Time -Domain to Frequency Domain I am constructing a MFCC and come to a section which is kind of confusing me.

It is:

Step 4: Fast Fourier Transform 

and has this equation:



Now I understand that FFT needs to be carried out, I just don't understand where the values are meant for:

h(t)

x(t)

H(w)

x(w)

Up to now, I have:


Inputted the raw signal (vector)
Pre-emphasis filtering on the signal
Carried out "Framing" (vector of vectors)
Computed Hamming Window


It's just this step I am unsure of.

Hope someone can help :)
By convention they mean the following:

$x(t)$ = Input in the time domain

$h(t)$ = Filter impulse response (time domain)

$H(w)$ = Filter frequency response

$X(w)$ = Input in the frequency domain

In the equation that you wrote the two "*" symbols mean different things.  In the time domain it is convolution, in the frequency domain it is multiplication.  The equation is just saying that convolution in the time domain (which is how you do time domain filtering) is equivalent to multiplication in the frequency domain.