Technology: Signal-To-Quantization-Noise-Ratio (SQNR)

The Centar FFT architecture allows all additions to be performed at full precision so that the round-off errors occur primarily in the twiddle multiplication multiplication steps. Consequently, the SQNR is much higher than found in other FFT archtectures for a given input bit length. The SQNR is defined by the expression

SQNR = 10 log* _{10}* (

where *z(n)* are the coefficient output magnitues and *z _{ref}(n) *are exact precision reference magnitudes. Based on this expression statistics are tabulated in Table 1 for 256-point and 1024-point FFTs with 16-bit fixed-point input word lengths and a 16-bit output mantissa plus a 5-bit exponent. For comparison the same values are calculated using the Altera streaming FFT circuits (v13.1) with 16-bit and 20-bit input/output word lengths using random real and inmaginary data based on Altera’s supplied Matlab model. The benefit of the Centar scaling approach is equivalent to approximately 4-bits, an advantage which is particularly important for smaller word lengths.

Centar 16-bit word |
Altera 16-bit word |
Altera 20-bit word |
||||

Transform Size |
256 | 1024 | 256 | 1024 | 256 | 1024 |

Mean |
86.6 | 82.8 | 63.5 | 57.1 | 87.8 | 81.2 |

Median |
86.7 | 82.8 | 63.5 | 57.1 | 87.8 | 81.3 |

Standard Deviation |
1.4 | 0.8 | 0.3 | 0.2 | 0.3 | 0.2 |

Maximum |
90.0 | 85.0 | 64.5 | 57.6 | 88.7 | 81.8 |

Minimum |
83.0 | 80.2 | 62.4 | 56.6 | 86.8 | 80.8 |

Table 1. SQNR statistics for fixed-point streaming FFTs (1000 FFT blocks of random data).