The finite word length effect of DSP

Due to the special hardware or computer software implementation of digital signal processing, the relevant parameters and the results of the operation process are stored in the finite word length of the storage unit, due to the limited precision representation of data, the original system will inevitably produce errors. The common error factors that cause the finite word length effect are:

The 1 A/D conversion transforms the analog signal into a set of quantization effects generated by a discrete level.

The quantization effect of 2 coefficients expressed by finite binary numbers

During the 3 operation, the mantissa processing error and the finite word length of the compression level, including the low-level limit cycle oscillation and the overflow oscillation effect.

quantization and quantization error theoretically, the decimal number can be used to denote an infinite number of binary digits x =β+σβn 2^-n n is 1 to infinity where β is the sign bit, βn is a valid digit bit, in practice, only the finite bit approximation (b+1) bit), this process is called quantization. Quantization method has 2, 1 truncated directly after the B-bit data 2 rounding the b+1 bit after the size of the data determines the value of B-bit data, greater than half, then into the position, or discard the quantization generated by quantization error has rounding error and truncation error, the difference lies in the The error symmetry distribution, the truncation error single polarity distribution, in general, the rounding error effect is small, the application of more. Floating-point quantization error processing involves only the word length of the mantissa, so it is the same as the fixed-point error analysis, but the error size is related to the order code.

The

1 A/D conversion transforms the analog signal into a set of quantization effects generated by a discrete level. The analog signal undergoes a/D conversion to B-bit digital signal   analog signal is converted to obtain accurate sampling signal and quantization error E[k] .   Analysis The quantization effect of A/D converter is to select the appropriate word length to meet the signal-to-noise ratio index. Statistical assumptions for E[k] 1) e[k] is a stationary random sequence 2) e[k] is white noise and e[k1] and E[k2] irrelevant 3) e[k] and x[k] irrelevant 4) e[k] equal probability distribution