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 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).