Hamming window

Hi 

Could anyone explain the Hamming window in REALLY simple terms and why it
is useful and how it could be implemented in MATLAB??

I would be grateful for any response.

"rajgerman" <rajgerman@msn.com> wrote in message 
news:Ju6dnZUigbhAfmXenZ2dneKdnZydnZ2d@giganews.com...
> Hi
>
> Could anyone explain the Hamming window in REALLY simple terms and why it
> is useful and how it could be implemented in MATLAB??
>
> I would be grateful for any response.
>
http://www.math.psu.edu/local_doc/matlab/toolbox/signal/hamming.html#1557

Best of luck - Mike

rajgerman wrote:
> Hi
>
> Could anyone explain the Hamming window in REALLY simple terms and why it
> is useful and how it could be implemented in MATLAB??
>
> I would be grateful for any response.

If you have the Signal Processing Toolbox, a Hamming window of length N
can be obtained from Matlab as follows:

w=hamming(N)

Window functions like Hamming are typically applied as a point by point
multiplication to the input of an FFT to control the level of adjacent
spectral artifacts that appear in the magnitude of the FFT results for
the case when the input frequencies do not correspond exactly with bin
centers. These artifacts are referred to as leakage.

Another common use for window functions is in the design of FIR filters
using the window method. In this case a sinx/x lowpass function is
multiplied point by point by a window to alter the frequency response
of the filter.

Google returns loads of useful information about window functions. Any
introductory DSP book will discuss them as well.

John

Thanks for that information but I'm still a little confused.

The thing is I have a brain signal which is an audio file which I have
fast fourier transformed. Now what I have to do is apply the Hamming
window to that. How would I do that using MATLAB?? It seems confusing.

Hi,

You can think of windowing in general as a convolution in frequency
domain (you are multiplying both functions in the time domain). The
result of this convolution on frequency domain is that samples outside
one frequency affect the amplitude value at that frequency !
Ideally you would want your window to be an impulse in frequency
domain, but note that you window would require infinite points in
time.Thinking in frequency domain:

So the goal of windowing can be thought as two fold, where we are
trying to approximate the impulse in frequency domain with finite
points:

1)Make the pass region of the window as narrow as possible.
2)Attenuate the other regions as much as possible

The Hanning window does #2 pretty good, and you can get #1 to desired
amount by increasing sample size. The rectangular window (which is the
window you actually use if you don't multiply your data signal at all)
is the best one on #1 (has the narrowest pas region), but is the worst
on #2 ( largest amount of leakage).

Check the posts above for implementation + additional info.
Let me know if this is not clear.

-Ikaro

rajgerman wrote:
> Thanks for that information but I'm still a little confused.
> 
> The thing is I have a brain signal which is an audio file which I have
> fast fourier transformed.

Why on earth? Are you sure there isn't something you misunderstood?

  Now what I have to do is apply the Hamming
> window to that. How would I do that using MATLAB?? It seems confusing.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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"rajgerman" <rajgerman@msn.com> wrote in message 
news:qdidnQ5Hzq7-bWXe4p2dnA@giganews.com...
> Thanks for that information but I'm still a little confused.
>
> The thing is I have a brain signal which is an audio file which I have
> fast fourier transformed. Now what I have to do is apply the Hamming
> window to that. How would I do that using MATLAB?? It seems confusing.
>

It's not likely that you want to window the FFTd sequence - as in multiply 
the FFTd sequence.
It's much more likely that you want(ed) to window the temporal sequence (as 
in multiply) before the FFT.
Or you could convolve in frequency to get the same affect.

You have a few choices:

1) Generate the temporal window function.  Someone has suggested how to do 
this in MATLAB.  The window should be the same length as the temporal record 
you have unless you're processing in blocks.

Then, either:

Using the temporal record, multiply point by point by the window function in 
time.
Then FFT if you need to.

Using the FFT record that you have, IFFT it and proceed as above.

FFT both the temporal data sequence and the temporal window.
Convolve the two in frequency.

Fred 

rajgerman wrote:
> Hi 
> 
> Could anyone explain the Hamming window in REALLY simple terms and why it
> is useful and how it could be implemented in MATLAB??
> 
> I would be grateful for any response.
> 
> 
Radjerman,

Assume we have a set of time-domain samples, that have been taken from a 
signal waveform (if we are going to perform a FFT) or have been 
calculated from a desired impulse-response function )if we are going to 
implement a FIR filter.)

When we selected the set of time-domain samples the selection process 
was in effect a 'chopping up' process that introduced high-frequency 
components that were not present originally in the continuously-sampled 
signal or in the unlimited impulse-response.

These introduced components show up as high-frequency peaks in the FFT 
or as high-frequency peaks in the response of the FIR filter, both 
effects are generally undesirable.

We can reduce the amplitude of these high-frequency components by 
'tapering off' the amplitudes of the samples towards each end of the set 
in some systematic way, and the Hamming window is one of many similar 
functions that will do this job for us.

If you look at the expression for a Hamming window you will see that if 
we multiply a set of signal samples by this function, the sample(s) at 
the centre of the set gets multiplied (or 'windowed')by the largest 
factor and this factor decreases in a smooth sinusoidal fashion as we go 
away from the centre, with the samples at each end being multiplied by zero.

The end result is that instead of an abruptly 'chopped' set of samples 
we now have a set of samples that has been heavily modulated by one 
cycle of a sinusoidal function.  The artifacts produced by this 
modulation are less objectionable for many applications.  In the FFT the 
artifacts show up as spectral 'leakage' into adjacent frequency bins. 
In a FIR filter the pass-band response is altered sightly.

In MATLAB, generate a set of values using the expression for the Hamming 
window function.   Then generate the dot product between the set of 
Hamming window values and the set of signal samples.

Regards,
John

>
> It's not likely that you want to window the FFTd sequence - as in multiply 
> the FFTd sequence.
> It's much more likely that you want(ed) to window the temporal sequence 
> (as in multiply) before the FFT.
> Or you could convolve in frequency to get the same affect.
>
> FFT both the temporal data sequence and the temporal window.
> Convolve the two in frequency.
>

Hello Fred,

Since the Hamming window is defined in terms of cosines, the Freq domain 
version turns out to have only 3 non-zero coefs. This makes for a pretty 
easy convolution. The coefs are -0.23, 0.54, -0.23

Clay

So are you saying that I do not need to fast fourier transform the audio
signal, but apply the hamminng window first and the nfast fourier
transform??

Sorry guys but I'm not to familiar with these topics but thanks for your
help.

If any of you would provide me their email address I could send you the
files to show you what I mean.