I design a AC power harmonic analyzer, But I need help!

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I design a AC power harmonic analyzer, But I need following help:
A、Ac source frequency is 47~63Hz,and I need to calculate 51st harmonic current value. then, how speed of AD converter is better for current sample? 10KHz or higher?
B、I use a power resistor to sense current and convert it to voltage signal, because sine wave have plus voltage and minus voltage, but AD converter only work in +5V, How can I use this AD converter to sample minus voltage signal?
Pls help me? Thanks advanced!
 

1) Nyquist Theorem states that the sampling frequency must be at least twice as high as the frequency of the desired signal. In you case, as you're interested in 51th harmonic of AC main power, so, the sampling frequency of ADC must be at least 63 x 51 x 2 = 6426 Hz. You can choose any ADC with sample frequency of 10kHz or higher.

2) You can use resistor network to offset the signal to be in the range of 0 - 5V. In other words, after offset, -VAC(peak) will be equal to 0V, VAC(0V) will be equal to 2.5V, and +VAC(peak) will be equal to 5V.
 

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