filtering in the frequency domain

[tjakeman]

Hello, and firstly appologies, I am a novice matlab user.

I want to filter some frequencies from a time domain signal (filter out everything below say 7 Hz). I was expecting to:

FFT time signal to frequency domain

Apply filter to frequency domain signal

inverse FFT filtered signal back to time domain.

What is wrong with this approach? When I plot the results, it seems to have applied the filter to the time domain signal....

Many thanks, Tom

my .m file so far:

function Hd = tjfilter

Fs = 200; % Sampling frequency
T = 1/Fs; % Sample time
L = 16384; % Length of signal(no. of data lines)
t = (0:L-1)*T; % Time vector

a = load('response_to_z.txt');

t = a,1);
x = a,2);

figure(1)
plot(t,x)

X = fft(x);

N = 200; % Order
Fstop = 7; % Stopband Frequency
Fpass = 10; % Passband Frequency
Wstop = 1; % Stopband Weight
Wpass = 1; % Passband Weight
dens = 20; % Density Factor

% Calculate the coefficients using the FIRPM function.
b = firpm(N, [0 Fstop Fpass Fs/2]/(Fs/2), [0 0 1 1], [Wstop Wpass], ...
{dens});
Hd = dfilt.dffir(b);

Y=filter(Hd,X);
fv = [0:0.005:100];

figure(2)
plot(fv,X);
figure(3)
plot(fv,Y);

y = (ifft(Y));
figure(4)
plot(t,y)

 

[GregLocock]

Your code seems to use a different syntax to

http://www.mathworks.com/access/helpdesk/help/toolbox/signal/firpm.html

Cheers

Greg Locock


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[tjakeman]

Hi Greg.

I used the FDA tool to design my filter, then exported it in to my m.file. The filter seems to work ok, but rather than filtering out the first 7 Hz from my frequency domain signal, it filters the first and last 7 seconds from my time domain signal. I've mis understood something along the way...

 

[SomptingGuy]

filter() works on time domain data, not frequency domain. The firpm() function designs a FIR filter to be used with your original time domain data. I suppose applying it in the frequency domain is effectively modifying the time response rather than the frequency response of your data. Interesting nevertheless.

- Steve

 

[electricpete]

So just to close the loop for original poster. Assuming it is an FIR filter. Then we presume the filter length is 7 seconds on each side of 0 based on symtpoms reported (does that square with the filter length and sample rate?). Then when we perform convolution of the signal with the FIR we need to start 7 seconds after the beginning of the signal and step 7 seconds before the end of the data, otherwise the filter extends to a region in time where there is no signal.

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[tjakeman]

Sompting guy - Thankyou!

so filter must do the fft - filter - ifft for you.?

If I filter my time domain data, then fft, I can see that the first 7Hz have gone. This is what I wanted.

Many thanks everyone. New filter file:

function Hd = tjfilter

Fs = 200; % Sampling frequency
T = 1/Fs; % Sample time
L = 20000; % Length of signal(no. of data lines)
t = (0:L-1)*T; % Time vector

a = load('response_to_z.txt');

t = a,1);
x = a,2);

figure(1)
plot(t,x)

X = fft(x);

N = 500; % Order
Fstop = 7; % Stopband Frequency
Fpass = 10; % Passband Frequency
Wstop = 1; % Stopband Weight
Wpass = 1; % Passband Weight
dens = 20; % Density Factor

% Calculate the coefficients using the FIRPM function.
b = firpm(N, [0 Fstop Fpass Fs/2]/(Fs/2), [0 0 1 1], [Wstop Wpass], ...
{dens});
Hd = dfilt.dffir(b);

NFFT = 2^nextpow2(L);
r=filter(Hd,x);

figure(2)
plot(t,r);

fv = Fs/L*(0(L/2)-1));
R = fft(r,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2+1);
RA=2*abs(R(1:NFFT/2+1));

figure(10)
plot(f,RA);

 

[electricpete]

You might think about whether a window is required depending on the characteristics of your original signal.

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[SomptingGuy]

tjakeman:

Filtering is done via convolution in the time domain. No fft/ifft required. The help page for filter() explains it all. Think of a filter as a glorified moving average, with unequal weights on each sample.

- Steve

 

[GregLocock]

Alternatively you can do it via spectrum shaping in the frequency domain, but that can have exciting repercussions when you ifft back to the time domain.

Cheers

Greg Locock


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