Resampling for interference cancellation

On 10/14/2010 8:14 AM, Fred Marshall wrote:
> On 10/14/2010 7:47 AM, Dirk Bell wrote:
>> On Oct 13, 8:07 pm, Fred Marshall<fmarshall_xremove_the...@xacm.org>
>> wrote:
>>> On 10/13/2010 4:44 PM, Tim Wescott wrote:
>>>
>>>
>>>
>>>> On 10/13/2010 03:01 PM, Dirk Bell wrote:
>>>>> On Oct 13, 12:37 pm, "bendous"<samir@n_o_s_p_a_m.eee.strath.ac.uk>
>>>>> wrote:
>>>>>> Hi all,
>>>
>>>>>> I am not a DSP expert so please go easy on me. I have a VLF radio
>>>>>> signal
>>>>>> centred at 3KHz. The signal is corrupted with the mains harmonics,
>>>>>> which
>>>>>> seem to be over 20dB higher than the signal!
>>>
>>>>>> I am trying to implement an algorithm that isolates an out-of-band
>>>>>> harmonic
>>>>>> using a band-pass filter, resamples it several times to obtain the
>>>>>> in-band
>>>>>> harmonics, and subtracts them from the corrupted signal.
>>>
>>>>>> Let's say I have a reference harmonic x with N samples and I do
>>>
>>>>>> y = resample(x,I,Q);
>>>
>>>>>> the length of y will be N*I/Q samples.
>>>
>>>>>> I need then to take the the fft of y and z (the corrupted signal),
>>>>>> subtract
>>>>>> them and reconstruct z using the ifft.
>>>
>>>>>> My understanding is that I need to use the same Nfft for both ffts in
>>>>>> order
>>>>>> to be able to subtract one from the other.
>>>
>>>>>> What value should that be? N or N*I/Q?
>>>>>> And what should the ifft factor be?
>>>
>>>>>> I would be very grateful if someone could give me some pointers. I am
>>>>>> doing
>>>>>> this in Matlab and any pieces of code will be very much appreciated.
>>>
>>>>>> Kind regards,
>>>>>> Samir.
>>>
>>>>> Samir,
>>>
>>>>> Keep in mind that the phase of the subsampled signals may not be
>>>>> correct; if you were going to actually subtract the complex FFTs, that
>>>>> would effect the amount of cancellation. Since the harmonics would
>>>>> probably (almost guaranteed) fall in more than a single FFT bin there
>>>>> are multiple FFT bin phases per harmonic to deal with.
>>>
>>>> Which is why I suggested a comb filter (inverse comb filter?
>>>> multiple-notch filter?). By the time you figure out the phase and
>>>> amplitude of each harmonic and inject them back into the signal "in
>>>> reverse" to cancel them, you've essentially built a comb filter but
>>>> in a
>>>> really wacky and hard-to-understand way.
>>>
>>>>> Is the signal bandwidth sufficiently low that significant low
>>>>> frequency harmonics can be removed by a lowpass filter?
>>>
>>>>> The best solution if it is possible, as Tim says below, is don't let
>>>>> the power line harmonics get in the signal in the first place.
>>>
>>>>> Dirk
>>>
>>> I agree with Tim and Dirk. Depending on how much data you have, this
>>> seems like relatively natural application for an automatic line
>>> canceller ALC. That is if the mains harmonics are relatively stable and
>>> the VLF signal has some dynamics that would not cause it to be
>>> cancelled. Effectively this is close to what you were trying to do with
>>> subtraction but without the FFT / IFFT.
>>>
>>> Comments anyone?
>>>
>>> If the harmonics are of 50/60Hz then there will be a lot of them around
>>> 3kHz, right?
>>>
>>> Fred- Hide quoted text -
>>>
>>> - Show quoted text -
>>
>> You would think the level of the harmonics would be pretty low at 3kHz
>> (20th/30th harmonic at 50/60 Hz). That is why I was asking about the
>> bandwidth and a highpass filter (originally typed lowpass while
>> thinking highpass) since the signal is centered at 3 KHz.
>>
>> A simple comb filter is potentially going to remove a lot of the
>> signal and the high attenuation part of the all of the notches is so
>> narrow that the first notch being off a little from the signal means
>> that the attenuation isn't nearly as good. It also means the
>> attenuation decreases as the harmonics go up because the mistuning
>> increases, so harmonics can be missed altogether. If the notch
>> frequencies are static, then power line frequency may wander into and
>> out of the deep part of the notches over time.
>>
>> With audio (not the target signal here) I have seen improvements in
>> descreasing the power line frequency and harmonics signals, but the
>> problem isn't solved as far as I know.
>>
>> Dirk
>
> That's why I was suggesting a line canceller. The objective is to get
> the adaptive FIR filter in the block diagram to become a comb passband
> filter for the interference only - for subsequent subtraction. To the
> extent that this block isn't too selective (i.e. long transient
> response) it will track noise phase because that's based on the input.
> Then, if the signal dynamics are OK, the signal won't be subtracted at
> the output.
>
> Depending on signal and noise dynamics (e.g. if the signal has a short
> correlation time relative to the noise) then one might delay one of the
> paths so that the signal isn't cancelled (because the two paths are
> uncorrelated) but the noise is.
>
> I'm sure I'm being a bit cryptic here but it's something that would have
> to be worked out with real signals.
>
> Fred

By "noise" I meant the *interfering* line signal that's actually not 
noiselike.

Fred