Bandpass Filter Not Filtering Signal

Hi, I've currently designed a bandpass filter to filter a signal between 1 and 30 Hz, but when plotting it, my signal still has a random spike at 60 Hz when plotted through an absolute value squared fft, despite the filter properly being set up to cap at 30.

My code is as follows:

y = data;
data2 = double(y);
fs = 2000
samples = length(y);
yfilt = bandpass(data2, [1,30], fs);
y1 = fft(data2);
power1 = abs(y1).^2/samples; 
y5 = fft(yfilt);
power5 = abs(y5).^2/samples;

which results in this large spike for the filtered data

can anyone explain what's causing this?

[Mathieu NOE]

can you share your data ?

Answer 1

[Cris LaPierre]

Filters have transition regions. The likely reason is that your filter steepness is not high enough to both pass a 30 Hz signal and attenuate to 60 dB a 60 Hz signal. You can read more about it here, where the description is accompanied by this figure.

For your case:

• 
• 
• Steepness, or s is 0.85
• 

From that, you can determine the value of to be 145.5 Hz, which means your bandpass filter does not fully attenuate higher frequencies until 30+145.5 Hz, or 175.5 Hz. This is why you still see 60 Hz in your filtered signal.

You would need to increase your steepness to at least 0.97 to fully attenuate a 60 Hz signal.

[Mathieu NOE]

hello

this is basically the example given in the doc of bandpass

was surprised to see that the filter will always exhibit sharp and brickwall characteristics even with 0.5 steepness factor

that will probably generate a very long transient response, that could be an issue with short signals

nevertheless we should have a 60 dB attenuation at 60 Hz , but that is true once you are out of the transient

that's the only explanation I can see for not having the expected attenuation

=> we need a fast transient bandpass filter (would recommend to use the good old butter command and use filtfilt)

that's why I asked the OP to share its data if possible

 Fs = 2000;
 x = randn(5000,1);
 [y1, D1] = bandpass(x,[1,30],Fs,'Steepness',0.5);
 [y2, D2] = bandpass(x,[1,30],Fs,'Steepness',0.8);
 [y3, D3] = bandpass(x,[1,30],Fs,'Steepness',0.95);
 pspectrum([y1 y2 y3], Fs)
 legend('Steepness = 0.5','Steepness = 0.8','Steepness = 0.95')
 fvt = fvtool(D1,D2,D3);
 legend(fvt,'Steepness = 0.5','Steepness = 0.8','Steepness = 0.95')

[Cris LaPierre]

Here is how I came up the values I presented. From the bandpass doc page

• Computes the upper transition width as

fny = 1000;
fpu = 30; 
s = 0.85;

Wu = (1-s)*(fny-fpu)

Wu = 145.5000

fsu = fpu + Wu

fsu = 175.5000

It does seem that the examples you and Star Strider have shared show a much narrower transition region.