Effect of Finite Word Length on FIR Filter Implemented on 8052 Microcontroller

Abstract

Digital filters have found important applications in an increasing number of fields in science and engineering, and design techniques have been developed to achieve desired filter characteristics. A digital filter operates on an input-sampled signal to produce an outputsampled signal by means of a computational algorithm. It can be simulated on a general purpose computer or can be constructed with special-purpose digital hardware. Despite the many advantages offered by digital filters, there is an inherent limitation on the accuracy of these filters due to the fact that all digital networks operate with only a finite number of bits. The three common sources of error due to finite word length are the quantization of the input signal into a set of discrete levels, the representation of the filter coefficients ak and bk by a finite number of bits, the accumulation of round-off errors committed at arithmetic operations. This thesis work, Effect of Finite Word Length on FIR Filter implemented on 8052 Microcontroller, includes the design and development of the hardware as well as software of the low pass Finite Impulse Response (FIR) digital filter. To find out the error introduced by finite word length on FIR filter, a low pass FIR filter is designed with the help of Matrix Laboratory (MATLAB) to compare with the FIR filter implemented on 8052 microcontroller. Blackman window, Hanning window and Rectangular window are used. 8051 is an 8-bit microcontroller so the word length of registers is limited to 8-bits. The filter coefficients and the input sequence are either truncated or rounded-off to 8-bit word length. The filter coefficients are convolved with the input sequence by using microcontroller. Results of the convolution are compared with results of convolution done with MATLAB.