FFT question (signal processing)

Hi,

I am trying to remove certain frequencies from a swept-sine signal by using a fourier transform, zeroing certain elements of the array, and then inverse transforming them. As far as I can tell I am doing it right, but obviously I am not because when I run the final comparison analysis the frequencies that aren't supposed to be there still exist.

clear all, clc, close all

T=5;       %time
A=1;        %amplitude
F1=20;      %startfrequency
F2=20000;   %endfrequency
P0=0;       %initialphase

FS=44100;   %samplerate
B=16;       %bitrate

R=(F2-F1)/T;    %sweeprate
t=0:1/FS:T;     %timevector
p=P0+2*pi*(F1+(R.*t)./2).*t;    %phasevector

% Linear sine sweep
y=A*sin(p);
L=size(y);

figure(1)
plot(t,y)

%sound(y,FS,B);

%%Analysis fft

NFFT = 2^nextpow2(L(2)); % Next power of 2 from length of y
yfa = fft(y,NFFT)/L(2);
f = FS/2*linspace(0,1,NFFT/2+1);

figure(2)
plot(f,2*abs(yfa(1:NFFT/2+1)))
title('Single-Sided Amplitude Spectrum of y(t)')
xlabel('Frequency (Hz)')
ylabel('|Y(f)|')

%%Inverse Transform

yf=fft(y);  % Pure fft
yf(1:50000)=0; % bin removal
z=real(ifft(yf));   % ifft

figure(3)
plot(t,z)

%%New Analysis fft (for comparison)

NFFT = 2^nextpow2(L(2)); % Next power of 2 from length of y
zfa = fft(z,NFFT)/L(2);
f = FS/2*linspace(0,1,NFFT/2+1);

figure(4)
plot(f,2*abs(zfa(1:NFFT/2+1)))
title('Single-Sided Amplitude Spectrum of y(t)')
xlabel('Frequency (Hz)')
ylabel('|Y(f)|')

pause(5)

%sound(z,FS,B)

The bit that seems to be causing me trouble is the %bin removal bit. Any ideas?

Thanks a lot

EDIT

Ok, so I figured out what was wrong with this part - it wasn't the bin removal section it was the ifft section. It shouldn't have included the excluded the imaginary parts:

%%Inverse Transform

yf=fft(y);  % Pure fft
yf(1:50000)=0; % bin removal
z=(ifft(yf));   % ifft

Now, my problem is that when I get the time domain plot of this: plot(t,real(z)) The frequencies that I deleted still exist, just at about half the amplitude. I would normally expect them to just disappear, should I?

Answer 1

[Wayne King]

You can't just remove the "positive" frequencies in the DFT. If you have a real-valued signal, you get energy at two complex exponentials, the positive and negative frequencies. You have to remove both.

Example:

    Fs = 1000;
    t = 0:1/Fs:1-1/Fs;
    x = cos(2*pi*100*t)+sin(2*pi*200*t);
    xdft = fft(x);
    % zero out 100-Hz occurs at bin 101 and 901
    xdft([101 901]) = 0;
    xhat = ifft(xdft);
    plot(t(1:200),x(1:200),'k',t(1:200),xhat(1:200),'r')

[Theo]

Thanks a lot!