digital signal prossecing, Cheat Sheet of Digital Signal Processing

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SECA1506 - Digital Signal Processing

Semester -V

DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

UNIT 3

FINITE WORD LENGTH EFFECTS

INTRODUCTION

 (^) This representation has fixed number of bits for integer part and for fractional part.  (^) Can store minimum value is 0000.0001 and maximum value is 9999.9999.  (^) There are three parts of a fixed-point number representation: the sign field, integer field, and fractional field. Fixed-Point Representation − We can represent these numbers using: Signed representation: range from -( (k-1) -1) to ( (k-1) -1), for k bits. 1’s complement representation: range from -( (k-1) -1) to ( (k-1) -1), for k bits. 2’s complementation representation: range from -( (k-1) ) to ( (k-1) -1), for k bits.

Example − Assume number is using 32-bit format which reserve 1 bit for the sign, 15 bits for the integer part and 16 bits for the fractional part. Then, -43.625 is represented as following: Where, 0 is used to represent + and 1 is used to represent. 000000000101011 is 15 bit binary value for decimal 43 and 1010000000000000 is 16 bit binary value for fractional 0.625. Fixed-Point Representation cont… −