removing noise from signal
in [Matlab]
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From: Anne Stewart on 2 Aug 2010 09:51 Hi all, i have a problem with removing noise from signal. so, this is my code: f = 7000 %frekvencija l = 100 %duljina signala T = 1/f t = (0:l)*T x = 0.1*sin(2*pi*45*t) + sin(4*pi*220*t) y = 0.7*sin(2*pi*750*t) + sin(2*pi*120*t) z = x + y subplot(2,1,1) plot(t,z) xlabel('t[s]') ylabel('A') Z = fft(z) N = size(z,2)/2 ampl = abs(Z)/N subplot(2,1,2) frek = (0:70)/(2*N*f) xlabel('frekvencija [Hz]') ylabel('amplituda') plot(frek, ampl (1:71)) % Imamo tri vrha [u 2.828*10^(-6), 8.486*10^(-6) i u 1.556*10^(-6)]. Prvi vrh ima amplitudu 0.84, drugi 0.85, a treci 0.68. % Sad cemo dodati random noise u signal. noise = 0.3*randn(1,size(z,2)) m = z + noise M = fft(m) n = size(m,2)/2 Ampl = abs(M)/n %spektar figure subplot(2,1,1) plot(t,m) xlabel('t(s)') ylabel('amplituda') subplot(2,1,2) Frek = (0:70)/(2*n*f) plot(Frek,Ampl(1:71)) xlabel('frekvencija [Hz]') ylabel('amplituda') % Pripadajuci vrhovi imaju iste amplitude kao i u signalu bez random noise, dok je ostatak noise, tj. šum i on ima amplitude manje od amplituda spomenutih vrhova. figure plot(Z/N,'r+') hold on plot(M/n,'bx') Ampl(find(Ampl<0.16)) = 0 iAmpl = ifft(Ampl) figure plot(t,iAmpl) xlabel('t[s]') ylabel('amplituda') i was wondering if i could get that 2nd figure, 2nd plot so that after 0.2 at time axe the noise is totaly zero, or less than it is now??
From: us on 2 Aug 2010 09:57 On Aug 2, 3:51 pm, "Anne Stewart" <mara.ko...(a)gmail.com> wrote: > Hi all, > > i have a problem with removing noise from signal. so, this is my code: > > f = 7000 %frekvencija > l = 100 %duljina signala > T = 1/f > t = (0:l)*T > x = 0.1*sin(2*pi*45*t) + sin(4*pi*220*t) > y = 0.7*sin(2*pi*750*t) + sin(2*pi*120*t) > z = x + y > subplot(2,1,1) > plot(t,z) > xlabel('t[s]') > ylabel('A') > Z = fft(z) > N = size(z,2)/2 > ampl = abs(Z)/N > subplot(2,1,2) > frek = (0:70)/(2*N*f) > xlabel('frekvencija [Hz]') > ylabel('amplituda') > plot(frek, ampl (1:71)) > % Imamo tri vrha [u 2.828*10^(-6), 8.486*10^(-6) i u 1.556*10^(-6)]. Prvi vrh ima amplitudu 0.84, drugi 0.85, a treci 0.68. > % Sad cemo dodati random noise u signal. > noise = 0.3*randn(1,size(z,2)) > m = z + noise > M = fft(m) > n = size(m,2)/2 > Ampl = abs(M)/n %spektar > figure > subplot(2,1,1) > plot(t,m) > xlabel('t(s)') > ylabel('amplituda') > subplot(2,1,2) > Frek = (0:70)/(2*n*f) > plot(Frek,Ampl(1:71)) > xlabel('frekvencija [Hz]') > ylabel('amplituda') > % Pripadajuci vrhovi imaju iste amplitude kao i u signalu bez random noise, dok je ostatak noise, tj. šum i on ima amplitude manje od amplituda spomenutih vrhova. > figure > plot(Z/N,'r+') > hold on > plot(M/n,'bx') > Ampl(find(Ampl<0.16)) = 0 > iAmpl = ifft(Ampl) > figure > plot(t,iAmpl) > xlabel('t[s]') > ylabel('amplituda') > > i was wondering if i could get that 2nd figure, 2nd plot so that after 0.2 at time axe the noise is totaly zero, or less than it is now?? a hint: help filter; % <- and its siblings... us
From: Anne Stewart on 4 Aug 2010 14:12 us <us(a)neurol.unizh.ch> wrote in message <93eead52-b641-4b46-9b07-b65c09bee2da(a)f20g2000pro.googlegroups.com>... > On Aug 2, 3:51 pm, "Anne Stewart" <mara.ko...(a)gmail.com> wrote: > > Hi all, > > > > i have a problem with removing noise from signal. so, this is my code: > > > > f = 7000 %frekvencija > > l = 100 %duljina signala > > T = 1/f > > t = (0:l)*T > > x = 0.1*sin(2*pi*45*t) + sin(4*pi*220*t) > > y = 0.7*sin(2*pi*750*t) + sin(2*pi*120*t) > > z = x + y > > subplot(2,1,1) > > plot(t,z) > > xlabel('t[s]') > > ylabel('A') > > Z = fft(z) > > N = size(z,2)/2 > > ampl = abs(Z)/N > > subplot(2,1,2) > > frek = (0:70)/(2*N*f) > > xlabel('frekvencija [Hz]') > > ylabel('amplituda') > > plot(frek, ampl (1:71)) > > % Imamo tri vrha [u 2.828*10^(-6), 8.486*10^(-6) i u 1.556*10^(-6)]. Prvi vrh ima amplitudu 0.84, drugi 0.85, a treci 0.68. > > % Sad cemo dodati random noise u signal. > > noise = 0.3*randn(1,size(z,2)) > > m = z + noise > > M = fft(m) > > n = size(m,2)/2 > > Ampl = abs(M)/n %spektar > > figure > > subplot(2,1,1) > > plot(t,m) > > xlabel('t(s)') > > ylabel('amplituda') > > subplot(2,1,2) > > Frek = (0:70)/(2*n*f) > > plot(Frek,Ampl(1:71)) > > xlabel('frekvencija [Hz]') > > ylabel('amplituda') > > % Pripadajuci vrhovi imaju iste amplitude kao i u signalu bez random noise, dok je ostatak noise, tj. šum i on ima amplitude manje od amplituda spomenutih vrhova. > > figure > > plot(Z/N,'r+') > > hold on > > plot(M/n,'bx') > > Ampl(find(Ampl<0.16)) = 0 > > iAmpl = ifft(Ampl) > > figure > > plot(t,iAmpl) > > xlabel('t[s]') > > ylabel('amplituda') > > > > i was wondering if i could get that 2nd figure, 2nd plot so that after 0.2 at time axe the noise is totaly zero, or less than it is now?? > > a hint: > > help filter; % <- and its siblings... > > us thanks for your reply, but here's the thing, i have to type filter myself, not like filter from the menu. oh and how could i get the plot on 4th figure to look more alike the original signal?? Anne
From: Anne Stewart on 4 Aug 2010 15:03 "Anne Stewart" <mara.kozic(a)gmail.com> wrote in message <i3cahk$31j$1(a)fred.mathworks.com>... > us <us(a)neurol.unizh.ch> wrote in message <93eead52-b641-4b46-9b07-b65c09bee2da(a)f20g2000pro.googlegroups.com>... > > On Aug 2, 3:51 pm, "Anne Stewart" <mara.ko...(a)gmail.com> wrote: > > > Hi all, > > > > > > i have a problem with removing noise from signal. so, this is my code: > > > > > > f = 7000 %frekvencija > > > l = 100 %duljina signala > > > T = 1/f > > > t = (0:l)*T > > > x = 0.1*sin(2*pi*45*t) + sin(4*pi*220*t) > > > y = 0.7*sin(2*pi*750*t) + sin(2*pi*120*t) > > > z = x + y > > > subplot(2,1,1) > > > plot(t,z) > > > xlabel('t[s]') > > > ylabel('A') > > > Z = fft(z) > > > N = size(z,2)/2 > > > ampl = abs(Z)/N > > > subplot(2,1,2) > > > frek = (0:70)/(2*N*f) > > > xlabel('frekvencija [Hz]') > > > ylabel('amplituda') > > > plot(frek, ampl (1:71)) > > > % Imamo tri vrha [u 2.828*10^(-6), 8.486*10^(-6) i u 1.556*10^(-6)]. Prvi vrh ima amplitudu 0.84, drugi 0.85, a treci 0.68. > > > % Sad cemo dodati random noise u signal. > > > noise = 0.3*randn(1,size(z,2)) > > > m = z + noise > > > M = fft(m) > > > n = size(m,2)/2 > > > Ampl = abs(M)/n %spektar > > > figure > > > subplot(2,1,1) > > > plot(t,m) > > > xlabel('t(s)') > > > ylabel('amplituda') > > > subplot(2,1,2) > > > Frek = (0:70)/(2*n*f) > > > plot(Frek,Ampl(1:71)) > > > xlabel('frekvencija [Hz]') > > > ylabel('amplituda') > > > % Pripadajuci vrhovi imaju iste amplitude kao i u signalu bez random noise, dok je ostatak noise, tj. šum i on ima amplitude manje od amplituda spomenutih vrhova. > > > figure > > > plot(Z/N,'r+') > > > hold on > > > plot(M/n,'bx') > > > Ampl(find(Ampl<0.16)) = 0 > > > iAmpl = ifft(Ampl) > > > figure > > > plot(t,iAmpl) > > > xlabel('t[s]') > > > ylabel('amplituda') > > > > > > i was wondering if i could get that 2nd figure, 2nd plot so that after 0.2 at time axe the noise is totaly zero, or less than it is now?? > > > > a hint: > > > > help filter; % <- and its siblings... > > > > us > > > thanks for your reply, > > but here's the thing, i have to type filter myself, not like filter from the menu. oh and how could i get the plot on 4th figure to look more alike the original signal?? > > Anne okay, i changed frequency and signal lenght so now the 2nd figure, 2nd plot looks fine (and it SHOULD look like that because i haven't done any noise removal at that point). the problem is when doing fft and ifft, the 4th figure is not even close to original signal (interference of those two sinusoids) - what's wrong??
From: Anne Stewart on 4 Aug 2010 16:05 okay i got the point, 2nd figure should be exactly as it is, but the problem is in the step between fft - ifft, i can't remove the noise in the last plot. here is the correction od frequency and signal time: f = 70000 %frekvencija l = 1000 %duljina signala T = 1/f t = (0:l)*T x = 0.1*sin(2*pi*45*t) + sin(4*pi*220*t) y = 0.7*sin(2*pi*750*t) + sin(2*pi*120*t) z = x + y subplot(2,1,1) plot(t,z) xlabel('t[s]') ylabel('A') Z = fft(z) N = size(z,2)/2 ampl = abs(Z)/N subplot(2,1,2) frek = (0:70)/(2*N*f) xlabel('frekvencija [Hz]') ylabel('amplituda') plot(frek, ampl (1:71)) % Imamo tri vrha [u 2.828*10^(-6), 8.486*10^(-6) i u 1.556*10^(-6)]. Prvi vrh ima amplitudu 0.84, drugi 0.85, a treci 0.68. % Sad cemo dodati random noise u signal. noise = 0.3*randn(1,size(z,2)) m = z + noise M = fft(m) n = size(m,2)/2 Ampl = abs(M)/n %spektar figure subplot(2,1,1) plot(t,m) xlabel('t[s]') ylabel('amplituda') subplot(2,1,2) Frek = (0:70)/(2*n*f) plot(Frek,Ampl(1:71)) xlabel('frekvencija [Hz]') ylabel('amplituda') % Pripadajuci vrhovi imaju iste amplitude kao i u signalu bez random noise, dok je ostatak noise, tj. šum i on ima amplitude manje od amplituda spomenutih vrhova. figure plot(Z/N,'r+') hold on plot(M/n,'bx') fM = fix(M/0.0945)*100 ifM = ifft(fM) W = real(ifM) figure plot(t,W) xlabel('t[s]') ylabel('amplituda')
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