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2

For removing mains hum from EEG signals, you can take advantage of the fact that the noise is stable in phase and frequency, albeit not necessarily in amplitude depending on the overall electrical environment. For that, the most popular EEG analysis software all support sine-wave fitting: EEGLAB via the CleanLine plugin and installable via EEGLAB's plugins ...

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First, all of the "elemental" filters will have the same corner or center frequency. The differences between them will be in their Q. Consider a second-order Butterworth lowpass filter with a corner frequency of 1 kHz, with a unity-gain passband. At 1 kHz, the response of the filter is -3 dB. The filter slope reaches -12 dB/octave. The response of a forth-...

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The impulse response of two filters in series is the convolution of each filters impulse response. You can multiply two polynomials by convolving their coefficients. Likewise you can factor or combine filters by factoring or multiplying their transfer functions described as polynomials. For example, a fourth order filter can be factored into two 2nd order ...

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A linear time-invariant (LTI) system is indeed completely described by its frequency response. Note that the frequency response is the Fourier transform of the impulse response, which also completely describes the system. So if the Fourier transform of the impulse response exists, then the resulting frequency response must represent a complete ...

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Was my prof wrong? No. You're right, you can find multiple systems with the same frequency response, or the same transfer function. But if you're using something as a (linear, which is often implied) filter, then all you care about is the frequency response (otherwise, you'd probably not be calling the thing "filter"). So, when I define a filter, it's ...

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I joined this community only to answer your question as I had a similar problem about 2 years ago, in ECG domain though. What I've found (unfortunately I cannot trace the source back) is a very simple solution for a digital notch filter of taking the signal delayed by half of the period of the frequency you want to filter out and get the average of it with ...

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This is an uncertainty principle kind of problem: there is no way to make a reliable filter with little delay that will suppress a narrow band around 50Hz since the narrowness of a criterion in frequency space necessitates a certain width of observation in the time domain. Basically the compactness of a phenomenon in time and in frequency cannot be ...

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I assume this a for real-time processing. Otherwise, you could simply discard the number of samples corresponding to the group delay. 1st solution - Use an IIR notch filter. You could use this solution Analytically designing a notch-filter for specified frequency 50 Hz The group delay will be minimal, probably negligible, if you're not close to 50 Hz. ...

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You could use a 2nd order IIR notch filter as I describe in this post Transfer function of second order notch filter - That post demonstrates a 50 Hz IIR notch with 1 KHz sampling. [Update: As @user47050 astutely points out in the comments, the IIR notch would also have minimal delay regardless of notch bandwidth, since the dominat delay in the IIR notch ...

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I understand, that this involves a lot of math. Not so much, in principle. The basic idea behind linear (or nonlinear) filtering is to remplace a inaccurate or noisy sample $s[n]$ by a combination of other samples, assuming that their values or location is somehow close to $s[n]$ (cf. local vs non-local filters). At a low level, when the filter is both ...

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I assume you'r talking about digital interpolators. An interpolator is basically an L times expander followed by an anti-imaging lowpass filter with gain L. The cutoff frquency of the lowpass filter is defined in the discrete-time frequency domain as $$w_c = \frac{\pi}{L}.$$ The analog equivalent of this cutoff frequency is  f_c = F'_s \frac{ w_c }{ ...

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Consider a moving average over N samples- this is a simple FIR filter where each new output is the average of the past N samples. It is easy to see how high frequency noise can be filtered out (so is a low pass filter), and the longer time duration we include in the averaging window the lower will be the frequency cut off (just compare a stock market 30 day ...

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