Filter out a particular frequency from a mixed signal

Hi All, I have a signal of mixed frequency 11 hrz, 50 hrz, 9000 hrz, and I want to filter out the 50 hrz signal from the mixed signal. The record length of the signal may be 10^6 long or may be more. Any help will be appreciated.

Thanks

Answer 1

[Star Strider]

With a 1 MHz sampling frequency, it is not possible to implement a discrete FIR or IIR filter for a 50 Hz signal that produces reliable output.

You either need to implement the 50 Hz notch (narrow bandstop) filter in hardware, or significantly decrease your sampling frequency (perhaps to 20 KHz).

Answer 2

[Pragati]

The statement that a discrete FIR or IIR filter cannot be implemented for a 50 Hz signal at a 1 MHz sampling rate is somewhat too strong.

A digital notch (bandstop) filter at 50 Hz is mathematically feasible even when the sampling frequency is 1 MHz. The challenge is that the normalized frequency is extremely small:

As a result, the filter poles and zeros are located very close to z=1, which can make the design numerically sensitive and difficult to visualize on standard frequency-response plots.

For example, the following filter can be designed in MATLAB:

d = designfilt('bandstopiir', ...

'FilterOrder',2, ...

'HalfPowerFrequency1',49.5, ...

'HalfPowerFrequency2',50.5, ...

'SampleRate',1e6);

When the frequency response is examined with sufficient resolution around 50 Hz, a notch is clearly visible. Therefore, the issue is not whether a digital filter can be designed, but rather whether it is the most robust and efficient approach for the application.

For a signal containing components at 11 Hz, 50 Hz, and 9 kHz, alternative approaches may be preferable:

• Decimate the signal (after appropriate anti-alias filtering) and then design the notch filter at the lower sample rate.
• Estimate and subtract the 50 Hz interference directly if it is a stable sinusoidal component.
• Use a higher-order notch filter if greater attenuation is required.

The best solution depends on the sampling frequency, the required attenuation at 50 Hz, and whether the 50 Hz component is a fixed power-line interference or part of a more complex signal. However, it is generally possible to implement a digital FIR or IIR notch filter for a 50 Hz component even when the original data is sampled at 1 MHz.