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 log10 (∑n z(n)2 / ∑n (z(n)-zref(n))2)),
where z(n) are the coefficient output magnitues and zref(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).