is used for the output. (b) Use the Matlab function firscale2 to scale the filter coefficients using this word size for the input sequence. (c) Repeat part 5 using the revised scaled filter coefficients. The input for this part of the problem should be scaled to the new word size using fscale. (d) Repeat part 6 to compare the output for the convolution of the revised fixed point coefficients and the input scaled to the new word size with the output from the floating point implementation.
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