Hey Trishneeta,
I believe "matrix is close to singular or badly scaled" warning in MATLAB, typically indicates numerical instability in the filter design or application.
The error is thrown in the 'filtfilt' function, which applies a zero-phase digital filter. This usually happens when:
- Filter coefficients '(b, a)' are poorly conditioned, often due to extreme or invalid cutoff frequencies.
- The data has NaNs or Infs, which can break the filtering process.
- The filter band is too narrow, especially for high-order filters.
Lookin closely in the code:
[b,a] = butter(6,[lowcut highcut]);
It is defined as:
highcut = (2191/100)/(2191/2); % which equals to 0.02
lowcut = (2191/250)/(2191/2); % which equals to 0.008
So the bandpass is '[0.008 0.02]', which is very narrow and close to 0. This can cause instability in a 6th-order Butterworth filter.
To rectify this issue we can
- Try reducing the filter order (e.g., from 6 to 4).
- Check for NaNs in 'sla' using 'any(isnan(sla))'.
- Normalize the data if it has very large or very small values.
For the second question,
In digital signal processing, filter design functions like 'butter' expects normalized frequencies:
- The Nyquist frequency is half the sampling rate.
- So, normalized frequency = (desired frequency) / (Nyquist frequency).
In this case:
- There is daily data 2191, so 1 sample/day.
- Nyquist frequency = 2191/2 cycles/day.
- A 100-day period corresponds to a frequency of 2191/100
- Normalized frequency = (2191/100)/ (2191/2) = 0.02.
So according to my understanding we are normalizing the frequency relative to the Nyquist frequency.
I hope it helps!
