Signal is not getting filtered properly

Hi,

I am trying to implement 4th order high pass elliptical filter with cut-off frequency at 500/510 Hz at 20 dB passband and 25 dB stopband attenuation. I have attached the plot for my original data and data after filtering. But if you see the filtered data, there is almost no data after 500

[b,a]=ellip(4,20,25,500/510,'high');
fvtool(b,a)
y2=audioread('fr1.mp3');
y_b2=filter(b,a,y2);
fs=44100;
N=length(y_b2);
time=N/fs;
t = linspace(0, time, N);
referenceLength=length(y_b2);
fref=fs*(1:referenceLength)/referenceLength;
R=fft(y_b2,referenceLength);
stor=R(1);
R(1)=0;
absR=abs(R);
plot(fref,absR);
xlim([0 2000]); 
ylim([0 200]); 
xticks([0 200 400 600 800 1000 1200 1400 1600 1800 2000]); 
yticks([0 25 50 75 100 125 150 175 200 300 400 500 600 700 800 900 1000]); 
grid on;
xlabel('Frequency(Hz)');
ylabel('Amplitude');

[Chunru]

what is you intention with the filter? The filter seems not well-designed.

[b,a]=ellip(4,20,25,500/510,'high');
%fvtool(b,a)
fs=44100;
freqz(b, a, 4096, fs);

[Giggs B.]

Hi, Thank you for the reply.

My intention is to remove the undesired frequency and only use the desired frequecy and then calculate the power of the signal. I am using elliptical since I want to remove undesired freq as much as possible (with lower order) opposed to the case of butterworth where the magnitude response is not straight (so the undesired freq remain at a larger amount compared to elliptical). Can you please explain, why did you say that my filter is well-designed? Also, would you be able to explain why is the magnitude response at ~2.5 KHz instead of 500 Hz?

[Chunru]

What is the undesired frequency? What is the desired frequency? What is the desired response? Is the filter response plotted avove is what you want?

[Giggs B.]

My desired freq is variable since I am still in developng stage of my project and finding the best cut-off frequency. But for now my desired frequencies are above 500 Hz and undesired frequencies are below 500 Hz. My desired filter response is also variable but considering 1 dB passband and 25 dB stopband attenution, I want the transition phase to be as small as possible so as to prevent frequencies below 500 Hz as much as possible, also I don't mind attenuating my signal by some amount (<20 dB for example).

But I don't understand why the transition phase is ~2.5 KHz instead of 500 Hz.

[Chunru]

the cut off is at (500/510) in normalized freq and (500/510)*fs/2=21618Hz (not ~2.5kHz) while you want a cut-off at 500Hz.

Answer 1

[Chunru]

Try design the filters as follows. The filter will attenuate the frequency content below 500Hz. When plotting spectrum, you may consider log scale of the ampiltude (20*log10(abs(filtered_date))).

fs=44100;
% The filter to have 1dB ripples in passband, 40 dB attenuation in stop
% band, the cut-off freq of 500Hz. (you may adjust the value as you want)
[b,a]=ellip(4, 1, 40, 500/(fs/2),'high');
%fvtool(b,a)

freqz(b, a, 8192, fs);