How to remove awgn from and ecg signal?

I'am doing this project on removing both PLI and AWGN in the ecg. I have downloaded the ecg code for generating the signal from matlab. I tried using Chebyshev2 and the Wiener filter to filter out the two noises. But that makes it even worse. Please to help me .I'll provide my code :

Fs = 1000;

Ts = 1/Fs;

x=0:Ts:10-Ts;

li=30/72;

a_pwav=0.25;

d_pwav=0.09;

t_pwav=0.16;

a_qwav=0.025;

d_qwav=0.066;

t_qwav=0.166;

a_qrswav=1.6;

d_qrswav=0.11;

a_swav=0.25;

d_swav=0.066;

t_swav=0.09;

a_twav=0.35;

d_twav=0.142;

t_twav=0.2;

a_uwav=0.035;

d_uwav=0.0476;

t_uwav=0.433;

pwav=p_wav(x,a_pwav,d_pwav,t_pwav,li);

%qwav output

qwav=q_wav(x,a_qwav,d_qwav,t_qwav,li);

%qrswav output

qrswav=qrs_wav(x,a_qrswav,d_qrswav,li);

%swav output

swav=s_wav(x,a_swav,d_swav,t_swav,li);

%twav output

twav=t_wav(x,a_twav,d_twav,t_twav,li);

%uwav output

uwav=u_wav(x,a_uwav,d_uwav,t_uwav,li);

%ecg output

ecg=pwav+qrswav+twav+swav+qwav+uwav;

figure(1)

plot(x,ecg);

xlabel('Time[s]')

ylabel('Amplitude')

title('ECG')

%pli

fNoise = 50; % Frequency [Hz]

aNoise = 1; % Amplitude

noise = aNoise*sin(2*pi.*x.*fNoise);

pliecg=ecg + noise;

%adding awgn

SNR=0;

noisy = awgn(pliecg,SNR,'measured')

figure(2)

plot(x,noisy)

xlabel('Time[s]')

ylabel('Amplitude')

title('Noisy')

function [pwav]=p_wav(x,a_pwav,d_pwav,t_pwav,li)

l=li;

a=a_pwav;

x=x+t_pwav;

b=(2*l)/d_pwav;

n=100;

p1=1/l;

p2=0;

for i = 1:n

harmonic1=(((sin((pi/(2*b))*(b-(2*i))))/(b-(2*i))+(sin((pi/(2*b))*(b+(2*i))))/(b+(2*i)))*(2/pi))*cos((i*pi*x)/l);

p2=p2+harmonic1;

end

pwav1=p1+p2;

pwav=a*pwav1;

end

function [qrswav]=qrs_wav(x,a_qrswav,d_qrswav,li)

l=li;

a=a_qrswav;

b=(2*l)/d_qrswav;

n=100;

qrs1=(a/(2*b))*(2-b);

qrs2=0;

for i = 1:n

harm=(((2*b*a)/(i*i*pi*pi))*(1-cos((i*pi)/b)))*cos((i*pi*x)/l);

qrs2=qrs2+harm;

end

qrswav=qrs1+qrs2;

end

function [qwav]=q_wav(x,a_qwav,d_qwav,t_qwav,li)

l=li;

x=x+t_qwav;

a=a_qwav;

b=(2*l)/d_qwav;

n=100;

q1=(a/(2*b))*(2-b);

q2=0;

for i = 1:n

harm5=(((2*b*a)/(i*i*pi*pi))*(1-cos((i*pi)/b)))*cos((i*pi*x)/l);

q2=q2+harm5;

end

qwav=-1*(q1+q2);

end

function [swav]=s_wav(x,a_swav,d_swav,t_swav,li)

l=li;

x=x-t_swav;

a=a_swav;

b=(2*l)/d_swav;

n=100;

s1=(a/(2*b))*(2-b);

s2=0;

for i = 1:n

harm3=(((2*b*a)/(i*i*pi*pi))*(1-cos((i*pi)/b)))*cos((i*pi*x)/l);

s2=s2+harm3;

end

swav=-1*(s1+s2);

end

function [twav]=t_wav(x,a_twav,d_twav,t_twav,li)

l=li;

a=a_twav;

x=x-t_twav-0.045;

b=(2*l)/d_twav;

n=100;

t1=1/l;

t2=0;

for i = 1:n

harm2=(((sin((pi/(2*b))*(b-(2*i))))/(b-(2*i))+(sin((pi/(2*b))*(b+(2*i))))/(b+(2*i)))*(2/pi))*cos((i*pi*x)/l);

t2=t2+harm2;

end

twav1=t1+t2;

twav=a*twav1;

end

function [uwav]=u_wav(x,a_uwav,d_uwav,t_uwav,li)

l=li;

a=a_uwav

x=x-t_uwav;

b=(2*l)/d_uwav;

n=100;

u1=1/l

u2=0

for i = 1:n

harm4=(((sin((pi/(2*b))*(b-(2*i))))/(b-(2*i))+(sin((pi/(2*b))*(b+(2*i))))/(b+(2*i)))*(2/pi))*cos((i*pi*x)/l);

u2=u2+harm4;

end

uwav1=u1+u2;

uwav=a*uwav1;

end

[Star Strider]

Since AWGN is by definition broadband noise, a frequency-selective filter will not work. The most likely option is to use wavelet denoising (or perhaps the Savitzky-Golay filter), however removing all the noise while retaining the necessary characteristics of the EKG will likely not be successful.

[v shikhashastri]

Can you please write the code for the filter? This is new to me, and I'm still understanding the DSP domain.

[Star Strider]

The documentation for sgolayfilt completely explains its design and application.

[v shikhashastri]

Thank you

[Star Strider]

My pleasure!

[v shikhashastri]

It isn't helping either. Any other way?

[Star Strider]

Try wavelet denoising (Wavelet Toolbox).

[v shikhashastri]

This also isn't helping.

[Star Strider]

The noise amplitude is simply too high to be able to recover the EKG signal, regardless of the technique.

If it was much lower, it would be possible to use an old technique (‘self-convolution’) to recover most of it —

 %pli
 fNoise = 50;    % Frequency [Hz]
 aNoise = 0.001;  % Amplitude                                   % Reduce Noise Amplitude
 noise = aNoise*sin(2*pi.*x.*fNoise);
 pliecg=ecg + noise;
 
 %adding awgn
 SNR=0;
 noisy = awgn(pliecg,SNR,'measured')
 figure(2)
 plot(x,noisy)
 xlabel('Time[s]')
 ylabel('Amplitude')
 title('Noisy')

ncn = conv(noisy, noisy, 'same');                               % Convolve Noisy Signal With Itself

figure
plot(x, ncn)
grid

However, even this approach fails to remove any of the noise in this signal.

[v shikhashastri]

Thank you so much

[Star Strider]

My pleasure!

[v shikhashastri]

any idea on firwiener.m matlab file

I was going through a journal and then came across the wiener filtering

[v shikhashastri]

And now when i searched for the firwiener.m matlab function, I'am not able to find it anywhere

[Star Strider]

I did a quick Interweb search and found several Weiner filter examples in the File Exchange. See if you can find something there that willl do what you want.

[v shikhashastri]

Yes yes... Sure.Thank you.

[Star Strider]

My pleasure!