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I have been working with some digital filters.
Previously the detector has been integrating 74 A-D samples to produce each 30 Hz sample. Then the 30 Hz samples are filtered by a Finite Impulse Response (FIR) filter to remove ground signals. The FIR filter is configured as a bandpass filter. So it removes both low frequency and high frequency noise. But it was not doing a good enough job on either type of noise.
A mathematical description of an FIR filter is:
yn = a0xn + a1xn-1 + a2xn-2 + a1xn-3 + a2xn-4
Y is an output from the filter, the x's are inputs, and the a's are coefficients. Each output depends on several previous inputs. That means that the previous inputs have to be stored in memory. I have been saving the 12 most recent inputs for each channel. I have only been using +1, -1 and 0 for coefficients so I would not have to do any multiplication.
To remove more of the high frequency noise I would have to use fractional coefficients which means having to do a multiplication for each input value. To get a sharper low frequency cutoff to remove more ground noise I would have to save more of the previous inputs and use fractional coefficients. I could afford the multiplies but not the extra memory (RAM) to store enough inputs.
I had previously tried a median filter and a single pole low pass filter behind the integrator to reduce high frequency noise. But neither of them was effective. So I decided to try a two pole Infinite Impulse Response (IIR) filter.
A mathematical description of an IIR filter is:
yn = a0xn + a1xn-1 + a2xn-2 - b1yn-1 - b2yn-2
Yn is an output from the filter, the x's are inputs, and the a's are coefficients for the inputs. The other y's are previous outputs from the filter, and the b's are coefficients for the previous outputs. Each output depends on previous inputs and previous outputs. The dependence on previous outputs means that there is feedback. This can be used to provide sharper cutoff for a given amount of memory space than an FIR filter.
I placed a 2 pole 4.5 Hz low pass IIR filter between the integrator and the FIR filter. This cut the high frequency noise about in half without affecting the target signal. This improvement in signal to noise ratio extended the range by more than half an inch on the 5.3 coil. It would probably be good for about an extra inch with the 950 coil.
Then I tried replacing the FIR filter with a 2 pole high pass IIR filter. This gives better rejection of low frequency ground signals, but I lost the extra high frequency filtering I was getting from the FIR and was not getting good results.
So I put the FIR filter back in after the high pass filter. But now the high pass filter cuts out the low frequency noise so I could use fewer stages in the FIR filter. I dropped it from 12 to 7 stages. And since the low pass filter gets rid of most of the high frequency noise I can still use just 1's and 0's for FIR coefficients. I was also able to use the FIR filter to reshape the signal coming from the high pass filter.
Robert
Previously the detector has been integrating 74 A-D samples to produce each 30 Hz sample. Then the 30 Hz samples are filtered by a Finite Impulse Response (FIR) filter to remove ground signals. The FIR filter is configured as a bandpass filter. So it removes both low frequency and high frequency noise. But it was not doing a good enough job on either type of noise.
A mathematical description of an FIR filter is:
yn = a0xn + a1xn-1 + a2xn-2 + a1xn-3 + a2xn-4
Y is an output from the filter, the x's are inputs, and the a's are coefficients. Each output depends on several previous inputs. That means that the previous inputs have to be stored in memory. I have been saving the 12 most recent inputs for each channel. I have only been using +1, -1 and 0 for coefficients so I would not have to do any multiplication.
To remove more of the high frequency noise I would have to use fractional coefficients which means having to do a multiplication for each input value. To get a sharper low frequency cutoff to remove more ground noise I would have to save more of the previous inputs and use fractional coefficients. I could afford the multiplies but not the extra memory (RAM) to store enough inputs.
I had previously tried a median filter and a single pole low pass filter behind the integrator to reduce high frequency noise. But neither of them was effective. So I decided to try a two pole Infinite Impulse Response (IIR) filter.
A mathematical description of an IIR filter is:
yn = a0xn + a1xn-1 + a2xn-2 - b1yn-1 - b2yn-2
Yn is an output from the filter, the x's are inputs, and the a's are coefficients for the inputs. The other y's are previous outputs from the filter, and the b's are coefficients for the previous outputs. Each output depends on previous inputs and previous outputs. The dependence on previous outputs means that there is feedback. This can be used to provide sharper cutoff for a given amount of memory space than an FIR filter.
I placed a 2 pole 4.5 Hz low pass IIR filter between the integrator and the FIR filter. This cut the high frequency noise about in half without affecting the target signal. This improvement in signal to noise ratio extended the range by more than half an inch on the 5.3 coil. It would probably be good for about an extra inch with the 950 coil.
Then I tried replacing the FIR filter with a 2 pole high pass IIR filter. This gives better rejection of low frequency ground signals, but I lost the extra high frequency filtering I was getting from the FIR and was not getting good results.
So I put the FIR filter back in after the high pass filter. But now the high pass filter cuts out the low frequency noise so I could use fewer stages in the FIR filter. I dropped it from 12 to 7 stages. And since the low pass filter gets rid of most of the high frequency noise I can still use just 1's and 0's for FIR coefficients. I was also able to use the FIR filter to reshape the signal coming from the high pass filter.
Robert