FPGA Central

Please excuse this question from a DSP novice. I want to filter an audi
signal to remove specific (varying) tones by reducing the magnitude o
their coefficients in the frequency domain. (So, for each "block" of inpu
samples I perform an FFT, symmetrically adjust the complex coefficients
perform an inverse FFT, and append the result to the output signal.) Afte
attenuating selective frequencies in a "notch-like" fashion and convertin
back to the time domain, I observe ripples near the edges of the signa
that create high-frequency noise. To remedy this, I have tried usin
constant-overlap-add, which has reduced but not eliminated th
high-frequency noise.

I understand that multiplication in the frequency domain = convolution i
the time domain, and that the attenuation operation I am performin
probably resembles the application of some FIR filter in the time domain.

What strategies are commonly used to avoid these time-domain artefact
from frequency-domain operations? Would a subsequent low-pass filter (i
the time domain) be the best I can do?

On Sep 7, 5:15*pm, "nigelh" <nigel.ho...@hydrix.com> wrote:
> ... *I want to filter an audio
> signal to remove specific (varying) tones by reducing the magnitude of
> their coefficients in the frequency domain. *(So, for each "block" of input
> samples I perform an FFT, symmetrically adjust the complex coefficients,
> perform an inverse FFT, and append the result to the output signal.) *After
> attenuating selective frequencies in a "notch-like" fashion and converting
> back to the time domain, I observe ripples near the edges of the signal
> that create high-frequency noise. *To remedy this, I have tried using
> constant-overlap-add, which has reduced but not eliminated the
> high-frequency noise.

do you know for sure that you're doing your overlap-add correctly?

you need to make sure that the impulse response associated with the
frequency response you just dialed in is limited in length to L
samples. then if N is the size of your FFT, the most you can advance
per frame with overlap-add (or overlap-save) is N-L+1 samples.

> I understand that multiplication in the frequency domain = convolution in
> the time domain,

with the Discrete Fourier Transform (which is what you are doing if
you're doing this with a computer), then multiplication in the
frequency domain causes *circular* convolution in the time domain.
this is a property of the DFT (or "FFT") that is fundamental. the DFT
or FFT really does things to periodic signals, so you need to do a
"work-around" to apply that circular tool to non-periodic signals.
overlap-add and overlap-save are the only work-arounds i know of to
perform linear convolution with something that inherently does
circular convolutions.

> and that the attenuation operation I am performing
> probably resembles the application of some FIR filter in the time domain.

yeah, in the *circular* time domain.

> What strategies are commonly used to avoid these time-domain artefacts
> from frequency-domain operations?

i think the only ones are overlap-add and overlap-save.

r b-j

nigelh wrote:
> Please excuse this question from a DSP novice. I want to filter an audio
> signal to remove specific (varying) tones by reducing the magnitude of
> their coefficients in the frequency domain. (So, for each "block" of input
> samples I perform an FFT, symmetrically adjust the complex coefficients,
> perform an inverse FFT, and append the result to the output signal.) After
> attenuating selective frequencies in a "notch-like" fashion and converting
> back to the time domain, I observe ripples near the edges of the signal
> that create high-frequency noise. To remedy this, I have tried using
> constant-overlap-add, which has reduced but not eliminated the
> high-frequency noise.
>
> I understand that multiplication in the frequency domain = convolution in
> the time domain, and that the attenuation operation I am performing
> probably resembles the application of some FIR filter in the time domain.
>
> What strategies are commonly used to avoid these time-domain artefacts
> from frequency-domain operations? Would a subsequent low-pass filter (in
> the time domain) be the best I can do?

The sharper a filter's cutoff, the more pronounced the ringing you
observe -- look up "Gibbs phenomenon" -- will be. Filtering by diddling
DFT coefficients is what the Marines call a "recruit" thing to do.

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On 7 Sep, 23:15, "nigelh" <nigel.ho...@hydrix.com> wrote:
> Please excuse this question from a DSP novice. *I want to filter an audio
> signal to remove specific (varying) tones by reducing the magnitude of
> their coefficients in the frequency domain. *(So, for each "block" of input
> samples I perform an FFT, symmetrically adjust the complex coefficients,
> perform an inverse FFT, and append the result to the output signal.) *After
> attenuating selective frequencies in a "notch-like" fashion and converting
> back to the time domain, I observe ripples near the edges of the signal
> that create high-frequency noise. *

This ripple ort ringing effect is the reason why no one
manipulate DFT coefficients directly.

> What strategies are commonly used to avoid these time-domain artefacts
> from frequency-domain operations? *

The way do do this is to

a) Realize that filter design is to come up with an acceptable
trade-off between desired effects and unwandted side effects
b) Learn how the desired effecst and unwanted side effects interact
c) Use a method that lets you balance the two.

You have already see a) in action - a very narrow filter
gives ringing in time domain. You have already seen explanations
that indicate that the cause of the ringing is a combination
of very narrow stopband and very steep edges towards the
passband.

The way to deal with the situation is to come up with a
'classic' filter response where you specify

1) What largest stop-band is acceptable
2) What smallest stop-band attenuation is acceptable
3) What largest transition band is acceptable
4) What largest passband ripple is acceptable

Once you have the spec, you use one of the standard filter
design packages to ctually come up with the filter
coefficients.

Rune