FPGA Central

I'm writing some code for power spectral estimation using FFT. The dat
format I used is Q15 fixed point format. Since I need to scale the origina
signal within the Q15 range between -1~0.9999, I need to choose a prope
scaling factor for the original data sequence. But how can I choose thi
scaling factor so that it does not cause overflow, nor does it caus
underflow? I tried several different values for this scaling factor but i
either resulted in overflow or underflow. I guess the reason is because th
power spectrum involves with successive accumulation of square magnitude o
FFT output, which may easily goes beyond [-1,1) range. But I don't know ho
to select this scaling factor in my case. Anyone has idea on this?

On Aug 11, 10:28 pm, "tonga" <binwei_w...@hotmail.com> wrote:
> I'm writing some code for power spectral estimation using FFT. The data
> format I used is Q15 fixed point format. Since I need to scale the original
> signal within the Q15 range between -1~0.9999, I need to choose a proper
> scaling factor for the original data sequence. But how can I choose this
> scaling factor so that it does not cause overflow, nor does it cause
> underflow? I tried several different values for this scaling factor but it
> either resulted in overflow or underflow. I guess the reason is because the
> power spectrum involves with successive accumulation of square magnitude of
> FFT output, which may easily goes beyond [-1,1) range. But I don't know how
> to select this scaling factor in my case. Anyone has idea on this?

You should divide each input sample by 32768 before windowing.
The window should be floating point between [-1,1].
The window should sum to one if you are looking for accurate tone
power.
Check the scaling performed by the forward FFT.
Divide each FFT mag^2 value by the total number of FFTs performed
before accumulating.
For a bin centered pure tone input, you should get a result of 1 == 0
dBFS at the the expected bin.

John

On Aug 11, 10:28*pm, "tonga" <binwei_w...@hotmail.com> wrote:
> I'm writing some code for power spectral estimation using FFT. The data
> format I used is Q15 fixed point format. Since I need to scale the original
> signal within the Q15 range between -1~0.9999, I need to choose a proper
> scaling factor for the original data sequence. But how can I choose this
> scaling factor so that it does not cause overflow, nor does it cause
> underflow? I tried several different values for this scaling factor but it
> either resulted in overflow or underflow. I guess the reason is because the
> power spectrum involves with successive accumulation of square magnitude of
> FFT output, which may easily goes beyond [-1,1) range. But I don't know how
> to select this scaling factor in my case. Anyone has idea on this? *

If you are writing or have access to the actual FFT code you can
incorporate fixed or conditional scaling at each stage of the FFT. For
example a standard radix-2 algorithm has a max gain at each stage of
2. At the output of each stage you could scale down by 2 to offset the
gain. Alternately, check the numbers at each stage, do the scaling
conditionally, and incorporate the net scaling in the final output
(possibly only by noting the scaling error, not actually scaling the
numbers). Also take a look at conditional block scaling. Probably find
all of this in Rabiner and Gold's DSP book from the 70's. Maybe
someone else could recommend a later book.

Dirk