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Noise Floor and Waveform Averaging
Waveform averaging, and the signal averaging inherent in the power spectrum calculation performed by Mac the Scope improves the noise floor of the signal beyond the sampling resolution limit, governed by the input sampling resolution (8 or 16 bits). The tables below show the improvement in theoretical noise floor gained from averaging and through using other control settings of Mac the Scope.
Noise Floor (- dB) = 1.76 + 6.02(bits of resolution) + 10log10(Waveform Output Points)
| Theoretical Noise Floor | ||||
| Waveform Input Points | Waveform Output Points | 8 bit Sampling Resolution | 16 bit Sampling Resolution | 24 bit Sampling Resolution |
| - | - | - 50 dB | - 98 dB | - 146 dB |
| 1024 | 512 | - 77 dB | - 125 dB | - 173 dB |
| 2048 (X2 mode) | 1024 | - 80 dB | - 128 dB | - 176 dB |
(The signal to noise ratio specification for the Macintosh 16-bit sound input, as provided by Apple, generally is in the 86 dB range.)
Likewise, the noise floor is improved when using Time Base Expansion modes greater than 1. The improvement is 20log10(n), where n is the time base expansion factor. Time Base Expansion applies a multi-tap infinite-impulse-response lowpass digital filter to the digitized input signal, before the signal is resampled to the needed number of waveform input points (1024 or 2048). Here, the noise floor improvement also is realized in TIME mode traces.
When using signal averaging (CONT or LIN modes), a similar improvement can be realized (20log10(number of averages)).
| Theoretical Noise Floor | Noise Floor based on Apple 86 dB SNR spec* | ||||
| Mac the Scope Time Base Expansion factor, n | 8 bit/512 pts | 8 bit/1024 pts | 16 bit/512 pts | 16 bit/1024 pts | 16 bit/1024 pts |
| 1 | -77 dB | - 80 dB | - 125 dB | - 128 dB | - 116 dB* |
| 2 | - 80 dB | - 83 dB | - 128 dB | - 131 dB | - 119 dB |
| 4 | - 83 dB | - 86 dB | - 131 dB | - 134 dB | - 122 dB |
| 8 | - 86 dB | - 89 dB | - 134 dB | - 137 dB | - 125 dB |
| 16 | - 89 dB | - 92 dB | - 137 dB | - 140 dB | - 128 dB |
| 32 | - 92 dB | - 95 dB | - 140 dB | - 143 dB | - 131 dB* |
* Compare to the noise floor plots shown here.
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