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I'm trying to write a function for spectral smoothing using the signal's
cepstrum in Matlab.

Here's what I have:

voice - a voice signal, 8192 samples long
win - a right window, 8192 samples long, with a variable cutoff:

1 |_____________
| \
| \
| \
0 |_________________\____________________
1 N 8192


N is set to 1024 for now.
I calculate the real cepstrum of the voice signal:

v_ceps = real(ifft(log(abs(fft(voice)))));

which I then multiply element-wise with my window:

v_ceps = v_ceps .* win;

transforming this back _should_ give me a smoothed spectrum.

smooth_spec = abs(fft(v_ceps));

The problem is, it doesn't work. The output isn't smooth and it doesn't
look similar to the original voice spectrum. Where did I go wrong?
I can't see any error in the algorithm nor the implementation.

Roman


PS: if you know any other good algortithms for spectral smoothing
(constant bandwidth preferred), go right ahead! :-)

Roman Katzer wrote:
> I'm trying to write a function for spectral smoothing using the signal's
> cepstrum in Matlab.
>
> Here's what I have:
>
> voice - a voice signal, 8192 samples long
> win - a right window, 8192 samples long, with a variable cutoff:
>
> 1 |_____________
> | \
> | \
> | \
> 0 |_________________\____________________
> 1 N 8192
>
>
> N is set to 1024 for now.
> I calculate the real cepstrum of the voice signal:
>
> v_ceps = real(ifft(log(abs(fft(voice)))));
>
> which I then multiply element-wise with my window:
>
> v_ceps = v_ceps .* win;
>
> transforming this back _should_ give me a smoothed spectrum.
>
> smooth_spec = abs(fft(v_ceps));
>
> The problem is, it doesn't work. The output isn't smooth and it doesn't
> look similar to the original voice spectrum. Where did I go wrong?
> I can't see any error in the algorithm nor the implementation.
>
> Roman
>
>
> PS: if you know any other good algortithms for spectral smoothing
> (constant bandwidth preferred), go right ahead! :-)

Roman:

I think the convolution should be something like this:

V = fft(voice);

H = fft(win);

VH = ifft( V .* H );

Good luck,
OUP

"Roman Katzer" <[email protected]> wrote in message
news[email protected]..
> I'm trying to write a function for spectral smoothing using the signal's
> cepstrum in Matlab.
>
> Here's what I have:
>
> voice - a voice signal, 8192 samples long
> win - a right window, 8192 samples long, with a variable cutoff:
>
> 1 |_____________
> | \
> | \
> | \
> 0 |_________________\____________________
> 1 N 8192
>
>
> N is set to 1024 for now.
> I calculate the real cepstrum of the voice signal:
>
> v_ceps = real(ifft(log(abs(fft(voice)))));
>
> which I then multiply element-wise with my window:
>
> v_ceps = v_ceps .* win;
>
> transforming this back _should_ give me a smoothed spectrum.
>
> smooth_spec = abs(fft(v_ceps));
>
> The problem is, it doesn't work. The output isn't smooth and it doesn't
> look similar to the original voice spectrum. Where did I go wrong?
> I can't see any error in the algorithm nor the implementation.
>
> Roman

What is a "right window"?

Fred

Hi OUP,

On Wed, 06 Aug 2003 17:36:25 -0500, One Usenet Poster wrote:
>I think the convolution should be something like this:

.... but I'm not trying to convolute

Roman

Roman Katzer <[email protected]> wrote in message news:<[email protected]>. ..
> I'm trying to write a function for spectral smoothing using the signal's
> cepstrum in Matlab.
>
> Here's what I have:
>
> voice - a voice signal, 8192 samples long
> win - a right window, 8192 samples long, with a variable cutoff:
>
> 1 |_____________
> | \
> | \
> | \
> 0 |_________________\____________________
> 1 N 8192
>
>
> N is set to 1024 for now.
> I calculate the real cepstrum of the voice signal:
>
> v_ceps = real(ifft(log(abs(fft(voice)))));
>
> which I then multiply element-wise with my window:
>
> v_ceps = v_ceps .* win;
>
> transforming this back _should_ give me a smoothed spectrum.
>
> smooth_spec = abs(fft(v_ceps));
>
> The problem is, it doesn't work. The output isn't smooth and it doesn't
> look similar to the original voice spectrum. Where did I go wrong?
> I can't see any error in the algorithm nor the implementation.
>
> Roman
>
>
> PS: if you know any other good algortithms for spectral smoothing
> (constant bandwidth preferred), go right ahead! :-)


The problem is that you are ignoring the negative frequencies in the
spectrum. Your window should be as follows

1 |_____________ ____________
| \ /
| \ /
| \ /
0 |_________________\____/_______________
1 N (8194-N) 8192

Then everything will work.

Do the following with your window.

Assuming your window is a row vector
win(8194-N:8192) = fliplr(win(2:N));

This way you will include the negative frequencies as well.

What you are doing NOW amounts to doing a single sideband filtering.

"Roman Katzer" <[email protected]> wrote in message
news[email protected]..
> I'm trying to write a function for spectral smoothing using the signal's
> cepstrum in Matlab.
>
> Here's what I have:
>
> voice - a voice signal, 8192 samples long
> win - a right window, 8192 samples long, with a variable cutoff:
>
> 1 |_____________
> | \
> | \
> | \
> 0 |_________________\____________________
> 1 N 8192
>
>
> N is set to 1024 for now.
> I calculate the real cepstrum of the voice signal:
>
> v_ceps = real(ifft(log(abs(fft(voice)))));
>
> which I then multiply element-wise with my window:
>
> v_ceps = v_ceps .* win;
>
> transforming this back _should_ give me a smoothed spectrum.
>
> smooth_spec = abs(fft(v_ceps));

This is not the inverse cepstrum.

Dirk

>
> The problem is, it doesn't work. The output isn't smooth and it doesn't
> look similar to the original voice spectrum. Where did I go wrong?
> I can't see any error in the algorithm nor the implementation.
>
> Roman
>
>
> PS: if you know any other good algortithms for spectral smoothing
> (constant bandwidth preferred), go right ahead! :-)

"Roman Katzer" <[email protected]> wrote in message
news:[email protected]..
> Hi Fred,
>
> On Wed, 6 Aug 2003 21:00:44 -0700, Fred Marshall wrote:
> >What is a "right window"?
>
> maybe my terminology is misleading. I mean the right half of a (hann)
> window, appended to a sequence of ones and followed by a sequence of
> zeros. It looks close to something like what I tried to show with ASCII
> characters below:
>
> >> win - a right window, 8192 samples long, with a variable cutoff:
> >>
> >> 1 |_____________
> >> | \
> >> | \
> >> | \
> >> 0 |_________________\____________________
> >> 1 N 8192
>
> Roman

The ifft will produce a complete sequence up to the equivalent sample time
epoch (equivalent to sampling frequency).

It repeats at T/2 (like fs/2). So, the filter need to be symmetric about
T/2 like this:

1 |___________ ___________|_
| \ / |
| \ / |
| \ / |
0 |______________ |__|_______________|_
1 N 8192-N 8192
<4096

T/2=4096

Thank you Mahesh,

I found a solution to my problem. I forgot two things:
a) I need a symmetric window
b) I need to exp(.) the real output of the second fft

Here's the program code:

function smspec = cepsmooth(sig, smoothing, falloff)
% CEPSMOOTH - return spectrally smoothed spectrum using cepstral
% smoothing
%
% usage:
% smspec = cepsmooth(sig, smoothing, falloff)
%
% sig - input time signal
% smoothing - 0..1 - smoothing strength, 0 strongest, 1 none
% falloff - 0..1 - smooth falloff portion, 0 none, 1 all

% created: 2003-08-05, Roman Katzer
% last modified: 2003-08-08

slen = length(sig);
tlen = round(slen*smoothing/2)*2;
hlen = round(tlen*falloff/2);
hwin = hann(2*hlen);
hl = hwin(1:hlen);
hr = hwin(hlen+1:end);

win = [ones(tlen/2-hlen, 1); hr; zeros(slen-tlen, 1); hl;
ones(tlen/2-hlen, 1)];

smspec = real(ifft(log(abs(fft(sig)))));
smspec = exp(real(fft(smspec .* win)));
smspec = 20*log10(abs(smspec(1:ceil(slen/2))));


Roman

Roman Katzer <[email protected]> wrote in message news:<[email protected]>. ..
> Thank you Mahesh,
>
> I found a solution to my problem. I forgot two things:
> a) I need a symmetric window
> b) I need to exp(.) the real output of the second fft
>

I just assumed that you were doing exp(.) naturally