FPGA Central

I need help with the knowledge ...

Let's assume I have an idea for a 1024 point filter. I know how th
frequency response should be: all points between 100 and 924 are 0 and al
other 1 (I think this should be a perfect low-pass (or maybe not?). So
know the f.response. Now how to filter my signal? What I think i
following:

1.) IFFT convert the frequency response to impulse response (fro
frequency to time domain);
2.) apply some kind of window (hamming for example) by multiplying all th
points after the IFFT with the formula of the window;
3.) now convolute with the signal I receive in time domain (by multiplyin
and summing all the signal's points from 1024 upwards with every point fro
the filter).
4.) What I received is the filtered signal ...

Is this true?

On 24 Mrz., 11:22, "fittipaldi" <em.fittipa...@abv.bg> wrote:
> Let's assume I have an idea for a 1024 point filter. I know how the
> frequency response should be: all points between 100 and 924 are 0 and all
> other 1 (I think this should be a perfect low-pass (or maybe not?). So I
> know the f.response. Now how to filter my signal? What I think is
> following:
>
> 1.) IFFT convert the frequency response to impulse response (from
> frequency to time domain);
> 2.) apply some kind of window (hamming for example) by multiplying all the
> points after the IFFT with the formula of the window;
> 3.) now convolute with the signal I receive in time domain (by multiplying
> and summing all the signal's points from 1024 upwards with every point from
> the filter).
> 4.) What I received is the filtered signal ...
>
> Is this true?

You can use the FFT to design filters and also to apply them
efficiently. For designing I would use a larger "FFT size" (for
example 8192) and reasonably smooth magnitude response (no quick
jumps) to fight wrap-around errors, apply the iFFT, apply window
function (now of length 1024). Et voila!

But in your case (lowpass filter) you should use the "windowed sinc"
design method. It's "equivalent" to the procedure above for "FFT-size
= infinity". ( http://www.dspguide.com/ch16.htm )

You may also be interested in the properties of various window
functions
( http://en.wikipedia.org/wiki/Window_function )

Cheers!
SG

>On 24 Mrz., 11:22, "fittipaldi" <em.fittipa...@abv.bg> wrote:
>> Let's assume I have an idea for a 1024 point filter. I know how the
>> frequency response should be: all points between 100 and 924 are 0 an
all
>> other 1 (I think this should be a perfect low-pass (or maybe not?). S
I
>> know the f.response. Now how to filter my signal? What I think is
>> following:
>>
>> 1.) IFFT convert the frequency response to impulse response (from
>> frequency to time domain);
>> 2.) apply some kind of window (hamming for example) by multiplying al
the
>> points after the IFFT with the formula of the window;
>> 3.) now convolute with the signal I receive in time domain (b
multiplying
>> and summing all the signal's points from 1024 upwards with every poin
from
>> the filter).
>> 4.) What I received is the filtered signal ...
>>
>> Is this true?
>
>You can use the FFT to design filters and also to apply them
>efficiently. For designing I would use a larger "FFT size" (for
>example 8192) and reasonably smooth magnitude response (no quick
>jumps) to fight wrap-around errors, apply the iFFT, apply window
>function (now of length 1024). Et voila!
>
>But in your case (lowpass filter) you should use the "windowed sinc"
>design method. It's "equivalent" to the procedure above for "FFT-size
>= infinity". ( http://www.dspguide.com/ch16.htm )
>
>You may also be interested in the properties of various window
>functions
>( http://en.wikipedia.org/wiki/Window_function )
>
>Cheers!
>SG
>
>

Yep, I use exactly the method from this book. My problem is I know th
frequency response and want to substitute in K (if we read chapter 16), th
sinc function, with my own filter idea ...

On 24 Mar, 11:22, "fittipaldi" <em.fittipa...@abv.bg> wrote:
> I need help with the knowledge ...
>
> Let's assume I have an idea for a 1024 point filter. I know how the
> frequency response should be: all points between 100 and 924 are 0 and all
> other 1 (I think this should be a perfect low-pass (or maybe not?).

Everybody *think* this is a perfect low-pass filter,
but it isn't. It's a disaster waiting to happen.
I'll show you below.

Just out of curiosity: If it is this easy to specify
a filter, why are there so many other methods for
filter design? Window functions, with the sidelobe
ripple and transition bandwidths; Optimization methods
with all these iterative computational nuisances?
Are these method there just because somebody wanted
to sell show-off books stuffed with maths, to screw
with student's minds in exams? Or could it be that
these methods actually are there for a reason?

Just contemplate those questions for a moment.

The the problem is that your specification above only
determines the filter response in a set of points along
the frequency axis. Those points are implicitly given
by the number of points in the data vector.

Some matlab code to illustrate:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%
N =32; % The number of samples in filter
H = zeros(N,1);
H(1:5) = 1;
H(end-3:end)=1; % 'Ideal' frequency response
w = (0:N-1)/N; % Frequency vector

clf
subplot(2,1,1)
stem(w,H,'b'),hold on % Plot the spec
title('Spectra')

h = fftshift(real(ifft(H)));
% Compute impulse response of filter
subplot(2,1,2)
stem(h,'b'),hold on % Plot impulse response
title('Impulse responses')

% At this point all looks well. The DFT of the filter
% looks like what you want, and you have got a FIR
% impulse response you can use.

% Let's see what happens if you apply the filter to
% a data set with a different number of samples.

h1 = [h; 0; 0 ;0]; % Append 3 samples to the FIR
stem(h1,'r') % Plot it ontop of the original,
% No difference in time domain

H1 = abs(fft(h1)); % Compute DFT of new filter
w1 = (0:length(H1)-1)/length(H1);
% and corresponding frequency
% vector
subplot(2,1,1)
stem(w1,H1,'r') % plot on top of original
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%

The DFT of the zero-padded filter doesn't quite look
like what you expected, right?

This is why your way of specifying the filter response
is a bad one. The usual methods specify responses in
bands, not points, so with them you control ripple in
the various bands. Stick with the usual methods and you
get no surprises like this.

Rune