Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm trying to understand the Hamming window concept (Signal Processing) and the equation looks like the following:

enter image description here

Where:

N = number of Samples in each frame

Y[n] = Output Signal

X(n) = Input Signal

W(n) = Hamming window

First Question: I have "framed" (split the signal into blocks), so therefore, in X(n) do I pass in the values for each block, and, not the block itself?

Second question regarding the Hamming Window:

The equation is given:

enter image description here

From this I get:

w(n) = new vector

e.g. w(0) = 0.54 - 0.46 cos()

This is where I get lost. Shameful I know. Right, I know this is really stupid of me to ask but could someone help me out understanding the rest of this equation? I.e. in english steps?

Hope someone can help.

share|improve this question
add comment

1 Answer

up vote 1 down vote accepted

First Question: I have "framed" (split the signal into blocks), so therefore, in X(n) do I pass in the values for each block, and, not the block itself?

You have divided your entire signal in blocks of length $N$ (perhaps overlaping), and what follows is to be done for each block. So, in what follows $X(n)$ represents your input signal with $n=0$ being the start of your particular block.

Second question regarding the Hamming Window:

(please dont post images for formulas here, learn to type equations in latex) It seems you confused $N$ (fixed, window size) with $n$. The formula is

$$ w(n) = 0.54 - 0.46 \cos\left(\frac{2 \pi \, n}{N-1} \right)$$

If you graph this (image on the left here), you see that it's a smooth window peaked in the center of your block (N/2). To get $y(n)$, you just multiply, value by value:

$$y(n) = x(n) \, w(n)$$

BTW, this kind of question is better suited to http://dsp.stackexchange.com/

share|improve this answer
    
Hey - Take N = (Number of samples in each frame) = 256 .. So therefore will the values for w(n) range from 0 - 255 because N - 1? –  Phorce Dec 1 '12 at 22:40
    
The values of $n$ range from 0 to 255, yes. –  leonbloy Dec 1 '12 at 22:41
    
So this equation.. w(0) = 0.54 - 0.46 * cos(2*pi / 255) = 0.28203645802 .. Is this correct? If so, the value shouldn't ever change, should it? Because every block N = 256 N-1 = 255 –  Phorce Dec 1 '12 at 22:44
    
You are forgettin the $n$ in the numerator –  leonbloy Dec 1 '12 at 23:00
    
but <mi>n</mi> is just ranging from 0 to 256 (block size) etc, right? –  Phorce Dec 1 '12 at 23:03
show 4 more comments

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.